ИСЧИСЛИТЕЛЬНАЯ ГЕОМЕТРИЯ: МЕТОД ШАЛЯ И ШУБЕРТА 1

&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave;
&Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
1. &Egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;
&Egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&agrave;&yuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&yuml; &ntilde;&divide;&egrave;&ograve;&agrave;&aring;&ograve; &divide;&egrave;&ntilde;&euml;&icirc; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&otilde; &icirc;&aacute;&uacute;&aring;&ecirc;&ograve;&icirc;&acirc; &ntilde; &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&igrave;&egrave; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave;&igrave;&egrave;. &Icirc;&auml;&iacute;&agrave; &egrave;&ccedil; &ntilde;&agrave;&igrave;&ucirc;&otilde; &iuml;&aring;&eth;&acirc;&ucirc;&otilde; &ccedil;&agrave;&auml;&agrave;&divide; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &yacute;&ograve;&icirc; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 1.1 (&Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&eacute;). &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &ntilde;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&oacute;&aring;&ograve; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &ograve;&eth;&frac14;&otilde;
&ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute; &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave;?
&Yacute;&ograve;&agrave; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &aacute;&ucirc;&euml;&agrave; &eth;&aring;&oslash;&aring;&iacute;&agrave; &aring;&ugrave;&frac14; &acirc; &Auml;&eth;&aring;&acirc;&iacute;&aring;&eacute; &Atilde;&eth;&aring;&ouml;&egrave;&egrave; &acirc; &ograve;&eth;&aring;&ograve;&uuml;&aring;&igrave; &acirc;&aring;&ecirc;&aring; &auml;&icirc; &iacute;&agrave;&oslash;&aring;&eacute; &yacute;&eth;&ucirc;.
&Icirc;&ograve;&acirc;&aring;&ograve; &ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&ograve; &icirc;&ograve; &acirc;&ccedil;&agrave;&egrave;&igrave;&iacute;&icirc;&atilde;&icirc; &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&yuml; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;. &Igrave;&ucirc; &iacute;&aring; &aacute;&oacute;&auml;&aring;&igrave; &eth;&agrave;&ntilde;&ntilde;&igrave;&agrave;&ograve;&eth;&egrave;&acirc;&agrave;&ograve;&uuml; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave; &egrave;&ccedil; &ograve;&eth;&frac14;&otilde; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &auml;&euml;&yuml; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &icirc;&ograve;&acirc;&aring;&ograve; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&aring;&iacute;. &Auml;&euml;&yuml;
&icirc;&ntilde;&ograve;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&eacute; &icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml;, &divide;&ograve;&icirc; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; &acirc;&icirc;&ntilde;&aring;&igrave;&uuml;, &agrave; &acirc;&icirc;&icirc;&aacute;&ugrave;&aring; &icirc;&ograve;&acirc;&aring;&ograve; &igrave;&icirc;&aelig;&aring;&ograve; &aacute;&ucirc;&ograve;&uuml; &egrave; &euml;&thorn;&aacute;&ucirc;&igrave; &igrave;&aring;&iacute;&uuml;&oslash;&egrave;&igrave; &divide;&egrave;&ntilde;&euml;&icirc;&igrave;, &ecirc;&eth;&icirc;&igrave;&aring; &ntilde;&aring;&igrave;&egrave;.
&Acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml; &acirc;&ntilde;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&aring;&ntilde;&yuml; &ograve;&eth;&frac14;&otilde; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde;, &igrave;&icirc;&aelig;&iacute;&icirc; &iacute;&agrave;&eacute;&ograve;&egrave;
&yuml;&acirc;&iacute;&icirc;. &Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &iuml;&icirc;&iuml;&eth;&icirc;&aacute;&oacute;&eacute;&ograve;&aring; &iuml;&icirc;&ntilde;&ograve;&eth;&icirc;&egrave;&ograve;&uuml; &ograve;&agrave;&ecirc;&egrave;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &ntilde; &iuml;&icirc;&igrave;&icirc;&ugrave;&uuml;&thorn; &ouml;&egrave;&eth;&ecirc;&oacute;&euml;&yuml; &egrave; &euml;&egrave;&iacute;&aring;&eacute;&ecirc;&egrave;. &Icirc;&auml;&iacute;&agrave;&ecirc;&icirc;, &acirc; &aacute;&icirc;&euml;&uuml;&oslash;&egrave;&iacute;&ntilde;&ograve;&acirc;&aring; &auml;&eth;&oacute;&atilde;&egrave;&otilde; &ccedil;&agrave;&auml;&agrave;&divide; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave;
&igrave;&icirc;&aelig;&iacute;&icirc; &iacute;&agrave;&eacute;&ograve;&egrave; &divide;&egrave;&ntilde;&euml;&icirc; &icirc;&aacute;&uacute;&aring;&ecirc;&ograve;&icirc;&acirc; &ntilde; &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&igrave;&egrave; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&igrave; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave;&igrave;&egrave;, &iacute;&aring; &iacute;&agrave;&otilde;&icirc;&auml;&yuml; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &ntilde;&agrave;&igrave;&egrave; &icirc;&aacute;&uacute;&aring;&ecirc;&ograve;&ucirc;. &times;&agrave;&ntilde;&ograve;&icirc; &auml;&agrave;&aelig;&aring; &aacute;&ucirc;&acirc;&agrave;&aring;&ograve;, &divide;&ograve;&icirc; &iacute;&agrave;&eacute;&ograve;&egrave; &yuml;&acirc;&iacute;&icirc; &ntilde;&agrave;&igrave;&egrave; &icirc;&aacute;&uacute;&aring;&ecirc;&ograve;&ucirc;
&iacute;&aring;&acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&icirc;, &ccedil;&agrave;&ograve;&icirc; &iacute;&aring;&ntilde;&euml;&icirc;&aelig;&iacute;&icirc; &acirc;&ucirc;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&uuml;, &ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &egrave;&otilde; &aacute;&oacute;&auml;&aring;&ograve;.
&Acirc; &auml;&aring;&acirc;&yuml;&ograve;&iacute;&agrave;&auml;&ouml;&agrave;&ograve;&icirc;&igrave; &acirc;&aring;&ecirc;&aring; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&agrave;&yuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&yuml; &aacute;&ucirc;&euml;&agrave; &icirc;&auml;&iacute;&icirc;&eacute; &egrave;&ccedil; &ntilde;&agrave;&igrave;&ucirc;&otilde; &iuml;&icirc;&iuml;&oacute;&euml;&yuml;&eth;&iacute;&ucirc;&otilde; &icirc;&aacute;&euml;&agrave;&ntilde;&ograve;&aring;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc;&egrave;. &Aacute;&ucirc;&euml;&icirc; &eth;&aring;&oslash;&aring;&iacute;&icirc; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; &ecirc;&icirc;&iacute;&ecirc;&eth;&aring;&ograve;&iacute;&ucirc;&otilde; &ccedil;&agrave;&auml;&agrave;&divide;, &agrave;
&ecirc;&eth;&icirc;&igrave;&aring; &ograve;&icirc;&atilde;&icirc;, &iacute;&aring;&igrave;&aring;&ouml;&ecirc;&egrave;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc; &Atilde;&aring;&eth;&igrave;&agrave;&iacute; &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &eth;&agrave;&ccedil;&eth;&agrave;&aacute;&icirc;&ograve;&agrave;&euml; &aring;&auml;&egrave;&iacute;&ucirc;&eacute; &yacute;&ocirc;&ocirc;&aring;&ecirc;&ograve;&egrave;&acirc;&iacute;&ucirc;&eacute; &igrave;&aring;&ograve;&icirc;&auml;, &iuml;&icirc;&ccedil;&acirc;&icirc;&euml;&yuml;&thorn;&ugrave;&egrave;&eacute; &eth;&aring;&oslash;&agrave;&ograve;&uuml; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &ntilde;&eth;&aring;&auml;&ntilde;&ograve;&acirc;&agrave;&igrave;&egrave; &agrave;&euml;&atilde;&aring;&aacute;&eth;&ucirc;. &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &iacute;&agrave;&ccedil;&acirc;&agrave;&euml; &ntilde;&acirc;&icirc;&eacute; &igrave;&aring;&ograve;&icirc;&auml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring;&igrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;, &iacute;&icirc; &ograve;&aring;&iuml;&aring;&eth;&uuml;
&igrave;&aring;&ograve;&icirc;&auml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &divide;&agrave;&ugrave;&aring; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ograve; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring;&igrave; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;. &Iuml;&eth;&icirc;&egrave;&euml;&euml;&thorn;&ntilde;&ograve;&eth;&egrave;&eth;&oacute;&aring;&igrave; &igrave;&aring;&ograve;&icirc;&auml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &iacute;&agrave; &ograve;&agrave;&ecirc;&icirc;&igrave; &iuml;&eth;&egrave;&igrave;&aring;&eth;&aring;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 1.2 (&Oslash;&oacute;&aacute;&aring;&eth;&ograve;). &Acirc; &ograve;&eth;&frac14;&otilde;&igrave;&aring;&eth;&iacute;&icirc;&igrave; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring; &ccedil;&agrave;&auml;&agrave;&iacute;&icirc; &divide;&aring;&ograve;&ucirc;&eth;&aring; &iuml;&icirc;&iuml;&agrave;&eth;&iacute;&icirc;
&ntilde;&ecirc;&eth;&aring;&ugrave;&egrave;&acirc;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &ntilde;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&oacute;&aring;&ograve; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde; &acirc;&ntilde;&aring; &divide;&aring;&ograve;&ucirc;&eth;&aring; &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;?
&Acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&ucirc;&otilde; &icirc;&ograve;&acirc;&aring;&ograve;&icirc;&acirc; &divide;&aring;&ograve;&ucirc;&eth;&aring;: &auml;&acirc;&aring;, &icirc;&auml;&iacute;&agrave;, &iacute;&egrave; &icirc;&auml;&iacute;&icirc;&eacute; &egrave;&euml;&egrave; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &igrave;&iacute;&icirc;&atilde;&icirc;.
&Yacute;&ograve;&oacute; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &igrave;&icirc;&aelig;&iacute;&icirc; &eth;&aring;&oslash;&agrave;&ograve;&uuml; &iuml;&icirc;-&eth;&agrave;&ccedil;&iacute;&icirc;&igrave;&oacute;. &Icirc;&auml;&egrave;&iacute; &egrave;&ccedil; &ntilde;&iuml;&icirc;&ntilde;&icirc;&aacute;&icirc;&acirc; &acirc;&ucirc;&ograve;&aring;&ecirc;&agrave;&aring;&ograve; &egrave;&ccedil; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;
1.3. &Igrave;&ucirc; &aelig;&aring; &eth;&agrave;&ccedil;&aacute;&aring;&eth;&frac14;&igrave; &eth;&aring;&oslash;&aring;&iacute;&egrave;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;. &Iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &iacute;&agrave;&ntilde; &aacute;&oacute;&auml;&oacute;&ograve; &egrave;&iacute;&ograve;&aring;&eth;&aring;&ntilde;&icirc;&acirc;&agrave;&ograve;&uuml; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &ograve;&aring; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave; &egrave;&ccedil; &divide;&aring;&ograve;&ucirc;&eth;&frac14;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &auml;&euml;&yuml; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &icirc;&ograve;&acirc;&aring;&ograve; &ecirc;&icirc;&iacute;&aring;&divide;&aring;&iacute; &egrave; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave;
1
2
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&ETH;&egrave;&ntilde;. 1
&igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&aring;&iacute;. &Icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml;, &divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &divide;&oacute;&ograve;&uuml;-&divide;&oacute;&ograve;&uuml; &iuml;&icirc;&auml;&acirc;&egrave;&atilde;&agrave;&ograve;&uuml; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; &acirc; &ograve;&agrave;&ecirc;&icirc;&eacute; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave;, &ograve;&icirc; &icirc;&ograve;&acirc;&aring;&ograve; &iacute;&aring; &egrave;&ccedil;&igrave;&aring;&iacute;&egrave;&ograve;&ntilde;&yuml;. &Yacute;&ograve;&icirc; &icirc;&auml;&egrave;&iacute; &egrave;&ccedil; &ocirc;&oacute;&iacute;&auml;&agrave;&igrave;&aring;&iacute;&ograve;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&icirc;&acirc;
&egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml; &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&aring;&iacute;&egrave;&yuml; &divide;&egrave;&ntilde;&euml;&agrave;. &Iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml;&ntilde;&uuml; &yacute;&ograve;&egrave;&igrave; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&icirc;&igrave;
&igrave;&icirc;&aelig;&iacute;&icirc; &ccedil;&agrave;&igrave;&aring;&iacute;&yuml;&ograve;&uuml; &icirc;&auml;&iacute;&oacute; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&thorn; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &iacute;&agrave; &auml;&eth;&oacute;&atilde;&oacute;&thorn;, &aacute;&icirc;&euml;&aring;&aring; &iuml;&eth;&icirc;&ntilde;&ograve;&oacute;&thorn;. &Egrave;&auml;&aring;&yuml;
&Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &divide;&aring;&ograve;&ucirc;&eth;&frac14;&otilde; &iuml;&icirc;&iuml;&agrave;&eth;&iacute;&icirc; &ntilde;&ecirc;&eth;&aring;&ugrave;&egrave;&acirc;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&aring;&ograve;&uuml; &ntilde;&euml;&aring;&auml;&oacute;&thorn;&ugrave;&egrave;&eacute; &ntilde;&iuml;&aring;&ouml;&egrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ntilde;&euml;&oacute;&divide;&agrave;&eacute;: &iuml;&eth;&yuml;&igrave;&ucirc;&aring; l1 &egrave; l2 &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ograve;&ntilde;&yuml;, &egrave; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; l3 &egrave; l4 &ograve;&icirc;&aelig;&aring; (&ntilde;&igrave;. &eth;&egrave;&ntilde;. 1). &Iuml;&oacute;&ntilde;&ograve;&uuml; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; l1 &egrave; l2 &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ograve;&ntilde;&yuml; &acirc; &ograve;&icirc;&divide;&ecirc;&aring; a. &Ograve;&icirc;&atilde;&auml;&agrave; &icirc;&iacute;&egrave; &euml;&aring;&aelig;&agrave;&ograve;
&acirc; &icirc;&auml;&iacute;&icirc;&eacute; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave;, &ecirc;&icirc;&ograve;&icirc;&eth;&oacute;&thorn; &igrave;&ucirc; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&egrave;&igrave; &divide;&aring;&eth;&aring;&ccedil; P . &Ograve;&icirc;&divide;&ecirc;&oacute; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;
l3 &egrave; l4 &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&egrave;&igrave; &divide;&aring;&eth;&aring;&ccedil; a0 , &agrave; &ntilde;&icirc;&auml;&aring;&eth;&aelig;&agrave;&ugrave;&oacute;&thorn; &egrave;&otilde; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; P 0 . &Euml;&aring;&atilde;&ecirc;&icirc; &auml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&ograve;&uuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;, &divide;&ograve;&icirc; &eth;&icirc;&acirc;&iacute;&icirc; &auml;&acirc;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ograve; &acirc;&ntilde;&aring; &divide;&aring;&ograve;&ucirc;&eth;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; l1 ,
l2 , l3 &egrave; l4 : &iuml;&eth;&yuml;&igrave;&agrave;&yuml;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&agrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&egrave; a &egrave; a0 , &egrave; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&aring;&eacute; P &egrave; P 0 . &Igrave;&ucirc; &aelig;&aring; &auml;&icirc;&ecirc;&agrave;&aelig;&aring;&igrave; &yacute;&ograve;&icirc; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave; &ntilde; &iuml;&icirc;&igrave;&icirc;&ugrave;&uuml;&thorn; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;.
&Iuml;&eth;&aring;&egrave;&igrave;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&icirc; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&atilde;&icirc; &igrave;&aring;&ograve;&icirc;&auml;&agrave; &acirc; &aring;&atilde;&icirc; &oacute;&iacute;&egrave;&acirc;&aring;&eth;&ntilde;&agrave;&euml;&uuml;&iacute;&icirc;&ntilde;&ograve;&egrave; &icirc;&iacute; &eth;&agrave;&aacute;&icirc;&ograve;&agrave;&aring;&ograve; &egrave;
&acirc; &aacute;&icirc;&euml;&aring;&aring; &ntilde;&euml;&icirc;&aelig;&iacute;&ucirc;&otilde; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde;, &atilde;&auml;&aring; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute; &egrave;&iacute;&ograve;&oacute;&egrave;&ouml;&egrave;&egrave; &oacute;&aelig;&aring; &iacute;&aring; &otilde;&acirc;&agrave;&ograve;&agrave;&aring;&ograve;.
&Icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&igrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; σi &iacute;&agrave; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; l &ograve;&agrave;&ecirc;&egrave;&igrave; &icirc;&aacute;&eth;&agrave;&ccedil;&icirc;&igrave;: &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; σi &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&icirc;,
&aring;&ntilde;&euml;&egrave; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; l &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&aring;&ograve; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; li . &Oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&ecirc;&euml;&agrave;&auml;&ucirc;&acirc;&agrave;&ograve;&uuml; &egrave; &oacute;&igrave;&iacute;&icirc;&aelig;&agrave;&ograve;&uuml;.
&Iuml;&icirc;&auml; &ntilde;&oacute;&igrave;&igrave;&icirc;&eacute; &iacute;&aring;&ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&egrave;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &aacute;&oacute;&auml;&aring;&igrave; &iuml;&icirc;&iacute;&egrave;&igrave;&agrave;&ograve;&uuml; &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&egrave;&aring; &otilde;&icirc;&ograve;&yuml; &aacute;&ucirc; &icirc;&auml;&iacute;&icirc;&atilde;&icirc;
&egrave;&ccedil; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; (&ograve;&icirc;, &divide;&ograve;&icirc; &acirc; &euml;&icirc;&atilde;&egrave;&ecirc;&aring; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &auml;&egrave;&ccedil;&uacute;&thorn;&iacute;&ecirc;&ouml;&egrave;&aring;&eacute;), &agrave; &iuml;&icirc;&auml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&aring;&igrave; &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&egrave;&aring; &acirc;&ntilde;&aring;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &icirc;&auml;&iacute;&icirc;&acirc;&eth;&aring;&igrave;&aring;&iacute;&iacute;&icirc; (&ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &ecirc;&icirc;&iacute;&uacute;&thorn;&iacute;&ecirc;&ouml;&egrave;&thorn;). &Ograve;&icirc;&atilde;&auml;&agrave;, &ntilde;&ecirc;&agrave;&aelig;&aring;&igrave;,
&oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; σ1 + σ2 &aring;&ntilde;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &ntilde; l1 &egrave;&euml;&egrave; l2 , &agrave; &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&egrave;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; σ1 σ2
&eth;&agrave;&acirc;&iacute;&icirc;&ntilde;&egrave;&euml;&uuml;&iacute;&icirc; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&thorn; &ntilde; &icirc;&aacute;&aring;&egrave;&igrave;&egrave; &iuml;&eth;&yuml;&igrave;&ucirc;&igrave;&egrave; l1 &egrave; l2 . &Oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; l &ntilde;&icirc; &acirc;&ntilde;&aring;&igrave;&egrave; &divide;&aring;&ograve;&ucirc;&eth;&uuml;&igrave;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&igrave;&egrave; l1 , l2 , l3 , l4 &yacute;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; σ1 σ2 σ3 σ4 . &Euml;&aring;&atilde;&ecirc;&icirc;
&iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; &ntilde;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&aring; &egrave; &oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&aring;&ograve; &icirc;&aacute;&ucirc;&divide;&iacute;&ucirc;&igrave; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave;&igrave; &ntilde;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&yuml; &egrave; &oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&yuml;, &ograve;&agrave;&ecirc;&egrave;&igrave; &ecirc;&agrave;&ecirc; &iuml;&aring;&eth;&aring;&igrave;&aring;&ntilde;&ograve;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&eacute;, &ntilde;&icirc;&divide;&aring;&ograve;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&eacute; &egrave;
&eth;&agrave;&ntilde;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&eacute; &ccedil;&agrave;&ecirc;&icirc;&iacute;&ucirc;. &Igrave;&ucirc; &aacute;&oacute;&auml;&aring;&igrave; &ntilde;&divide;&egrave;&ograve;&agrave;&ograve;&uuml; &auml;&acirc;&agrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &eth;&agrave;&acirc;&iacute;&ucirc;&igrave;&egrave;, &aring;&ntilde;&euml;&egrave; &egrave;&igrave;
&oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ograve; &icirc;&auml;&iacute;&egrave; &egrave; &ograve;&aring; &aelig;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;. &Iacute;&agrave;&oslash;&agrave; &ouml;&aring;&euml;&uuml; &ccedil;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; σ1 σ2 σ3 σ4
&iacute;&agrave; &eth;&agrave;&acirc;&iacute;&icirc;&aring; &aring;&igrave;&oacute;, &iacute;&icirc; &aacute;&icirc;&euml;&aring;&aring; &iuml;&eth;&icirc;&ntilde;&ograve;&icirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring;.
&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave; &Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
3
&Icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&egrave;&igrave; &ccedil;&agrave; ρa &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring;, &divide;&ograve;&icirc; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; l &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; a, &agrave; &ccedil;&agrave; τP &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring;, &divide;&ograve;&icirc; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; l &euml;&aring;&aelig;&egrave;&ograve; &acirc; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; P . &Ograve;&icirc;&atilde;&auml;&agrave; &euml;&aring;&atilde;&ecirc;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; σ1 σ2 =
ρa + τP . &Agrave;&iacute;&agrave;&euml;&icirc;&atilde;&egrave;&divide;&iacute;&icirc;, σ3 σ4 = ρa0 + τP 0 . &Ntilde;&euml;&aring;&auml;&icirc;&acirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;,
σ1 σ2 σ3 σ4 = ρa ρa0 + ρa τP 0 + τP ρa0 + τP τP 0 .
&Ograve;&aring;&iuml;&aring;&eth;&uuml; &ccedil;&agrave;&igrave;&aring;&iacute;&egrave;&igrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &acirc; &euml;&aring;&acirc;&icirc;&eacute; &divide;&agrave;&ntilde;&ograve;&egrave; &egrave; &ecirc;&agrave;&aelig;&auml;&icirc;&aring; &egrave;&ccedil; &divide;&aring;&ograve;&ucirc;&eth;&frac14;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &acirc; &iuml;&eth;&agrave;&acirc;&icirc;&eacute;
&divide;&agrave;&ntilde;&ograve;&egrave; &iacute;&agrave; &divide;&egrave;&ntilde;&euml;&icirc; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ugrave;&egrave;&otilde; &yacute;&ograve;&icirc;&igrave;&oacute; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&thorn;. &Ccedil;&auml;&aring;&ntilde;&uuml; &igrave;&ucirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&aring;&igrave;
&aring;&ugrave;&frac14; &icirc;&auml;&egrave;&iacute; &ocirc;&oacute;&iacute;&auml;&agrave;&igrave;&aring;&iacute;&ograve;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&aring;
&ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&agrave; &iacute;&agrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &iuml;&eth;&egrave; &ograve;&agrave;&ecirc;&egrave;&otilde; &ccedil;&agrave;&igrave;&aring;&iacute;&agrave;&otilde; &auml;&agrave;&thorn;&ograve; &acirc;&aring;&eth;&iacute;&ucirc;&aring; &divide;&egrave;&ntilde;&euml;&aring;&iacute;&iacute;&ucirc;&aring; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&agrave;.
&Euml;&aring;&atilde;&ecirc;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; &ecirc;&agrave;&aelig;&auml;&icirc;&igrave;&oacute; &egrave;&ccedil; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; ρa ρa0 &egrave; τP τP 0 &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&aring;&ograve; &eth;&icirc;&acirc;&iacute;&icirc;
&icirc;&auml;&iacute;&agrave; &iuml;&eth;&yuml;&igrave;&agrave;&yuml;, &agrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;&igrave; ρa τP 0 &egrave; τP ρa0 &iacute;&egrave; &icirc;&auml;&iacute;&icirc;&eacute;. &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &igrave;&ucirc; &icirc;&iuml;&yuml;&ograve;&uuml; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&igrave;,
&divide;&ograve;&icirc; &divide;&egrave;&ntilde;&euml;&icirc; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde; l1 , l2 , l3 , l4 , &eth;&agrave;&acirc;&iacute;&icirc; &auml;&acirc;&oacute;&igrave;.
&Iuml;&eth;&egrave;&igrave;&aring;&eth;&iacute;&icirc; &ograve;&agrave;&ecirc;&egrave;&igrave; &icirc;&aacute;&eth;&agrave;&ccedil;&icirc;&igrave; &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &ntilde;&acirc;&icirc;&auml;&egrave;&euml; &ntilde;&euml;&icirc;&aelig;&iacute;&ucirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &ecirc; &aacute;&icirc;&euml;&aring;&aring; &iuml;&eth;&icirc;&ntilde;&ograve;&ucirc;&igrave;
&egrave; &acirc; &auml;&eth;&oacute;&atilde;&egrave;&otilde; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde;. &Ograve;&icirc;, &divide;&ograve;&icirc; &ntilde;&iuml;&aring;&ouml;&egrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ntilde;&euml;&oacute;&divide;&agrave;&eacute; &auml;&agrave;&ntilde;&ograve; &ograve;&icirc;&ograve; &aelig;&aring; &icirc;&ograve;&acirc;&aring;&ograve;, &divide;&ograve;&icirc; &egrave; &icirc;&aacute;&ugrave;&egrave;&eacute;,
&Oslash;&oacute;&aacute;&aring;&eth;&ograve; &iacute;&aring; &icirc;&aacute;&icirc;&ntilde;&iacute;&icirc;&acirc;&ucirc;&acirc;&agrave;&euml;, &egrave; &iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &aring;&atilde;&icirc; &ntilde;&icirc;&acirc;&eth;&aring;&igrave;&aring;&iacute;&iacute;&egrave;&ecirc;&egrave; &iacute;&aring;&icirc;&auml;&iacute;&icirc;&ecirc;&eth;&agrave;&ograve;&iacute;&icirc; &iuml;&ucirc;&ograve;&agrave;&euml;&egrave;&ntilde;&uuml;
&oacute;&euml;&egrave;&divide;&egrave;&ograve;&uuml; &aring;&atilde;&icirc;, &iuml;&eth;&egrave;&acirc;&icirc;&auml;&yuml; &iuml;&eth;&egrave;&igrave;&aring;&eth;&ucirc;, &acirc; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&eacute; &ntilde;&euml;&oacute;&divide;&agrave;&eacute; &auml;&agrave;&frac14;&ograve; &iacute;&aring;&acirc;&aring;&eth;&iacute;&ucirc;&eacute;
&icirc;&ograve;&acirc;&aring;&ograve;. &Icirc;&auml;&iacute;&agrave;&ecirc;&icirc;, &acirc;&icirc; &acirc;&ntilde;&aring;&otilde; &acirc;&ucirc;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml;&otilde; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &icirc;&ograve;&acirc;&aring;&ograve; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&euml;&ntilde;&yuml; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&igrave;.
&Auml;&agrave;&acirc;&egrave;&auml; &Atilde;&egrave;&euml;&uuml;&aacute;&aring;&eth;&ograve; &acirc;&ecirc;&euml;&thorn;&divide;&egrave;&euml; &iuml;&eth;&icirc;&aacute;&euml;&aring;&igrave;&oacute; &icirc;&aacute;&icirc;&ntilde;&iacute;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &acirc; &ntilde;&acirc;&icirc;&eacute;
&ccedil;&iacute;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&ucirc;&eacute; &ntilde;&iuml;&egrave;&ntilde;&icirc;&ecirc; &iuml;&eth;&icirc;&aacute;&euml;&aring;&igrave; &iuml;&icirc;&auml; &iacute;&icirc;&igrave;&aring;&eth;&icirc;&igrave; 15. &Iuml;&icirc;&iuml;&ucirc;&ograve;&ecirc;&egrave; &eth;&aring;&oslash;&egrave;&ograve;&uuml; &yacute;&ograve;&oacute; &iuml;&eth;&icirc;&aacute;&euml;&aring;&igrave;&oacute;
&ntilde;&iuml;&icirc;&ntilde;&icirc;&aacute;&ntilde;&ograve;&acirc;&icirc;&acirc;&agrave;&euml;&egrave; &eth;&agrave;&ccedil;&acirc;&egrave;&ograve;&egrave;&thorn; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &acirc;&agrave;&aelig;&iacute;&ucirc;&otilde; &iacute;&agrave;&iuml;&eth;&agrave;&acirc;&euml;&aring;&iacute;&egrave;&eacute; &ntilde;&icirc;&acirc;&eth;&aring;&igrave;&aring;&iacute;&iacute;&icirc;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc;&egrave;, &ograve;&agrave;&ecirc;&egrave;&otilde; &ecirc;&agrave;&ecirc; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&agrave;&yuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&yuml;. &Ntilde; &ograve;&aring;&otilde; &iuml;&icirc;&eth; &igrave;&aring;&ograve;&icirc;&auml;&ucirc; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &aacute;&ucirc;&euml;&egrave;
&divide;&agrave;&ntilde;&ograve;&egrave;&divide;&iacute;&icirc; &icirc;&aacute;&icirc;&ntilde;&iacute;&icirc;&acirc;&agrave;&iacute;&ucirc; &ntilde; &iuml;&icirc;&igrave;&icirc;&ugrave;&uuml;&thorn; &ograve;&aring;&icirc;&eth;&egrave;&egrave; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&eacute; (&iuml;&icirc;&ntilde;&euml;&aring;&auml;&iacute;&yuml;&yuml; &egrave; &aacute;&ucirc;&euml;&agrave; &ntilde;&icirc;&ccedil;&auml;&agrave;&iacute;&agrave; &acirc;&icirc; &igrave;&iacute;&icirc;&atilde;&icirc;&igrave; &auml;&euml;&yuml; &ograve;&icirc;&atilde;&icirc;, &divide;&ograve;&icirc;&aacute;&ucirc; &ocirc;&icirc;&eth;&igrave;&agrave;&euml;&egrave;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;), &iacute;&icirc; &acirc;
&iuml;&icirc;&euml;&iacute;&icirc;&igrave; &icirc;&aacute;&uacute;&frac14;&igrave;&aring; 15-&yuml; &iuml;&eth;&icirc;&aacute;&euml;&aring;&igrave;&agrave; &Atilde;&egrave;&euml;&uuml;&aacute;&aring;&eth;&ograve;&agrave; &iuml;&icirc;&ecirc;&agrave; &iacute;&aring; &eth;&aring;&oslash;&aring;&iacute;&agrave;.
&Egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&thorn; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &egrave; &aring;&atilde;&icirc; &igrave;&iacute;&icirc;&atilde;&icirc;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&iacute;&ucirc;&igrave; &iuml;&eth;&egrave;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&yuml;&igrave; &ecirc; &ecirc;&icirc;&iacute;&ecirc;&eth;&aring;&ograve;&iacute;&ucirc;&igrave; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&igrave; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &iuml;&icirc;&ntilde;&acirc;&yuml;&ograve;&egrave;&euml; &ouml;&aring;&euml;&oacute;&thorn; &ecirc;&iacute;&egrave;&atilde;&oacute; Kalk
ul der
abzahlenden Geometrie, &egrave;&ccedil;&auml;&agrave;&iacute;&iacute;&oacute;&thorn; &acirc; 1879 &atilde;&icirc;&auml;&oacute;. &Ntilde;&iuml;&oacute;&ntilde;&ograve;&yuml; &ntilde;&ograve;&icirc; &euml;&aring;&ograve; &ecirc;&iacute;&egrave;&atilde;&agrave; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;
&aacute;&ucirc;&euml;&agrave; &acirc;&iuml;&aring;&eth;&acirc;&ucirc;&aring; &iuml;&aring;&eth;&aring;&egrave;&ccedil;&auml;&agrave;&iacute;&agrave;, &agrave; &egrave;&iacute;&ograve;&aring;&eth;&aring;&ntilde; &ecirc; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &acirc;&iacute;&icirc;&acirc;&uuml; &acirc;&ucirc;&eth;&icirc;&ntilde; &icirc;&ecirc;&agrave;&ccedil;&agrave;&euml;&icirc;&ntilde;&uuml;, &divide;&ograve;&icirc; &icirc;&iacute;&agrave; &acirc;&agrave;&aelig;&iacute;&agrave; &auml;&euml;&yuml; &ograve;&aring;&icirc;&eth;&egrave;&egrave; &ntilde;&ograve;&eth;&oacute;&iacute;, &iacute;&icirc;&acirc;&icirc;&eacute; &ocirc;&egrave;&ccedil;&egrave;&ecirc;&icirc;&igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute;
&ograve;&aring;&icirc;&eth;&egrave;&egrave;, &iuml;&eth;&egrave;&ccedil;&acirc;&agrave;&iacute;&iacute;&icirc;&eacute; &aring;&auml;&egrave;&iacute;&ucirc;&igrave; &icirc;&aacute;&eth;&agrave;&ccedil;&icirc;&igrave; &icirc;&aacute;&uacute;&yuml;&ntilde;&iacute;&egrave;&ograve;&uuml; &iuml;&eth;&egrave;&eth;&icirc;&auml;&oacute; &acirc;&ntilde;&aring;&otilde; &ocirc;&egrave;&ccedil;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&otilde; &acirc;&ccedil;&agrave;&egrave;&igrave;&icirc;&auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&eacute;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 1.3. &Auml;&icirc;&ecirc;&agrave;&aelig;&egrave;&ograve;&aring;, &divide;&ograve;&icirc; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; &acirc; &ograve;&eth;&frac14;&otilde;&igrave;&aring;&eth;&iacute;&icirc;&igrave; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;, &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&aring; &ograve;&eth;&egrave; &iuml;&icirc;&iuml;&agrave;&eth;&iacute;&icirc; &ntilde;&ecirc;&eth;&aring;&ugrave;&egrave;&acirc;&agrave;&thorn;&ugrave;&egrave;&aring;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;, &ccedil;&agrave;&igrave;&aring;&ograve;&agrave;&thorn;&ograve; &iuml;&icirc;&acirc;&aring;&eth;&otilde;&iacute;&icirc;&ntilde;&ograve;&uuml;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&oacute;&thorn;
&oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; &ntilde;&ograve;&aring;&iuml;&aring;&iacute;&egrave; &auml;&acirc;&agrave;. (&Iacute;&agrave; &ntilde;&agrave;&igrave;&icirc;&igrave; &auml;&aring;&euml;&aring;, &ograve;&agrave;&ecirc;&agrave;&yuml; &iuml;&icirc;&acirc;&aring;&eth;&otilde;&iacute;&icirc;&ntilde;&ograve;&uuml; &euml;&egrave;&aacute;&icirc; &icirc;&auml;&iacute;&icirc;&iuml;&icirc;&euml;&icirc;&ntilde;&ograve;&iacute;&ucirc;&eacute; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&icirc;&egrave;&auml;, &euml;&egrave;&aacute;&icirc; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&eacute; &iuml;&agrave;&eth;&agrave;&aacute;&icirc;&euml;&icirc;&egrave;&auml;, &iacute;&icirc; &auml;&euml;&yuml; &eth;&aring;&oslash;&aring;&iacute;&egrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;
&Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &yacute;&ograve;&icirc; &iacute;&aring;&acirc;&agrave;&aelig;&iacute;&icirc;.)
2. &Ccedil;&agrave;&auml;&agrave;&divide;&agrave; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;
&Ograve;&aring;&iuml;&aring;&eth;&uuml; &igrave;&ucirc; &icirc;&aacute;&ntilde;&oacute;&auml;&egrave;&igrave; &icirc;&auml;&iacute;&oacute; &egrave;&ccedil; &ntilde;&agrave;&igrave;&ucirc;&otilde; &ccedil;&iacute;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&ucirc;&otilde; &ccedil;&agrave;&auml;&agrave;&divide; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &auml;&aring;&acirc;&yuml;&ograve;&iacute;&agrave;&auml;&ouml;&agrave;&ograve;&icirc;&atilde;&icirc; &acirc;&aring;&ecirc;&agrave;, &icirc;&aacute;&icirc;&aacute;&ugrave;&agrave;&thorn;&ugrave;&oacute;&thorn; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml;. &Ccedil;&agrave;&auml;&agrave;&divide;&oacute; &iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&euml;
&egrave;&ccedil;&acirc;&aring;&ntilde;&ograve;&iacute;&ucirc;&eacute; &iacute;&aring;&igrave;&aring;&ouml;&ecirc;&egrave;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth; &szlig;&ecirc;&icirc;&aacute; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth; &acirc; 1848 &atilde;&icirc;&auml;&oacute;, &agrave; &eth;&aring;&oslash;&egrave;&euml; &egrave;&ccedil;&acirc;&aring;&ntilde;&ograve;&iacute;&ucirc;&eacute;
4
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&ocirc;&eth;&agrave;&iacute;&ouml;&oacute;&ccedil;&ntilde;&ecirc;&egrave;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth; &Igrave;&egrave;&oslash;&aring;&euml;&uuml; &Oslash;&agrave;&euml;&uuml; &acirc; 1864 &atilde;&icirc;&auml;&oacute;. &times;&ograve;&icirc;&aacute;&ucirc; &ntilde;&ocirc;&icirc;&eth;&igrave;&oacute;&euml;&egrave;&eth;&icirc;&acirc;&agrave;&ograve;&uuml; &ccedil;&agrave;&auml;&agrave;&divide;&oacute;, &igrave;&ucirc; &ntilde;&iacute;&agrave;&divide;&agrave;&euml;&agrave; &icirc;&aacute;&icirc;&aacute;&ugrave;&egrave;&igrave; &iuml;&icirc;&iacute;&yuml;&ograve;&egrave;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &ograve;&agrave;&ecirc;, &divide;&ograve;&icirc;&aacute;&ucirc; &icirc;&iacute;&icirc; &acirc;&ecirc;&euml;&thorn;&divide;&egrave;&euml;&icirc; &acirc;
&ntilde;&aring;&aacute;&yuml; &ograve;&agrave;&ecirc;&egrave;&otilde; &aacute;&euml;&egrave;&aelig;&agrave;&eacute;&oslash;&egrave;&otilde; &eth;&icirc;&auml;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&egrave;&ecirc;&icirc;&acirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ecirc;&agrave;&ecirc; &yacute;&euml;&euml;&egrave;&iuml;&ntilde;&ucirc;, &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&ucirc; &egrave;
&iuml;&agrave;&eth;&agrave;&aacute;&icirc;&euml;&ucirc;. &Acirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&agrave;&otilde; (x, y) &acirc;&ntilde;&aring; &yacute;&ograve;&egrave; &ecirc;&eth;&egrave;&acirc;&ucirc;&aring; &igrave;&icirc;&aelig;&iacute;&icirc; &ccedil;&agrave;&auml;&agrave;&ograve;&uuml; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave;
ax2 + bxy + cy 2 + dx + ey + f = 0
(∗)
&iuml;&eth;&egrave; &iuml;&icirc;&auml;&otilde;&icirc;&auml;&yuml;&ugrave;&aring;&igrave; &acirc;&ucirc;&aacute;&icirc;&eth;&aring; &ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&icirc;&acirc; a, b, c, d, e &egrave; f . &Ecirc;&eth;&egrave;&acirc;&agrave;&yuml;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&agrave;&yuml;
&oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; (∗) &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &ecirc;&eth;&egrave;&acirc;&icirc;&eacute; &acirc;&ograve;&icirc;&eth;&icirc;&atilde;&icirc; &iuml;&icirc;&eth;&yuml;&auml;&ecirc;&agrave; &egrave;&euml;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute;, &aring;&ntilde;&euml;&egrave; a, b &egrave;
c &iacute;&aring; &eth;&agrave;&acirc;&iacute;&ucirc; &iacute;&oacute;&euml;&thorn; &icirc;&auml;&iacute;&icirc;&acirc;&eth;&aring;&igrave;&aring;&iacute;&iacute;&icirc;. &Acirc;&ograve;&icirc;&eth;&icirc;&aring; &iacute;&agrave;&ccedil;&acirc;&agrave;&iacute;&egrave;&aring; &ntilde;&acirc;&yuml;&ccedil;&agrave;&iacute;&icirc; &ntilde; &ograve;&aring;&igrave;, &divide;&ograve;&icirc; &euml;&thorn;&aacute;&oacute;&thorn;
&ecirc;&icirc;&iacute;&egrave;&ecirc;&oacute; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&icirc;&euml;&oacute;&divide;&egrave;&ograve;&uuml; &ecirc;&agrave;&ecirc; &ecirc;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&aring; &ntilde;&aring;&divide;&aring;&iacute;&egrave;&aring;, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&aring; &iuml;&eth;&yuml;&igrave;&icirc;&atilde;&icirc;
&ecirc;&eth;&oacute;&atilde;&icirc;&acirc;&icirc;&atilde;&icirc; &ecirc;&icirc;&iacute;&oacute;&ntilde;&agrave;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&icirc;&atilde;&icirc; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; αz 2 = x2 + y 2 (&iuml;&eth;&egrave; &iuml;&icirc;&auml;&otilde;&icirc;&auml;&yuml;&ugrave;&aring;&igrave; &acirc;&ucirc;&aacute;&icirc;&eth;&aring;
&iuml;&icirc;&euml;&icirc;&aelig;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave; α), &ntilde; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml;&thorn; &acirc; &ograve;&eth;&frac14;&otilde;&igrave;&aring;&eth;&iacute;&icirc;&igrave; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;.
&Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&thorn;&ograve;&ntilde;&yuml;, &ecirc;&icirc;&atilde;&auml;&agrave; &ntilde;&acirc;&aring;&ograve; &icirc;&ograve; &iacute;&agrave;&ntilde;&ograve;&icirc;&euml;&uuml;&iacute;&icirc;&eacute; &euml;&agrave;&igrave;&iuml;&ucirc; &ntilde; &agrave;&aacute;&agrave;&aelig;&oacute;&eth;&icirc;&igrave;
&ecirc;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute; &ocirc;&icirc;&eth;&igrave;&ucirc; &iuml;&agrave;&auml;&agrave;&aring;&ograve; &iacute;&agrave; &ntilde;&ograve;&aring;&iacute;&ucirc;. &Aacute;&oacute;&auml;&aring;&igrave; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&ograve;&uuml; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&igrave;&egrave; &ograve;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&aring; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&thorn;&ograve;&ntilde;&yuml; &ecirc;&agrave;&ecirc; &ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &ecirc;&icirc;&iacute;&oacute;&ntilde;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&yuml;&igrave;&egrave;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&igrave;&egrave; &divide;&aring;&eth;&aring;&ccedil;
&iacute;&agrave;&divide;&agrave;&euml;&icirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;. &Acirc;&ntilde;&aring; &icirc;&ntilde;&ograve;&agrave;&euml;&uuml;&iacute;&ucirc;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &iacute;&agrave;&ccedil;&icirc;&acirc;&frac14;&igrave; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&igrave;&egrave;.
&Oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; 2.1. &Iuml;&eth;&icirc;&acirc;&aring;&eth;&uuml;&ograve;&aring;, &divide;&ograve;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &yacute;&ograve;&icirc; &egrave;&euml;&egrave; &yacute;&euml;&euml;&egrave;&iuml;&ntilde;
(&icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml; &igrave;&ucirc; &ntilde;&divide;&egrave;&ograve;&agrave;&aring;&igrave; &divide;&agrave;&ntilde;&ograve;&iacute;&ucirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring;&igrave; &yacute;&euml;&euml;&egrave;&iuml;&ntilde;&agrave;), &egrave;&euml;&egrave; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&agrave;, &egrave;&euml;&egrave; &iuml;&agrave;&eth;&agrave;&aacute;&icirc;&euml;&agrave;, &agrave; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &yacute;&ograve;&icirc; &ograve;&icirc;&divide;&ecirc;&agrave;, &iuml;&eth;&yuml;&igrave;&agrave;&yuml; &egrave;&euml;&egrave; &iuml;&agrave;&eth;&agrave; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;.
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &oslash;&aring;&ntilde;&ograve;&uuml;&thorn; &ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&agrave;&igrave;&egrave; (a, b, c, d, e, f ),
&iacute;&icirc; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &iuml;&eth;&icirc;&eth;&iuml;&icirc;&eth;&ouml;&egrave;&icirc;&iacute;&agrave;&euml;&uuml;&iacute;&ucirc;&aring; &iacute;&agrave;&aacute;&icirc;&eth;&ucirc; &ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&icirc;&acirc; (&ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &iacute;&agrave;&aacute;&icirc;&eth;&ucirc; (a, b,
c, d, e, f ) &egrave; (λa, λb, λc, λd, λe, λf ), &atilde;&auml;&aring; λ 6= 0) &ccedil;&agrave;&auml;&agrave;&thorn;&ograve; &icirc;&auml;&iacute;&oacute; &egrave; &ograve;&oacute; &aelig;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&oacute;. &Ograve;&agrave;&ecirc;
&divide;&ograve;&icirc; &iacute;&agrave; &ntilde;&agrave;&igrave;&icirc;&igrave; &auml;&aring;&euml;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &ccedil;&agrave;&acirc;&egrave;&ntilde;&yuml;&ograve; &icirc;&ograve; &iuml;&yuml;&ograve;&egrave; &iacute;&aring;&ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&igrave;&ucirc;&otilde; &iuml;&agrave;&eth;&agrave;&igrave;&aring;&ograve;&eth;&icirc;&acirc;. &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &acirc;&icirc;
&acirc;&ntilde;&aring;&otilde; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&otilde; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde; &eth;&aring;&divide;&uuml; &iuml;&icirc;&eacute;&auml;&frac14;&ograve; &icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave;&otilde;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&yuml;&ograve;&uuml;&thorn; &iacute;&aring;&ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&igrave;&ucirc;&igrave;&egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;&igrave;&egrave; (&ograve;&icirc;&atilde;&auml;&agrave; &divide;&egrave;&ntilde;&euml;&icirc; &ograve;&agrave;&ecirc;&egrave;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ecirc;&agrave;&ecirc; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&icirc;, &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc;). &Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;,
&aring;&ntilde;&ograve;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&igrave; &icirc;&aacute;&icirc;&aacute;&ugrave;&aring;&iacute;&egrave;&aring;&igrave; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml; &aacute;&oacute;&auml;&aring;&ograve; &ograve;&agrave;&ecirc;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 2.2 (&Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;). &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&yuml;&ograve;&egrave;
&ecirc;&icirc;&iacute;&egrave;&ecirc;?
&Ecirc;&agrave;&ecirc; &egrave; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;, &iacute;&agrave;&ntilde; &egrave;&iacute;&ograve;&aring;&eth;&aring;&ntilde;&oacute;&aring;&ograve; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&icirc; &acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&ucirc;&eacute; &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&ucirc;&eacute;
&icirc;&ograve;&acirc;&aring;&ograve;. &Acirc;&igrave;&aring;&ntilde;&ograve;&aring; &ntilde; &ccedil;&agrave;&auml;&agrave;&divide;&aring;&eacute; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth; &ntilde;&eth;&agrave;&ccedil;&oacute; &auml;&agrave;&euml; &egrave; &icirc;&ograve;&acirc;&aring;&ograve;, &iacute;&icirc; &iacute;&aring;&acirc;&aring;&eth;&iacute;&ucirc;&eacute;. &Icirc;&ograve;&acirc;&aring;&ograve; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; 7776 (&yacute;&ograve;&icirc; 65 ). &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth; &iacute;&aring; &iuml;&eth;&egrave;&acirc;&icirc;&auml;&egrave;&euml; &iuml;&icirc;&euml;&iacute;&icirc;&atilde;&icirc; &eth;&aring;&oslash;&aring;&iacute;&egrave;&yuml;, &agrave; &euml;&egrave;&oslash;&uuml; &ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&euml;,
&divide;&ograve;&icirc; &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &divide;&aring;&ograve;&ucirc;&eth;&aring; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &eth;&agrave;&acirc;&iacute;&icirc; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&oacute;&igrave; 6 (&yacute;&ograve;&icirc; &iuml;&eth;&agrave;&acirc;&auml;&agrave;, &ecirc;&agrave;&ecirc; &igrave;&ucirc; &acirc;&ntilde;&ecirc;&icirc;&eth;&aring; &oacute;&acirc;&egrave;&auml;&egrave;&igrave;), &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;,
&ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &auml;&acirc;&oacute;&otilde; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &ograve;&eth;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &eth;&agrave;&acirc;&iacute;&icirc;
&igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&oacute;&igrave; 62 (&egrave; &yacute;&ograve;&icirc; &iuml;&eth;&agrave;&acirc;&auml;&agrave;), &agrave; &auml;&agrave;&euml;&aring;&aring; &iuml;&icirc; &agrave;&iacute;&agrave;&euml;&icirc;&atilde;&egrave;&egrave;. &Iacute;&agrave; &ntilde;&agrave;&igrave;&icirc;&igrave; &auml;&aring;&euml;&aring;, &oacute;&aelig;&aring; &divide;&egrave;&ntilde;&euml;&icirc;
&ecirc;&icirc;&iacute;&egrave;&ecirc;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &ograve;&eth;&frac14;&otilde; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;
&acirc;&ntilde;&aring;&atilde;&auml;&agrave; &ntilde;&ograve;&eth;&icirc;&atilde;&icirc; &igrave;&aring;&iacute;&uuml;&oslash;&aring; &divide;&aring;&igrave; 63 . &Acirc; 1859 &atilde;&icirc;&auml;&oacute; &ocirc;&eth;&agrave;&iacute;&ouml;&oacute;&ccedil;&ntilde;&ecirc;&egrave;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc; &Yacute;&eth;&iacute;&aring;&ntilde;&ograve; &auml;&aring;
&AElig;&icirc;&iacute;&ecirc;&uuml;&aring;&eth; &iacute;&agrave;&oslash;&frac14;&euml; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;, &iacute;&icirc; &iacute;&aring; &eth;&aring;&oslash;&egrave;&euml;&ntilde;&yuml; &icirc;&iuml;&oacute;&aacute;&euml;&egrave;&ecirc;&icirc;&acirc;&agrave;&ograve;&uuml; &aring;&atilde;&icirc;, &iacute;&agrave;&ntilde;&ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &aacute;&ucirc;&euml; &acirc;&aring;&euml;&egrave;&ecirc; &agrave;&acirc;&ograve;&icirc;&eth;&egrave;&ograve;&aring;&ograve; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;. &Auml;&aring; &AElig;&icirc;&iacute;&ecirc;&uuml;&aring;&eth; &aacute;&ucirc;&euml; &oacute;&divide;&aring;&iacute;&egrave;&ecirc;&icirc;&igrave; &Oslash;&agrave;&euml;&yuml; &egrave;, &iuml;&icirc;&igrave;&egrave;&igrave;&icirc; &ccedil;&agrave;&iacute;&yuml;&ograve;&egrave;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc;&icirc;&eacute;, &ntilde;&euml;&oacute;&aelig;&egrave;&euml; &acirc;&icirc; &ocirc;&eth;&agrave;&iacute;&ouml;&oacute;&ccedil;&ntilde;&ecirc;&icirc;&igrave; &ocirc;&euml;&icirc;&ograve;&aring;,
&atilde;&auml;&aring; &auml;&icirc;&ntilde;&euml;&oacute;&aelig;&egrave;&euml;&ntilde;&yuml; &auml;&icirc; &divide;&egrave;&iacute;&agrave; &agrave;&auml;&igrave;&egrave;&eth;&agrave;&euml;&agrave;.
&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave; &Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
5
&Iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; 3264. &Iuml;&aring;&eth;&acirc;&ucirc;&igrave; &aring;&atilde;&icirc; &icirc;&iuml;&oacute;&aacute;&euml;&egrave;&ecirc;&icirc;&acirc;&agrave;&euml; &Oslash;&agrave;&euml;&uuml;. &Oslash;&agrave;&euml;&uuml; &eth;&aring;&oslash;&egrave;&euml; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; (&egrave; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; &auml;&eth;&oacute;&atilde;&egrave;&otilde; &ccedil;&agrave;&auml;&agrave;&divide; &iuml;&eth;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;), &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring;
&oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;, &iuml;&icirc;&otilde;&icirc;&aelig;&aring;&aring; &iacute;&agrave; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;, &iacute;&icirc; &acirc; &aacute;&icirc;&euml;&aring;&aring; &atilde;&eth;&icirc;&igrave;&icirc;&ccedil;&auml;&ecirc;&icirc;&eacute; &ocirc;&icirc;&eth;&igrave;&aring;, &ograve;&agrave;&ecirc; &ecirc;&agrave;&ecirc;
&Oslash;&agrave;&euml;&uuml; &igrave;&aring;&iacute;&uuml;&oslash;&aring; &iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&euml;&ntilde;&yuml; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&igrave;&egrave; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&agrave;&igrave;&egrave; &iuml;&eth;&egrave; &acirc;&ucirc;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml;&otilde; &ntilde;
&oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;&igrave;&egrave;. &Igrave;&ucirc; &eth;&agrave;&ccedil;&aacute;&aring;&eth;&frac14;&igrave; &eth;&aring;&oslash;&aring;&iacute;&egrave;&aring; &Oslash;&agrave;&euml;&yuml; &acirc; &egrave;&ccedil;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&egrave; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;.
&Acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; (&ecirc;&agrave;&ecirc; &egrave; &acirc; &auml;&eth;&oacute;&atilde;&egrave;&otilde; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave; &auml;&aring;&acirc;&yuml;&ograve;&iacute;&agrave;&auml;&ouml;&agrave;&ograve;&icirc;&atilde;&icirc; &acirc;&aring;&ecirc;&agrave;) &eth;&aring;&divide;&uuml; &egrave;&auml;&frac14;&ograve; &icirc; &divide;&egrave;&ntilde;&euml;&aring; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&ucirc;
a, b, c, d, e, f &igrave;&icirc;&atilde;&oacute;&ograve; &aacute;&ucirc;&ograve;&uuml; &euml;&thorn;&aacute;&ucirc;&igrave;&egrave; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&igrave;&egrave; &divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave;. &Yacute;&ograve;&icirc; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &oacute;&iuml;&eth;&icirc;&ugrave;&agrave;&aring;&ograve;, &iuml;&icirc;&ograve;&icirc;&igrave;&oacute; &divide;&ograve;&icirc; &auml;&euml;&yuml; &iuml;&icirc;&divide;&ograve;&egrave; &acirc;&ntilde;&aring;&otilde; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&eacute; &egrave;&ccedil; &iuml;&yuml;&ograve;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&ograve;&ntilde;&yuml; &icirc;&auml;&egrave;&iacute;
&egrave; &ograve;&icirc;&ograve; &aelig;&aring; &icirc;&ograve;&acirc;&aring;&ograve;, &agrave; &egrave;&igrave;&aring;&iacute;&iacute;&icirc;, &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&icirc; &acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&ucirc;&eacute; &ntilde;&eth;&aring;&auml;&egrave; &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&ucirc;&otilde;. &Acirc; &divide;&agrave;&ntilde;&ograve;&iacute;&icirc;&ntilde;&ograve;&egrave;, &euml;&thorn;&aacute;&ucirc;&aring; &iuml;&yuml;&ograve;&uuml; &ecirc;&icirc;&iacute;&egrave;&ecirc; &acirc;&ntilde;&aring;&atilde;&auml;&agrave; &igrave;&icirc;&aelig;&iacute;&icirc; &divide;&oacute;&ograve;&uuml;-&divide;&oacute;&ograve;&uuml; &iuml;&icirc;&auml;&acirc;&egrave;&atilde;&agrave;&ograve;&uuml; &ograve;&agrave;&ecirc;, &divide;&ograve;&icirc;&aacute;&ucirc; &icirc;&ograve;&acirc;&aring;&ograve;
&acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; &auml;&euml;&yuml; &iacute;&icirc;&acirc;&icirc;&eacute; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave; &aacute;&ucirc;&euml; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&ucirc;&igrave; &ntilde;&eth;&aring;&auml;&egrave; &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&ucirc;&otilde; &icirc;&ograve;&acirc;&aring;&ograve;&icirc;&acirc;. &Ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml; &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&aring;&iacute;&egrave;&yuml; &divide;&egrave;&ntilde;&euml;&agrave; &acirc; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring; &ntilde;&egrave;&euml;&uuml;&iacute;&aring;&aring;
&divide;&aring;&igrave;, &acirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&igrave;. &Ntilde;&acirc;&yuml;&ccedil;&agrave;&iacute;&icirc; &yacute;&ograve;&icirc; &ntilde; &ograve;&aring;&igrave;, &divide;&ograve;&icirc; &euml;&thorn;&aacute;&icirc;&aring; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&iacute;&icirc;&aring; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring; &egrave;&igrave;&aring;&aring;&ograve;
&auml;&acirc;&agrave; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&otilde; &ecirc;&icirc;&eth;&iacute;&yuml; &ntilde; &oacute;&divide;&frac14;&ograve;&icirc;&igrave; &ecirc;&eth;&agrave;&ograve;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ograve;&icirc;&atilde;&auml;&agrave; &ecirc;&agrave;&ecirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&eth;&iacute;&aring;&eacute;
&igrave;&icirc;&aelig;&aring;&ograve; &aacute;&ucirc;&ograve;&uuml; &egrave;&euml;&egrave; &auml;&acirc;&agrave;, &egrave;&euml;&egrave; &iacute;&egrave; &icirc;&auml;&iacute;&icirc;&atilde;&icirc;.
&Aring;&ntilde;&euml;&egrave; &aelig;&aring; &egrave;&ntilde;&ecirc;&agrave;&ograve;&uuml; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &divide;&egrave;&ntilde;&euml;&icirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ograve;&icirc; &icirc;&ograve;&acirc;&aring;&ograve; (&ecirc;&agrave;&ecirc; &egrave; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring;
&Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml;) &aacute;&oacute;&auml;&aring;&ograve; &ntilde;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc; &ccedil;&agrave;&acirc;&egrave;&ntilde;&aring;&ograve;&uuml; &icirc;&ograve; &acirc;&ucirc;&aacute;&icirc;&eth;&agrave; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave; &egrave;&ccedil; &iuml;&yuml;&ograve;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;. &Acirc; &iacute;&agrave;&oslash;&aring; &acirc;&eth;&aring;&igrave;&yuml; &icirc;&divide;&aring;&iacute;&uuml; &iuml;&icirc;&iuml;&oacute;&euml;&yuml;&eth;&iacute;&agrave; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&agrave;&yuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&yuml;,
&ecirc;&icirc;&ograve;&icirc;&eth;&agrave;&yuml;, &acirc; &divide;&agrave;&ntilde;&ograve;&iacute;&icirc;&ntilde;&ograve;&egrave;, &egrave;&ugrave;&aring;&ograve; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave;, &auml;&euml;&yuml; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &acirc;&ntilde;&aring; &eth;&aring;&oslash;&aring;&iacute;&egrave;&yuml; &icirc;&ecirc;&agrave;&aelig;&oacute;&ograve;&ntilde;&yuml; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&igrave;&egrave;. &Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; &ntilde;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&oacute;&aring;&ograve; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&yuml; &egrave;&ccedil;
&iuml;&yuml;&ograve;&egrave; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;, &auml;&euml;&yuml; &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &acirc;&ntilde;&aring; 3264 &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ograve;&ntilde;&yuml; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&igrave;&egrave; (1997,
Ronga, Tognoli, Vust). &Ecirc;&eth;&icirc;&igrave;&aring; &ograve;&icirc;&atilde;&icirc;, &auml;&euml;&yuml; &euml;&thorn;&aacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&egrave; &egrave;&ccedil; &iuml;&yuml;&ograve;&egrave; &yacute;&euml;&euml;&egrave;&iuml;&ntilde;&icirc;&acirc; &ntilde;
&iacute;&aring;&iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&igrave;&egrave;&ntilde;&yuml; &acirc;&iacute;&oacute;&ograve;&eth;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&yuml;&igrave;&egrave;, &iacute;&agrave;&eacute;&auml;&frac14;&ograve;&ntilde;&yuml; &iuml;&icirc; &ecirc;&eth;&agrave;&eacute;&iacute;&aring;&eacute; &igrave;&aring;&eth;&aring; 32 &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&aring;&ntilde;&yuml; &acirc;&ntilde;&aring;&otilde; &iuml;&yuml;&ograve;&egrave; &yacute;&euml;&euml;&egrave;&iuml;&ntilde;&icirc;&acirc; (2005,Welschinger). &Auml;&euml;&yuml; &icirc;&ntilde;&ograve;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde;
&ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&eacute; &iacute;&egrave;&ecirc;&agrave;&ecirc;&egrave;&otilde; &icirc;&ouml;&aring;&iacute;&icirc;&ecirc; &iacute;&agrave; &divide;&egrave;&ntilde;&euml;&icirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &eth;&aring;&oslash;&aring;&iacute;&egrave;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; &iuml;&icirc;&ecirc;&agrave; &iacute;&aring; &egrave;&ccedil;&acirc;&aring;&ntilde;&ograve;&iacute;&icirc;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 2.3. &Iuml;&eth;&egrave; &ecirc;&agrave;&ecirc;&icirc;&igrave; &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&egrave; &ograve;&eth;&frac14;&otilde; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute; &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &Agrave;&iuml;&icirc;&euml;&euml;&icirc;&iacute;&egrave;&yuml; &auml;&euml;&yuml; &iacute;&egrave;&otilde; &egrave;&igrave;&aring;&aring;&ograve; 8 &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &eth;&aring;&oslash;&aring;&iacute;&egrave;&eacute;?
3. &ETH;&aring;&oslash;&aring;&iacute;&egrave;&aring; &Oslash;&agrave;&euml;&yuml;
&Ntilde;&iacute;&agrave;&divide;&agrave;&euml;&agrave; &iuml;&aring;&eth;&aring;&ocirc;&icirc;&eth;&igrave;&oacute;&euml;&egrave;&eth;&oacute;&aring;&igrave; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave; &iacute;&agrave; &yuml;&ccedil;&ucirc;&ecirc;&aring; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;.
&Iuml;&oacute;&ntilde;&ograve;&uuml; κQ &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; Q. &Iacute;&agrave;&igrave; &iacute;&oacute;&aelig;&iacute;&icirc; &iacute;&agrave;&eacute;&ograve;&egrave; &divide;&egrave;&ntilde;&euml;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ugrave;&egrave;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&thorn; κQ1 &middot; . . . &middot; κQ5 &auml;&euml;&yuml; &iuml;&yuml;&ograve;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde;
&ecirc;&icirc;&iacute;&egrave;&ecirc; Q1 ,. . . , Q5 . &Auml;&euml;&yuml; &iuml;&eth;&icirc;&ntilde;&ograve;&icirc;&ograve;&ucirc; &igrave;&ucirc; &aacute;&oacute;&auml;&aring;&igrave; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&agrave;&ograve;&uuml; &acirc;&ntilde;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; κQi &divide;&aring;&eth;&aring;&ccedil; κ.
&Ograve;&agrave;&ecirc;&agrave;&yuml; &acirc;&icirc;&euml;&uuml;&iacute;&icirc;&ntilde;&ograve;&uuml; &acirc; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml;&otilde; &icirc;&iuml;&eth;&agrave;&acirc;&auml;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&icirc;&igrave; &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&aring;&iacute;&egrave;&yuml; &divide;&egrave;&ntilde;&euml;&agrave; &acirc;
&ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring; &iacute;&agrave;&ntilde; &acirc;&aring;&auml;&uuml; &egrave;&iacute;&ograve;&aring;&eth;&aring;&ntilde;&oacute;&aring;&ograve; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc; (&agrave; &iacute;&aring; &ntilde;&agrave;&igrave;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;), &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ugrave;&egrave;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&thorn; κQ1 &middot; . . . &middot; κQ5 , &agrave; &divide;&egrave;&ntilde;&euml;&icirc; &aacute;&oacute;&auml;&aring;&ograve; &icirc;&auml;&iacute;&egrave;&igrave; &egrave; &ograve;&aring;&igrave; &aelig;&aring; &auml;&euml;&yuml;
&iuml;&icirc;&divide;&ograve;&egrave; &acirc;&ntilde;&aring;&otilde; &iacute;&agrave;&aacute;&icirc;&eth;&icirc;&acirc; Q1 ,. . . , Q5 . &Acirc;&icirc;&icirc;&aacute;&ugrave;&aring;, &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&aring; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &acirc;&icirc; &igrave;&iacute;&icirc;&atilde;&icirc;&igrave; &icirc;&ntilde;&iacute;&icirc;&acirc;&agrave;&iacute;&icirc; &iacute;&agrave; &ograve;&agrave;&ecirc;&egrave;&otilde; &auml;&acirc;&oacute;&ntilde;&igrave;&ucirc;&ntilde;&euml;&aring;&iacute;&iacute;&ucirc;&otilde; (&egrave; &auml;&agrave;&aelig;&aring; &igrave;&iacute;&icirc;&atilde;&icirc;&ntilde;&igrave;&ucirc;&ntilde;&euml;&aring;&iacute;&iacute;&ucirc;&otilde;) &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml;&otilde;, &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&aring;
&iuml;&icirc;&ccedil;&acirc;&icirc;&euml;&yuml;&thorn;&ograve; &icirc;&iuml;&aring;&eth;&egrave;&eth;&icirc;&acirc;&agrave;&ograve;&uuml; &ntilde; &eth;&agrave;&ccedil;&iacute;&ucirc;&igrave;&egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;&igrave;&egrave; &ecirc;&agrave;&ecirc; &ntilde; &yacute;&ecirc;&acirc;&egrave;&acirc;&agrave;&euml;&aring;&iacute;&ograve;&iacute;&ucirc;&igrave;&egrave;. &Ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &ntilde;
6
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&eth;&agrave;&ccedil;&acirc;&egrave;&ograve;&egrave;&aring;&igrave; &ograve;&aring;&icirc;&eth;&egrave;&egrave; &atilde;&icirc;&igrave;&icirc;&euml;&icirc;&atilde;&egrave;&eacute; &acirc; &iuml;&aring;&eth;&acirc;&icirc;&eacute; &iuml;&icirc;&euml;&icirc;&acirc;&egrave;&iacute;&aring; &auml;&acirc;&agrave;&auml;&ouml;&agrave;&ograve;&icirc;&atilde;&icirc; &acirc;&aring;&ecirc;&agrave; &ntilde;&ograve;&agrave;&euml;&icirc; &acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&ucirc;&igrave; &ntilde;&ograve;&eth;&icirc;&atilde;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&uuml; &yacute;&ecirc;&acirc;&egrave;&acirc;&agrave;&euml;&aring;&iacute;&ograve;&iacute;&icirc;&ntilde;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;, &ntilde;&iuml;&eth;&yuml;&ograve;&agrave;&iacute;&iacute;&oacute;&thorn; &acirc; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml;&otilde;
&Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave;.
&Oslash;&agrave;&euml;&uuml; &auml;&icirc;&atilde;&agrave;&auml;&agrave;&euml;&ntilde;&yuml;, &divide;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; κ &igrave;&icirc;&aelig;&iacute;&icirc; &acirc;&ucirc;&eth;&agrave;&ccedil;&egrave;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &aacute;&icirc;&euml;&aring;&aring; &iuml;&eth;&icirc;&ntilde;&ograve;&ucirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;. &Acirc; &ecirc;&agrave;&divide;&aring;&ntilde;&ograve;&acirc;&aring; &ntilde;&agrave;&igrave;&ucirc;&otilde; &iuml;&eth;&icirc;&ntilde;&ograve;&ucirc;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute; &Oslash;&agrave;&euml;&uuml; &acirc;&ccedil;&yuml;&euml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &iuml;&eth;&icirc;&otilde;&icirc;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil;
&auml;&agrave;&iacute;&iacute;&oacute;&thorn; &ograve;&icirc;&divide;&ecirc;&oacute; &egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; (&ograve;&eth;&agrave;&auml;&egrave;&ouml;&egrave;&icirc;&iacute;&iacute;&icirc; &yacute;&ograve;&egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;
&icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&agrave;&thorn;&ograve;&ntilde;&yuml; &aacute;&oacute;&ecirc;&acirc;&agrave;&igrave;&egrave; &micro; &egrave; ν , &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;). &Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &micro; &egrave; ν &igrave;&icirc;&aelig;&iacute;&icirc; &oacute;&igrave;&iacute;&icirc;&aelig;&agrave;&ograve;&uuml; &iacute;&agrave; &iacute;&agrave;&ograve;&oacute;&eth;&agrave;&euml;&uuml;&iacute;&ucirc;&aring; &divide;&egrave;&ntilde;&euml;&agrave;. &Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&igrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; 2&micro; &ecirc;&agrave;&ecirc; c&oacute;&igrave;&igrave;&oacute; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &iuml;&eth;&icirc;&otilde;&icirc;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; a1 &egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &iuml;&eth;&icirc;&otilde;&icirc;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute;
a2 , &atilde;&auml;&aring; a1 &egrave; a2 &eth;&agrave;&ccedil;&euml;&egrave;&divide;&iacute;&ucirc; (&ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &igrave;&ucirc; &icirc;&iuml;&yuml;&ograve;&uuml; &ccedil;&euml;&icirc;&oacute;&iuml;&icirc;&ograve;&eth;&aring;&aacute;&euml;&yuml;&aring;&igrave; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml;&igrave;&egrave; &egrave;
&iuml;&egrave;&oslash;&aring;&igrave; 2&micro; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &micro;a1 + &micro;a2 ).
&Iuml;&oacute;&ntilde;&ograve;&uuml; &iacute;&agrave;&igrave; &oacute;&auml;&agrave;&euml;&icirc;&ntilde;&uuml; &iuml;&eth;&aring;&auml;&ntilde;&ograve;&agrave;&acirc;&egrave;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; κ &acirc; &acirc;&egrave;&auml;&aring; &ntilde;&oacute;&igrave;&igrave;&ucirc; m&micro; + nν &auml;&euml;&yuml; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &ouml;&aring;&euml;&ucirc;&otilde; &iacute;&aring;&icirc;&ograve;&eth;&egrave;&ouml;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&otilde; &divide;&egrave;&ntilde;&aring;&euml; m &egrave; n. &Ograve;&icirc;&atilde;&auml;&agrave; κ5 = (m&micro; + nν)5 &igrave;&icirc;&aelig;&iacute;&icirc;
&ocirc;&icirc;&eth;&igrave;&agrave;&euml;&uuml;&iacute;&icirc; &iuml;&eth;&aring;&icirc;&aacute;&eth;&agrave;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml;, &eth;&agrave;&ntilde;&ecirc;&eth;&ucirc;&acirc;&agrave;&yuml; &ntilde;&ecirc;&icirc;&aacute;&ecirc;&egrave;:
κ5 = m5 &micro;5 + 5m4 n&micro;4 ν + 10m3 n2 &micro;3 ν 2 + 10m2 n3 &micro;2 ν 3 + 5mn4 &micro;ν 4 + n5 ν 5 .
(1)
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &ecirc;&agrave;&aelig;&auml;&icirc;&igrave;&oacute; &igrave;&icirc;&iacute;&icirc;&igrave;&oacute; &micro;k ν 5−k &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&egrave;&auml;&agrave;&ograve;&uuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&eacute; &ntilde;&igrave;&ucirc;&ntilde;&euml; &yacute;&ograve;&icirc; &acirc; &ograve;&icirc;&divide;&iacute;&icirc;&ntilde;&ograve;&egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring;, &divide;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &divide;&aring;&eth;&aring;&ccedil; k &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc; &egrave; &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; (5 − k) &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Egrave;&ccedil; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&agrave; &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&aring;&iacute;&egrave;&yuml; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc; &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&igrave;, &divide;&ograve;&icirc;
&ocirc;&icirc;&eth;&igrave;&agrave;&euml;&uuml;&iacute;&icirc;&aring; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&icirc; (1) &icirc;&ntilde;&ograve;&agrave;&iacute;&aring;&ograve;&ntilde;&yuml; &acirc;&aring;&eth;&iacute;&ucirc;&igrave;, &aring;&ntilde;&euml;&egrave; &ccedil;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&uuml; κ5 &iacute;&agrave; &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;,
&ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &iuml;&yuml;&ograve;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &agrave; &ecirc;&agrave;&aelig;&auml;&ucirc;&eacute; &igrave;&icirc;&iacute;&icirc;&igrave; &micro;k ν 5−k &iacute;&agrave; &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;,
&iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; k &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; (5 − k) &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Ntilde;&agrave;&igrave;
&Oslash;&agrave;&euml;&uuml; &yacute;&ograve;&egrave;&igrave; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&icirc;&igrave; &iacute;&aring; &iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&euml;&ntilde;&yuml;, &egrave; &euml;&egrave;&oslash;&uuml; &acirc; 1873 &atilde;&icirc;&auml;&oacute; &ocirc;&eth;&agrave;&iacute;&ouml;&oacute;&ccedil;&ntilde;&ecirc;&egrave;&eacute; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc; &AElig;&icirc;&eth;&aelig;-&Agrave;&iacute;&eth;&egrave; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute; &ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&euml;, &divide;&ograve;&icirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&iacute;&egrave;&aring; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&agrave; (1) &oacute;&iuml;&eth;&icirc;&ugrave;&agrave;&aring;&ograve;
&eth;&agrave;&ntilde;&ntilde;&oacute;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &Oslash;&agrave;&euml;&yuml;. &Egrave;&igrave;&aring;&iacute;&iacute;&icirc; &ccedil;&agrave;&igrave;&aring;&divide;&agrave;&iacute;&egrave;&aring; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute;&agrave; &iuml;&icirc;&auml;&ograve;&icirc;&euml;&ecirc;&iacute;&oacute;&euml;&icirc; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&agrave; &ecirc; &ntilde;&icirc;&ccedil;&auml;&agrave;&iacute;&egrave;&thorn; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;. &Acirc; &ntilde;&euml;&aring;&auml;&oacute;&thorn;&ugrave;&aring;&igrave; &eth;&agrave;&ccedil;&auml;&aring;&euml;&aring; &igrave;&ucirc; &iacute;&agrave;&eacute;&auml;&frac14;&igrave;, &divide;&ograve;&icirc; &micro;5 = ν 5 = 1,
&micro;4 ν = &micro;ν 4 = 2, &micro;3 ν 2 = &micro;2 ν 3 = 4. &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute;
|κ5 | = m5 + 10m4 n + 40m3 n2 + 40m2 n3 + 10mn4 + n5 ,
(2)
&atilde;&auml;&aring; |κ5 | &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&agrave;&aring;&ograve; &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ugrave;&egrave;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&thorn; κ5 . &Iuml;&eth;&egrave;&divide;&frac14;&igrave; &yacute;&ograve;&icirc; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&icirc; &ntilde;&iuml;&eth;&agrave;&acirc;&aring;&auml;&euml;&egrave;&acirc;&icirc; &auml;&euml;&yuml; &euml;&thorn;&aacute;&icirc;&atilde;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; κ, &iuml;&eth;&aring;&auml;&ntilde;&ograve;&agrave;&acirc;&egrave;&igrave;&icirc;&atilde;&icirc; &acirc; &acirc;&egrave;&auml;&aring; m&micro; + nν (&igrave;&ucirc;
&iuml;&icirc;&ecirc;&agrave; &iacute;&egrave;&atilde;&auml;&aring; &iacute;&aring; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&euml;&egrave;, &divide;&ograve;&icirc; κ &yacute;&ograve;&icirc; &egrave;&igrave;&aring;&iacute;&iacute;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute;).
&Acirc; &ntilde;&euml;&aring;&auml;&oacute;&thorn;&ugrave;&aring;&igrave; &eth;&agrave;&ccedil;&auml;&aring;&euml;&aring; &igrave;&ucirc;, &iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml;&ntilde;&uuml; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&icirc;&eacute; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml;&thorn;, &auml;&icirc;&ecirc;&agrave;&aelig;&aring;&igrave;,
&divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&aring;&auml;&ntilde;&ograve;&agrave;&acirc;&egrave;&ograve;&uuml; &acirc; &acirc;&egrave;&auml;&aring; m&micro;+nν , &ograve;&icirc; &ograve;&icirc;&atilde;&auml;&agrave;
&icirc;&aacute;&yuml;&ccedil;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc; m = n, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; κ = n(&micro; + ν). &Icirc;&ntilde;&ograve;&agrave;&euml;&icirc;&ntilde;&uuml; &iacute;&agrave;&eacute;&ograve;&egrave; n. &Ntilde;&euml;&aring;&auml;&oacute;&yuml; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&oacute;, &igrave;&ucirc; &icirc;&iuml;&yuml;&ograve;&uuml; &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&egrave;&igrave; &ntilde;&iuml;&aring;&ouml;&egrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ntilde;&euml;&oacute;&divide;&agrave;&eacute; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &icirc;&aacute;&ugrave;&aring;&atilde;&icirc;. &Acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;
&ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; κQ &ntilde; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; Q (&ntilde;&ecirc;&agrave;&aelig;&aring;&igrave;, &ntilde; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&icirc;&eacute; xy − 1 = 0),
&iuml;&icirc;&iuml;&eth;&icirc;&aacute;&oacute;&aring;&igrave; &icirc;&iuml;&egrave;&ntilde;&agrave;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; κQ0 &ntilde; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; Q0 , &ntilde;&icirc;&ntilde;&ograve;&icirc;&yuml;&ugrave;&aring;&eacute;
&egrave;&ccedil; &iuml;&agrave;&eth;&ucirc; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; l1 &egrave; l2 (&iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&ucirc; &igrave;&icirc;&aelig;&iacute;&icirc;
&acirc;&ccedil;&yuml;&ograve;&uuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&oacute; xy = 0). &Ograve;&icirc;&atilde;&auml;&agrave; &euml;&aring;&atilde;&ecirc;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; Q0
&ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; Q0 , &aring;&ntilde;&euml;&egrave; &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&icirc; &icirc;&auml;&iacute;&icirc; &egrave;&ccedil; &ograve;&eth;&frac14;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;: &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; Q0 &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml;
&iuml;&eth;&yuml;&igrave;&icirc;&eacute; l1 , &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; l2 , &egrave;&euml;&egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; p &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;
&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave; &Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
7
l1 &egrave; l2 . &Iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &auml;&icirc;&ntilde;&ograve;&agrave;&ograve;&icirc;&divide;&iacute;&icirc; &auml;&agrave;&euml;&aring;&ecirc;&icirc; &icirc;&ograve; &ograve;&icirc;&divide;&ecirc;&egrave; p &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&oacute;&thorn; &ecirc;&icirc;&iacute;&egrave;&ecirc;&oacute; Q0 &igrave;&icirc;&aelig;&iacute;&icirc; &icirc;&divide;&aring;&iacute;&uuml; &otilde;&icirc;&eth;&icirc;&oslash;&icirc; &iuml;&eth;&egrave;&aacute;&euml;&egrave;&ccedil;&egrave;&ograve;&uuml; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; Q (&iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;,
&atilde;&egrave;&iuml;&aring;&eth;&aacute;&icirc;&euml;&agrave; xy = 1 &otilde;&icirc;&eth;&icirc;&oslash;&icirc; &iuml;&eth;&egrave;&aacute;&euml;&egrave;&aelig;&agrave;&aring;&ograve; &iuml;&agrave;&eth;&oacute; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; xy = 0 &acirc;&auml;&agrave;&euml;&egrave; &icirc;&ograve; &iacute;&agrave;&divide;&agrave;&euml;&agrave;
&ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;). &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; κQ = m&micro; + 2ν , &icirc;&ograve;&ecirc;&oacute;&auml;&agrave; n = 2.
&Iuml;&icirc;&auml;&ntilde;&ograve;&agrave;&acirc;&egrave;&acirc; m = n = 2 &acirc; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&icirc; (2), &iuml;&icirc;&euml;&oacute;&divide;&egrave;&igrave; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring;
&Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;:
|κ5 | = 25 (1 + 10 + 40 + 40 + 10 + 1) = 25 &middot; 102 = 3264.
&Oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; 3.1 (&iuml;&eth;&icirc;&acirc;&aring;&eth;&ecirc;&agrave; &eth;&agrave;&ntilde;&ntilde;&oacute;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;). &Auml;&euml;&yuml; k = 1, 2, 3, 4, &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&eacute;&ograve;&aring; &igrave;&aring;&ograve;&icirc;&auml; &Oslash;&agrave;&euml;&yuml;, &divide;&ograve;&icirc;&aacute;&ucirc; &iacute;&agrave;&eacute;&ograve;&egrave; &divide;&egrave;&ntilde;&euml;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; k &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; (5 − k) &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc;.
&Igrave;&ucirc; (&ecirc;&agrave;&ecirc; &egrave; &Oslash;&agrave;&euml;&uuml;) &iacute;&aring; &icirc;&aacute;&icirc;&ntilde;&iacute;&icirc;&acirc;&agrave;&euml;&egrave;, &divide;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; &acirc;&ucirc;&eth;&agrave;&aelig;&agrave;&aring;&ograve;&ntilde;&yuml; &divide;&aring;&eth;&aring;&ccedil; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &micro; &egrave; ν . &Yacute;&ograve;&icirc; &iacute;&aring;&ograve;&eth;&egrave;&acirc;&egrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ocirc;&agrave;&ecirc;&ograve;. &Iuml;&icirc;&divide;&aring;&igrave;&oacute;, &iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &iacute;&aring;&euml;&uuml;&ccedil;&yuml;
&acirc;&ucirc;&eth;&agrave;&ccedil;&egrave;&ograve;&uuml; &yacute;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &divide;&aring;&eth;&aring;&ccedil; &micro;? &Acirc;&icirc;&icirc;&aacute;&ugrave;&aring;, &egrave;&auml;&aring;&yuml; &acirc;&ucirc;&eth;&agrave;&aelig;&agrave;&ograve;&uuml; &ntilde;&euml;&icirc;&aelig;&iacute;&ucirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &iuml;&eth;&icirc;&ntilde;&ograve;&ucirc;&aring; &iuml;&icirc;&yuml;&acirc;&egrave;&euml;&agrave;&ntilde;&uuml; &ntilde;&iacute;&agrave;&divide;&agrave;&euml;&agrave; &oacute; &auml;&aring; &AElig;&icirc;&iacute;&ecirc;&uuml;&aring;&eth;&agrave;, &egrave; &icirc;&iacute; &ecirc;&agrave;&ecirc; &eth;&agrave;&ccedil; &iuml;&ucirc;&ograve;&agrave;&euml;&ntilde;&yuml;
&acirc;&ucirc;&eth;&agrave;&aelig;&agrave;&ograve;&uuml; &acirc;&ntilde;&frac14; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &divide;&aring;&eth;&aring;&ccedil; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &micro;. &Aring;&ntilde;&euml;&egrave; &aacute;&ucirc; &igrave;&ucirc; &ograve;&agrave;&ecirc; &auml;&aring;&eacute;&ntilde;&ograve;&acirc;&icirc;&acirc;&agrave;&euml;&egrave;, &ograve;&icirc; &igrave;&ucirc; &aacute;&ucirc;
&iuml;&icirc;&euml;&oacute;&divide;&egrave;&euml;&egrave;, &divide;&ograve;&icirc; κ = 6&micro;, &iuml;&icirc;&ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&oacute; |κ&micro;4 | = 6 (&iuml;&icirc;&ntilde;&euml;&aring;&auml;&iacute;&aring;&aring; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&icirc; &ntilde;&euml;&aring;&auml;&oacute;&aring;&ograve; &egrave;&ccedil;
&oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&yuml; 3.1, &iacute;&icirc; &aring;&atilde;&icirc; &igrave;&icirc;&aelig;&iacute;&icirc; &acirc;&ucirc;&acirc;&aring;&ntilde;&ograve;&egrave;, &iacute;&aring; &iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml;&ntilde;&uuml; &igrave;&aring;&ograve;&icirc;&auml;&icirc;&igrave; &Oslash;&agrave;&euml;&yuml;). &Ograve;&icirc;&atilde;&auml;&agrave;
|κ5 | = 65 |&micro;5 | = 65 , &agrave; &yacute;&ograve;&icirc; &acirc; &ograve;&icirc;&divide;&iacute;&icirc;&ntilde;&ograve;&egrave; &iacute;&aring;&iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;. &Icirc;&auml;&iacute;&agrave;&ecirc;&icirc; &igrave;&aring;&ograve;&icirc;&auml; &Oslash;&agrave;&euml;&yuml; (&acirc;&ucirc;&eth;&agrave;&aelig;&agrave;&ograve;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &micro; &egrave; ν ) &auml;&agrave;&frac14;&ograve; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&uuml;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve;. &Acirc;&ntilde;&ecirc;&icirc;&eth;&aring; &iuml;&icirc;&ntilde;&euml;&aring;
&ograve;&icirc;&atilde;&icirc;, &ecirc;&agrave;&ecirc; &Oslash;&agrave;&euml;&uuml; &icirc;&iuml;&oacute;&aacute;&euml;&egrave;&ecirc;&icirc;&acirc;&agrave;&euml; &ntilde;&acirc;&icirc;&eacute; &igrave;&aring;&ograve;&icirc;&auml;, &ntilde;&eth;&agrave;&ccedil;&oacute; &iacute;&aring;&ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&ecirc;&icirc;&acirc; (&acirc; &ograve;&icirc;&igrave;
&divide;&egrave;&ntilde;&euml;&aring; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute;, &Ocirc;&aring;&eth;&auml;&egrave;&iacute;&agrave;&iacute;&auml; &Euml;&egrave;&iacute;&auml;&aring;&igrave;&agrave;&iacute;&iacute;, &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &egrave; &aring;&atilde;&icirc; &oacute;&divide;&aring;&iacute;&egrave;&ecirc; 17-&euml;&aring;&ograve;&iacute;&egrave;&eacute; &atilde;&egrave;&igrave;&iacute;&agrave;&ccedil;&egrave;&ntilde;&ograve; &Agrave;&auml;&icirc;&euml;&uuml;&ocirc; &Atilde;&oacute;&eth;&acirc;&egrave;&ouml;) &ntilde;&ograve;&eth;&icirc;&atilde;&icirc; &auml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&euml;&egrave; &iuml;&eth;&egrave;&igrave;&aring;&iacute;&egrave;&igrave;&icirc;&ntilde;&ograve;&uuml; &igrave;&aring;&ograve;&icirc;&auml;&agrave; &Oslash;&agrave;&euml;&yuml; &acirc; &aacute;&icirc;&euml;&uuml;&oslash;&icirc;&igrave;
&divide;&egrave;&ntilde;&euml;&aring; &ntilde;&euml;&oacute;&divide;&agrave;&aring;&acirc; (&acirc; &ograve;&icirc;&igrave; &divide;&egrave;&ntilde;&euml;&aring;, &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;).
&Ecirc;&agrave;&ccedil;&agrave;&euml;&icirc;&ntilde;&uuml;, &divide;&ograve;&icirc; &igrave;&aring;&ograve;&icirc;&auml; &Oslash;&agrave;&euml;&yuml; &oacute;&iacute;&egrave;&acirc;&aring;&eth;&ntilde;&agrave;&euml;&aring;&iacute;. &Icirc;&auml;&iacute;&agrave;&ecirc;&icirc; &acirc; 1876 &atilde;&icirc;&auml;&oacute; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute; &iuml;&eth;&egrave;&acirc;&frac14;&euml;
&iuml;&eth;&egrave;&igrave;&aring;&eth; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &iacute;&agrave; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&aring; &iacute;&aring;&euml;&uuml;&ccedil;&yuml; &acirc;&ucirc;&eth;&agrave;&ccedil;&egrave;&ograve;&uuml; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc;
&divide;&aring;&eth;&aring;&ccedil; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &micro; &egrave; ν . &Yacute;&ograve;&icirc; &iuml;&icirc;&euml;&icirc;&aelig;&egrave;&euml;&icirc; &iacute;&agrave;&divide;&agrave;&euml;&icirc; &auml;&icirc;&euml;&atilde;&icirc;&eacute; &auml;&egrave;&ntilde;&ecirc;&oacute;&ntilde;&ntilde;&egrave;&egrave; &igrave;&aring;&aelig;&auml;&oacute; &Oslash;&oacute;&aacute;&aring;&eth;&ograve;&icirc;&igrave;
&egrave; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute;&icirc;&igrave;. &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &ntilde;&divide;&egrave;&ograve;&agrave;&euml;, &divide;&ograve;&icirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml; &acirc;&ntilde;&frac14; &eth;&agrave;&acirc;&iacute;&icirc; &iacute;&oacute;&aelig;&iacute;&icirc; &acirc;&ucirc;&eth;&agrave;&aelig;&agrave;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &micro; &egrave;
ν , &agrave; &ograve;&icirc;, &divide;&ograve;&icirc; &icirc;&ograve;&acirc;&aring;&ograve; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &iacute;&aring; &aacute;&oacute;&auml;&aring;&ograve; &egrave;&igrave;&aring;&ograve;&uuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml; (&ecirc;&agrave;&ecirc; &icirc;&ograve;&acirc;&aring;&ograve;
&Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;), &iacute;&aring; &ograve;&agrave;&ecirc; &acirc;&agrave;&aelig;&iacute;&icirc;. &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute; &aelig;&aring; &ntilde;&divide;&egrave;&ograve;&agrave;&euml;, &divide;&ograve;&icirc; &iacute;&oacute;&aelig;&iacute;&icirc; &acirc;&acirc;&icirc;&auml;&egrave;&ograve;&uuml; &auml;&icirc;&iuml;&icirc;&euml;&iacute;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&aring; &aacute;&agrave;&ccedil;&icirc;&acirc;&ucirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&yuml;, &otilde;&icirc;&ograve;&yuml; &yacute;&ograve;&icirc; &egrave; &auml;&aring;&euml;&agrave;&aring;&ograve; &igrave;&aring;&ograve;&icirc;&auml; &Oslash;&agrave;&euml;&yuml; &aacute;&icirc;&euml;&aring;&aring; &atilde;&eth;&icirc;&igrave;&icirc;&ccedil;&auml;&ecirc;&egrave;&igrave; (&ograve;&agrave;&ecirc; &ecirc;&agrave;&ecirc;
&igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&egrave;&auml;&oacute;&igrave;&agrave;&ograve;&uuml; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&oacute;&thorn; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &iuml;&eth;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &eth;&aring;&oslash;&aring;&iacute;&egrave;&aring; &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &ograve;&eth;&aring;&aacute;&oacute;&aring;&ograve; &euml;&thorn;&aacute;&icirc;&atilde;&icirc; &iacute;&agrave;&iuml;&aring;&eth;&frac14;&auml; &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave; &aacute;&agrave;&ccedil;&icirc;&acirc;&ucirc;&otilde; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&eacute;). &Acirc; &icirc;&aacute;&ugrave;&aring;&igrave;, &ntilde;&iuml;&icirc;&eth; &oslash;&frac14;&euml; &icirc; &ograve;&icirc;&igrave;,
&divide;&ograve;&icirc; &euml;&oacute;&divide;&oslash;&aring; &ecirc;&eth;&agrave;&ntilde;&egrave;&acirc;&agrave;&yuml; &ograve;&aring;&icirc;&eth;&egrave;&yuml; &egrave;&euml;&egrave; &iuml;&icirc;&euml;&aring;&ccedil;&iacute;&ucirc;&aring; &iuml;&eth;&egrave;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&yuml;. &Acirc; &ecirc;&icirc;&iacute;&ouml;&aring; &ecirc;&icirc;&iacute;&ouml;&icirc;&acirc; &Oslash;&oacute;&aacute;&aring;&eth;&ograve; &ntilde;&icirc;&atilde;&euml;&agrave;&ntilde;&egrave;&euml;&ntilde;&yuml; &ntilde; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute;&icirc;&igrave;, &agrave; &egrave;&auml;&aring;&egrave; &Atilde;&agrave;&euml;&uuml;&ocirc;&aring;&iacute;&agrave; &iuml;&eth;&egrave;&ntilde;&oacute;&ograve;&ntilde;&ograve;&acirc;&oacute;&thorn;&ograve; &ograve;&aring;&iuml;&aring;&eth;&uuml; &acirc;&icirc; &igrave;&iacute;&icirc;&atilde;&egrave;&otilde;
&ecirc;&eth;&agrave;&ntilde;&egrave;&acirc;&ucirc;&otilde; &egrave; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &oacute;&iacute;&egrave;&acirc;&aring;&eth;&ntilde;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde; &eth;&aring;&ccedil;&oacute;&euml;&uuml;&ograve;&agrave;&ograve;&agrave;&otilde;, &ntilde;&acirc;&yuml;&ccedil;&agrave;&iacute;&iacute;&ucirc;&otilde; &ntilde; &egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&eacute;
&atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&aring;&eacute;.
4. &Egrave;&ntilde;&divide;&egrave;&ntilde;&euml;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&agrave;&yuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;
&Acirc; &yacute;&ograve;&icirc;&igrave; &eth;&agrave;&ccedil;&auml;&aring;&euml;&aring; &igrave;&ucirc; &eth;&aring;&oslash;&egrave;&igrave; &acirc;&ntilde;&aring; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &iuml;&eth;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &icirc;&ograve;&acirc;&aring;&ograve;&ucirc; &acirc; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &igrave;&ucirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&euml;&egrave; &iuml;&eth;&egrave; &eth;&aring;&oslash;&aring;&iacute;&egrave;&egrave; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;. &Auml;&euml;&yuml; &ecirc;&agrave;&aelig;&auml;&icirc;&atilde;&icirc; k = 0, 1,. . . , 5, &igrave;&ucirc;
&iacute;&agrave;&eacute;&auml;&frac14;&igrave; &divide;&egrave;&ntilde;&euml;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; k &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc; &iacute;&agrave;
8
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; (5 − k) &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Ecirc;&agrave;&ecirc; &acirc;&ntilde;&aring;&atilde;&auml;&agrave;, &iacute;&agrave;&ntilde; &aacute;&oacute;&auml;&aring;&ograve; &egrave;&iacute;&ograve;&aring;&eth;&aring;&ntilde;&icirc;&acirc;&agrave;&ograve;&uuml; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve;. &Iacute;&agrave;&divide;&iacute;&frac14;&igrave; &ntilde; &ntilde;&agrave;&igrave;&icirc;&eacute; &iuml;&eth;&icirc;&ntilde;&ograve;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 4.1. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &divide;&aring;&eth;&aring;&ccedil; &iuml;&yuml;&ograve;&uuml; &ograve;&icirc;&divide;&aring;&ecirc;?
&Iuml;&icirc;&iacute;&yuml;&ograve;&iacute;&icirc;, &divide;&ograve;&icirc; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &iuml;&agrave;&eth;&ucirc; (&acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&icirc;&acirc;&iuml;&agrave;&auml;&agrave;&thorn;&ugrave;&egrave;&otilde;)
&iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iacute;&aring; &igrave;&icirc;&atilde;&oacute;&ograve; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &iuml;&yuml;&ograve;&uuml; &ograve;&icirc;&divide;&aring;&ecirc;, &egrave;&ccedil; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &iacute;&egrave;&ecirc;&agrave;&ecirc;&egrave;&aring; &ograve;&eth;&egrave; &iacute;&aring; &euml;&aring;&aelig;&agrave;&ograve; &iacute;&agrave; &icirc;&auml;&iacute;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &ntilde;&euml;&icirc;&acirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&eacute; &acirc; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&egrave; &yacute;&ograve;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;
&igrave;&icirc;&aelig;&iacute;&icirc; &icirc;&iuml;&oacute;&ntilde;&ograve;&egrave;&ograve;&uuml;. &Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&agrave;&yuml; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; (∗), &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve;
&divide;&aring;&eth;&aring;&ccedil; &auml;&agrave;&iacute;&iacute;&oacute;&thorn; &ograve;&icirc;&divide;&ecirc;&oacute; &ntilde; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&agrave;&igrave;&egrave; (x0 , y0 ), &ograve;&icirc; &ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&ucirc; (a, b, c, d, e, f )
&oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ograve; &icirc;&auml;&iacute;&icirc;&eth;&icirc;&auml;&iacute;&icirc;&igrave;&oacute; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&igrave;&oacute; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&thorn;
ax20 + bx0 y0 + cy02 + dx0 + ey0 + f = 0.
&Ecirc;&icirc;&yacute;&ocirc;&ocirc;&egrave;&ouml;&egrave;&aring;&iacute;&ograve;&ucirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&aring;&eacute; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;, &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ograve;
&auml;&acirc;&oacute;&igrave; &icirc;&auml;&iacute;&icirc;&eth;&icirc;&auml;&iacute;&ucirc;&igrave; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&ucirc;&igrave; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&yuml;&igrave; &ntilde;&iuml;&aring;&ouml;&egrave;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &acirc;&egrave;&auml;&agrave;. &Yacute;&ograve;&icirc; &iacute;&agrave;&aacute;&euml;&thorn;&auml;&aring;&iacute;&egrave;&aring;
&euml;&aring;&aelig;&egrave;&ograve; &acirc; &icirc;&ntilde;&iacute;&icirc;&acirc;&aring; &ograve;&agrave;&ecirc;&icirc;&atilde;&icirc; &iuml;&eth;&egrave;&frac14;&igrave;&agrave;. &Ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&aring; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &auml;&agrave;&iacute;&iacute;&ucirc;&aring;
&ograve;&icirc;&divide;&ecirc;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc; &ccedil;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&uuml; &iacute;&agrave; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;. &Auml;&aring;&euml;&icirc; &acirc; &ograve;&icirc;&igrave;, &divide;&ograve;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &yacute;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &oacute;&auml;&icirc;&acirc;&euml;&aring;&ograve;&acirc;&icirc;&eth;&yuml;&thorn;&ugrave;&egrave;&aring; &auml;&acirc;&oacute;&igrave; &icirc;&auml;&iacute;&icirc;&eth;&icirc;&auml;&iacute;&ucirc;&igrave; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&ucirc;&igrave; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&yuml;&igrave;:
a = c,
b = 0.
&Iacute;&agrave; &ntilde;&agrave;&igrave;&icirc;&igrave; &auml;&aring;&euml;&aring;, &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc; &icirc;&otilde;&agrave;&eth;&agrave;&ecirc;&ograve;&aring;&eth;&egrave;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml; &ecirc;&agrave;&ecirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&aring;
&divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &ocirc;&egrave;&ecirc;&ntilde;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;, &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &ograve;&icirc;&divide;&ecirc;&egrave; &yacute;&ograve;&egrave; &aacute;&oacute;&auml;&oacute;&ograve; &igrave;&iacute;&egrave;&igrave;&ucirc;&igrave;&egrave; &egrave; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &oacute;&auml;&agrave;&euml;&frac14;&iacute;&iacute;&ucirc;&igrave;&egrave;.
&Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &iuml;&eth;&egrave; k ≥ 2 &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &divide;&egrave;&ntilde;&euml;&agrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; k &ograve;&icirc;&divide;&aring;&ecirc; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; (5 − k) &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &igrave;&icirc;&aelig;&iacute;&icirc; &egrave;&ntilde;&ecirc;&agrave;&ograve;&uuml; &divide;&egrave;&ntilde;&euml;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil;
(k − 2) &ograve;&icirc;&divide;&ecirc;&egrave; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; (5 − k) &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Yacute;&ograve;&icirc; &iuml;&eth;&icirc;&ugrave;&aring;, &ograve;&agrave;&ecirc; &ecirc;&agrave;&ecirc; &igrave;&icirc;&aelig;&iacute;&icirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&oacute;&thorn; &egrave;&iacute;&ograve;&oacute;&egrave;&ouml;&egrave;&thorn;. &Aacute;&icirc;&euml;&aring;&aring; &ograve;&icirc;&atilde;&icirc;, &iuml;&eth;&egrave; k = 2, 4, 5, &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&icirc;&auml;&icirc;&aacute;&eth;&agrave;&ograve;&uuml;
&ecirc;&icirc;&iacute;&ocirc;&egrave;&atilde;&oacute;&eth;&agrave;&ouml;&egrave;&thorn; &egrave;&ccedil; (k − 2) &ograve;&icirc;&divide;&aring;&ecirc; &egrave; k &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &ograve;&agrave;&ecirc;, &divide;&ograve;&icirc; &acirc;&ntilde;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &icirc;&ecirc;&agrave;&aelig;&oacute;&ograve;&ntilde;&yuml;
&acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&igrave;&egrave;. &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &igrave;&icirc;&aelig;&iacute;&icirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml; &egrave; &iacute;&agrave;&oslash;&egrave; &ccedil;&iacute;&agrave;&iacute;&egrave;&yuml; &egrave;&ccedil; &iuml;&euml;&agrave;&iacute;&egrave;&igrave;&aring;&ograve;&eth;&egrave;&egrave;.
&Acirc; &divide;&agrave;&ntilde;&ograve;&iacute;&icirc;&ntilde;&ograve;&egrave;, &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &iuml;&yuml;&ograve;&uuml; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc;, &eth;&agrave;&acirc;&iacute;&icirc; &divide;&egrave;&ntilde;&euml;&oacute; (&acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde;) &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &ograve;&eth;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;. &Ecirc;&agrave;&ecirc; &igrave;&ucirc;
&ccedil;&iacute;&agrave;&aring;&igrave;, &divide;&aring;&eth;&aring;&ccedil; &ograve;&eth;&egrave; &ograve;&icirc;&divide;&ecirc;&egrave;, &iacute;&aring; &euml;&aring;&aelig;&agrave;&ugrave;&egrave;&aring; &iacute;&agrave; &icirc;&auml;&iacute;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &eth;&icirc;&acirc;&iacute;&icirc; &icirc;&auml;&iacute;&agrave;
&icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;.
&times;&ograve;&icirc;&aacute;&ucirc; &iuml;&eth;&egrave;&auml;&agrave;&ograve;&uuml; &ograve;&icirc;&divide;&iacute;&ucirc;&eacute; &ntilde;&igrave;&ucirc;&ntilde;&euml; &ograve;&aring;&eth;&igrave;&egrave;&iacute;&oacute; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &oacute;&auml;&agrave;&euml;&frac14;&iacute;&iacute;&agrave;&yuml; &ograve;&icirc;&divide;&ecirc;&agrave; &iacute;&oacute;&aelig;&iacute;&icirc; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&icirc;&eacute; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; (∗), &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&aring;&ograve;&uuml; &ecirc;&icirc;&iacute;&oacute;&ntilde; &acirc; &ograve;&eth;&frac14;&otilde;&igrave;&aring;&eth;&iacute;&icirc;&igrave; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&ucirc;&eacute;
&icirc;&auml;&iacute;&icirc;&eth;&icirc;&auml;&iacute;&ucirc;&igrave; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave;
ax2 + bxy + cy 2 + dxz + eyz + f z 2 = 0.
(∗∗)
&Ograve;&icirc;&atilde;&auml;&agrave; &egrave;&ntilde;&otilde;&icirc;&auml;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &aacute;&oacute;&auml;&aring;&ograve; &ntilde;&aring;&divide;&aring;&iacute;&egrave;&aring;&igrave; &ecirc;&icirc;&iacute;&oacute;&ntilde;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml;&thorn; z = 1. &Aring;&ntilde;&ograve;&uuml; &acirc;&ccedil;&agrave;&egrave;&igrave;&iacute;&icirc;-&icirc;&auml;&iacute;&icirc;&ccedil;&iacute;&agrave;&divide;&iacute;&icirc;&aring;
&ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&egrave;&aring; &igrave;&aring;&aelig;&auml;&oacute; &ograve;&icirc;&divide;&ecirc;&agrave;&igrave;&egrave; &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; z = 1 &egrave; &iuml;&eth;&yuml;&igrave;&ucirc;&igrave;&egrave; &acirc; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&igrave;&egrave; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; (0, 0, 0) &egrave; &iacute;&aring; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc;&igrave;&egrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; z = 1: &ograve;&icirc;&divide;&ecirc;&aring; (x0 , y0 ) &iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&igrave; &acirc; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&egrave;&aring;
&iuml;&eth;&yuml;&igrave;&oacute;&thorn;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&oacute;&thorn; &divide;&aring;&eth;&aring;&ccedil; &iacute;&agrave;&divide;&agrave;&euml;&icirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve; &egrave; &ograve;&icirc;&divide;&ecirc;&oacute; (x0 , y0 , 1). &Iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &ograve;&icirc;&divide;&ecirc;&agrave;&igrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; (∗)
&aacute;&oacute;&auml;&oacute;&ograve; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&icirc;&acirc;&agrave;&ograve;&uuml; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; &iacute;&agrave; &ecirc;&icirc;&iacute;&oacute;&ntilde;&aring; (∗∗). &Iacute;&icirc; &iacute;&agrave; &ecirc;&icirc;&iacute;&oacute;&ntilde;&aring; &igrave;&icirc;&atilde;&oacute;&ograve; &aacute;&ucirc;&ograve;&uuml; &aring;&ugrave;&frac14; &auml;&acirc;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&igrave; &iacute;&egrave;&ecirc;&agrave;&ecirc;&egrave;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &iacute;&aring; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&oacute;&thorn;&ograve; &yacute;&ograve;&icirc; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;, &iuml;&icirc; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&igrave; &ecirc;&icirc;&iacute;&oacute;&ntilde; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&aring;&ograve;&ntilde;&yuml; &ntilde;
&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave; &Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
9
&iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml;&thorn; z = 0. &Iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&aring; &igrave;&icirc;&aelig;&iacute;&icirc; &ccedil;&agrave;&auml;&agrave;&ograve;&uuml; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&yuml;&igrave;&egrave; ax2 + bxy + cy 2 = 0 &egrave; z = 0. &Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &iacute;&agrave;&auml; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&igrave;&egrave; &divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring; ax2 + bxy + cy 2 = 0 &acirc;&ntilde;&aring;&atilde;&auml;&agrave; &eth;&agrave;&ntilde;&ecirc;&euml;&agrave;&auml;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &iacute;&agrave;
&auml;&acirc;&agrave; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&ucirc;&otilde; &igrave;&iacute;&icirc;&aelig;&egrave;&ograve;&aring;&euml;&yuml;, &iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &acirc; &ntilde;&euml;&oacute;&divide;&agrave;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;, &egrave;&igrave;&aring;&aring;&igrave; a(x2 +y 2 ) = a(x+iy)(x−iy).
&Ntilde; &ograve;&icirc;&divide;&ecirc;&egrave; &ccedil;&eth;&aring;&iacute;&egrave;&yuml; &iuml;&eth;&icirc;&aring;&ecirc;&ograve;&egrave;&acirc;&iacute;&icirc;&eacute; &atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&egrave;, &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &yacute;&ograve;&icirc; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; &acirc;&ntilde;&aring;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &iacute;&agrave; &ecirc;&icirc;&iacute;&oacute;&ntilde;&aring; (∗∗),
&iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&aring; &divide;&aring;&eth;&aring;&ccedil; &iacute;&agrave;&divide;&agrave;&euml;&icirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve; &egrave; &ograve;&icirc;&divide;&ecirc;&oacute; (1, i, 0) &egrave;&euml;&egrave; (1, −i, 0) &auml;&agrave;&thorn;&ograve; &iacute;&agrave;&igrave;
&auml;&acirc;&aring; &iuml;&icirc;&euml;&iacute;&icirc;&iuml;&eth;&agrave;&acirc;&iacute;&ucirc;&otilde; &ograve;&icirc;&divide;&ecirc;&egrave; &iacute;&agrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&aring;.
&Ccedil;&agrave;&igrave;&aring;&iacute;&yuml;&yuml; &iacute;&agrave; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&aring; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;, &igrave;&icirc;&aelig;&iacute;&icirc; &eth;&aring;&oslash;&egrave;&ograve;&uuml;
&egrave; &ograve;&agrave;&ecirc;&oacute;&thorn; &ccedil;&agrave;&auml;&agrave;&divide;&oacute;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 4.2. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve; &divide;&aring;&eth;&aring;&ccedil; &divide;&aring;&ograve;&ucirc;&eth;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;?
&ETH;&aring;&oslash;&aring;&iacute;&egrave;&aring; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; 4.2 &iuml;&eth;&aring;&auml;&icirc;&ntilde;&ograve;&agrave;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &divide;&egrave;&ograve;&agrave;&ograve;&aring;&euml;&thorn;.
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &auml;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &igrave;&icirc;&aelig;&aring;&ograve; &aacute;&ucirc;&ograve;&uuml; &ecirc;&agrave;&ecirc; &auml;&acirc;&aring; &egrave;&euml;&egrave; &icirc;&auml;&iacute;&agrave; (&aring;&ntilde;&euml;&egrave; &ograve;&icirc;&divide;&ecirc;&egrave; &euml;&aring;&aelig;&agrave;&ograve; &iuml;&icirc; &icirc;&auml;&iacute;&oacute; &ntilde;&ograve;&icirc;&eth;&icirc;&iacute;&oacute; &icirc;&ograve;
&iuml;&eth;&yuml;&igrave;&icirc;&eacute;), &ograve;&agrave;&ecirc; &egrave; &iacute;&egrave; &icirc;&auml;&iacute;&icirc;&eacute; (&aring;&ntilde;&euml;&egrave; &ograve;&icirc;&divide;&ecirc;&egrave; &icirc;&ecirc;&agrave;&ccedil;&agrave;&euml;&egrave;&ntilde;&uuml; &acirc; &eth;&agrave;&ccedil;&iacute;&ucirc;&otilde; &iuml;&icirc;&euml;&oacute;&iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&yuml;&otilde;). &Iacute;&icirc; &ntilde; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&igrave;&egrave;
&divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave; &ograve;&agrave;&ecirc;&icirc;&eacute; &ntilde;&euml;&icirc;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &iacute;&aring; &acirc;&icirc;&ccedil;&iacute;&egrave;&ecirc;&agrave;&aring;&ograve;. &Aring;&ntilde;&euml;&egrave; &igrave;&ucirc; &auml;&icirc;&iuml;&oacute;&ntilde;&ecirc;&agrave;&aring;&igrave; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&aring; &ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve; x &egrave; y , &ograve;&icirc; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; &iuml;&aring;&eth;&aring;&ntilde;&ograve;&agrave;&frac14;&ograve; &auml;&aring;&euml;&egrave;&ograve;&uuml; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; &iacute;&agrave; &auml;&acirc;&aring; &iuml;&icirc;&euml;&oacute;&iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave;! &Acirc;&icirc;&ccedil;&uuml;&igrave;&frac14;&igrave;, &ecirc; &iuml;&eth;&egrave;&igrave;&aring;&eth;&oacute;,
&iuml;&eth;&yuml;&igrave;&oacute;&thorn; y = 0 &egrave; &ograve;&icirc;&divide;&ecirc;&egrave; (0, 1) &egrave; (0, −1). &Ograve;&icirc;&atilde;&auml;&agrave; &egrave;&ccedil; &icirc;&auml;&iacute;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&icirc;&eacute;&ograve;&egrave; &acirc; &auml;&eth;&oacute;&atilde;&oacute;&thorn; &iuml;&icirc; &iuml;&oacute;&ograve;&egrave;,
&iacute;&aring; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&aring;&igrave;&oacute; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; y = 0 (&iuml;&icirc;&eacute;&auml;&frac14;&igrave;, &iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &iuml;&icirc; &iuml;&oacute;&ograve;&egrave; (0, cos(πt) + i sin(πt)), &atilde;&auml;&aring; t &iuml;&eth;&icirc;&aacute;&aring;&atilde;&agrave;&aring;&ograve; &acirc;&ntilde;&aring; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&aring; &divide;&egrave;&ntilde;&euml;&agrave; &icirc;&ograve; 0 &auml;&icirc; 1). &Yacute;&ograve;&icirc; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&icirc; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &egrave; &aring;&atilde;&icirc; &icirc;&aacute;&icirc;&aacute;&ugrave;&aring;&iacute;&egrave;&yuml;
&euml;&aring;&aelig;&agrave;&ograve; &acirc; &icirc;&ntilde;&iacute;&icirc;&acirc;&aring; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&agrave; &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&aring;&iacute;&egrave;&yuml; &divide;&egrave;&ntilde;&euml;&agrave;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 4.3. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ograve;&ntilde;&yuml; &ograve;&eth;&frac14;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde; &egrave; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ograve; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;?
&Iacute;&oacute;&aelig;&iacute;&icirc; &iacute;&agrave;&eacute;&ograve;&egrave; &divide;&egrave;&ntilde;&euml;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &ograve;&eth;&frac14;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&agrave;&euml;&uuml;&iacute;&ucirc;&eacute; &ecirc;&icirc;&iacute;&aring;&divide;&iacute;&ucirc;&eacute; &icirc;&ograve;&acirc;&aring;&ograve; &iuml;&icirc;&euml;&oacute;&divide;&egrave;&ograve;&ntilde;&yuml;, &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &aring;&ntilde;&euml;&egrave; &iacute;&egrave;&ecirc;&agrave;&ecirc;&egrave;&aring; &auml;&acirc;&aring;
&iuml;&eth;&yuml;&igrave;&ucirc;&aring; &auml;&eth;&oacute;&atilde; &auml;&eth;&oacute;&atilde;&oacute; &iacute;&aring; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc;. &Acirc; &yacute;&ograve;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring;, &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&egrave;&igrave; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&egrave;&ecirc;
&ntilde; &acirc;&aring;&eth;&oslash;&egrave;&iacute;&agrave;&igrave;&egrave; &acirc; &ograve;&icirc;&divide;&ecirc;&agrave;&otilde; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Ograve;&icirc;&atilde;&auml;&agrave; &euml;&aring;&atilde;&ecirc;&icirc; &acirc;&egrave;&auml;&aring;&ograve;&uuml;, &divide;&ograve;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &acirc;&ntilde;&aring;&otilde; &ntilde;&ograve;&icirc;&eth;&icirc;&iacute; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&egrave;&ecirc;&agrave; &egrave;&euml;&egrave; &egrave;&otilde; &iuml;&eth;&icirc;&auml;&icirc;&euml;&aelig;&aring;&iacute;&egrave;&eacute; &aacute;&oacute;&auml;&aring;&ograve; &divide;&aring;&ograve;&ucirc;&eth;&aring;:
&icirc;&auml;&iacute;&agrave; &acirc;&iuml;&egrave;&ntilde;&agrave;&iacute;&iacute;&agrave;&yuml; &egrave; &ograve;&eth;&egrave; &acirc;&iacute;&aring;&acirc;&iuml;&egrave;&ntilde;&agrave;&iacute;&iacute;&ucirc;&otilde;.
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &icirc;&ograve;&acirc;&aring;&ograve; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; 4.3 &egrave;&ccedil;&igrave;&aring;&iacute;&egrave;&ograve;&ntilde;&yuml;, &aring;&ntilde;&euml;&egrave; &icirc;&iuml;&oacute;&ntilde;&ograve;&egrave;&ograve;&uuml; &ograve;&eth;&aring;&aacute;&icirc;&acirc;&agrave;&iacute;&egrave;&aring; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave;. &Auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave;, &ccedil;&agrave;&auml;&agrave;&iacute;&iacute;&agrave;&yuml; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring;&igrave; (px+
qy + r)2 = 0 (&ograve;&agrave;&ecirc;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &auml;&acirc;&icirc;&eacute;&iacute;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;), &aacute;&oacute;&auml;&aring;&ograve; &ecirc;&agrave;&ntilde;&agrave;&ograve;&uuml;&ntilde;&yuml; &ntilde;&eth;&agrave;&ccedil;&oacute;
&acirc;&ntilde;&aring;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; px + qy + r = 0. &Atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave; &yacute;&ograve;&icirc; &igrave;&icirc;&aelig;&aring;&ograve;
&iuml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&ograve;&uuml;&ntilde;&yuml; &iacute;&aring;&igrave;&icirc;&ograve;&egrave;&acirc;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&iacute;&ucirc;&igrave;, &iacute;&icirc; &euml;&aring;&atilde;&ecirc;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&eth;&yuml;&aring;&ograve;&ntilde;&yuml; &ntilde; &iuml;&icirc;&igrave;&icirc;&ugrave;&uuml;&thorn; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&atilde;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&yuml; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &ntilde; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;: &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &aring;&ntilde;&euml;&egrave; &acirc;
&icirc;&atilde;&eth;&agrave;&iacute;&egrave;&divide;&aring;&iacute;&egrave;&egrave; &iacute;&agrave; &yacute;&ograve;&oacute; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &egrave;&igrave;&aring;&aring;&ograve; &ecirc;&eth;&agrave;&ograve;&iacute;&ucirc;&eacute; &ecirc;&icirc;&eth;&aring;&iacute;&uuml;. &Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; (∗) &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; y = 0, &aring;&ntilde;&euml;&egrave; &oacute;&eth;&agrave;&acirc;&iacute;&aring;&iacute;&egrave;&aring; ax2 + dx + f &egrave;&igrave;&aring;&aring;&ograve; &ecirc;&eth;&agrave;&ograve;&iacute;&ucirc;&eacute; &ecirc;&icirc;&eth;&aring;&iacute;&uuml;. &Acirc;&ucirc;&aacute;&aring;&eth;&aring;&igrave; &divide;&egrave;&ntilde;&euml;&agrave; p, q &egrave; r &ograve;&agrave;&ecirc; &divide;&ograve;&icirc;&aacute;&ucirc; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; px + qy + r = 0 &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&euml;&agrave;
&divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &egrave;&ccedil; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; 4.3. &Ograve;&icirc;&atilde;&auml;&agrave; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; (px + qy + r)2 = 0,
10
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&aacute;&oacute;&auml;&aring;&ograve; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &yacute;&ograve;&egrave; &auml;&acirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &egrave; &ecirc;&agrave;&ntilde;&agrave;&ograve;&uuml;&ntilde;&yuml; &euml;&thorn;&aacute;&ucirc;&otilde; &ograve;&eth;&frac14;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iacute;&aring; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; px + qy + r = 0, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &auml;&agrave;&ntilde;&ograve; &euml;&egrave;&oslash;&iacute;&aring;&aring; &eth;&aring;&oslash;&aring;&iacute;&egrave;&aring; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring;
4.3.
&Ograve;&aring;&iuml;&aring;&eth;&uuml; &eth;&aring;&oslash;&egrave;&igrave; &ntilde;&agrave;&igrave;&oacute;&thorn;, &iacute;&agrave; &iuml;&aring;&eth;&acirc;&ucirc;&eacute; &acirc;&ccedil;&atilde;&euml;&yuml;&auml;, &ntilde;&euml;&icirc;&aelig;&iacute;&oacute;&thorn; &ccedil;&agrave;&auml;&agrave;&divide;&oacute;.
&Ccedil;&agrave;&auml;&agrave;&divide;&agrave; 4.4. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &ecirc;&agrave;&ntilde;&agrave;&aring;&ograve;&ntilde;&yuml; &iuml;&yuml;&ograve;&egrave; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;?
&Ccedil;&auml;&aring;&ntilde;&uuml; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave; &ograve;&icirc;&aelig;&aring; &ntilde;&oacute;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;. &Aring;&ntilde;&euml;&egrave; &aring;&atilde;&icirc; &icirc;&ograve;&aacute;&eth;&icirc;&ntilde;&egrave;&ograve;&uuml;, &ograve;&icirc;
&eth;&aring;&oslash;&aring;&iacute;&egrave;&eacute; &aacute;&oacute;&auml;&aring;&ograve; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &igrave;&iacute;&icirc;&atilde;&icirc; &acirc;&ntilde;&aring; &auml;&acirc;&icirc;&eacute;&iacute;&ucirc;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&aring;, &iacute;&aring; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc;&aring; &iuml;&yuml;&ograve;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&igrave; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&igrave;, &aacute;&oacute;&auml;&oacute;&ograve; &eth;&aring;&oslash;&aring;&iacute;&egrave;&yuml;&igrave;&egrave;. &Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave; &aacute;&icirc;&euml;&uuml;&oslash;&aring;
&iacute;&aring; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ograve; &divide;&aring;&eth;&aring;&ccedil; &auml;&acirc;&aring; &ocirc;&egrave;&ecirc;&ntilde;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&iacute;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave;, &iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &egrave;&otilde; &iacute;&aring;&euml;&uuml;&ccedil;&yuml; &ccedil;&agrave;&igrave;&aring;&iacute;&egrave;&ograve;&uuml; &iacute;&agrave;
&icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;. &ETH;&aring;&oslash;&egrave;&ograve;&uuml; &yacute;&ograve;&oacute; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &iacute;&agrave;&igrave; &iuml;&icirc;&igrave;&icirc;&aelig;&aring;&ograve; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&agrave;&yuml; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml;. &Igrave;&ucirc;
&ntilde;&iacute;&agrave;&divide;&agrave;&euml;&agrave; &iacute;&agrave;&iuml;&icirc;&igrave;&iacute;&egrave;&igrave;, &ecirc;&agrave;&ecirc; &icirc;&iacute;&agrave; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &acirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring;.
&Aring;&ntilde;&euml;&egrave; &ccedil;&agrave;&ocirc;&egrave;&ecirc;&ntilde;&egrave;&eth;&icirc;&acirc;&agrave;&ograve;&uuml; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml; C &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave;, &ograve;&icirc; &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&aring; &igrave;&icirc;&aelig;&iacute;&icirc;
&ntilde;&icirc;&iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&ograve;&uuml; &iuml;&eth;&yuml;&igrave;&oacute;&thorn;, &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&igrave;&oacute;&thorn; &iuml;&icirc;&euml;&yuml;&eth;&icirc;&eacute; &yacute;&ograve;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave;. &Egrave; &iacute;&agrave;&icirc;&aacute;&icirc;&eth;&icirc;&ograve;, &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&ograve;&uuml; &acirc; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&egrave;&aring; &ograve;&icirc;&divide;&ecirc;&oacute; &iuml;&icirc;&euml;&thorn;&ntilde;. &Auml;&aring;&euml;&agrave;&aring;&ograve;&ntilde;&yuml; &yacute;&ograve;&icirc; &ograve;&agrave;&ecirc;. &Iuml;&oacute;&ntilde;&ograve;&uuml;
p &ograve;&icirc;&divide;&ecirc;&agrave; &acirc;&iacute;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C . &Iuml;&eth;&icirc;&acirc;&aring;&auml;&frac14;&igrave; &egrave;&ccedil; &ograve;&icirc;&divide;&ecirc;&egrave; p &ecirc;&agrave;&ntilde;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&aring; &ecirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;
C . &Iuml;&eth;&yuml;&igrave;&agrave;&yuml; lp , &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&agrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&egrave; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml;, &egrave; &aacute;&oacute;&auml;&aring;&ograve; &iuml;&icirc;&euml;&yuml;&eth;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave; p, &agrave; &ograve;&icirc;&divide;&ecirc;&agrave; p &aacute;&oacute;&auml;&aring;&ograve; &iuml;&icirc;&euml;&thorn;&ntilde;&icirc;&igrave; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; lp . &Ograve;&aring;&igrave; &ntilde;&agrave;&igrave;&ucirc;&igrave;, &igrave;&ucirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&euml;&egrave; &iuml;&icirc;&euml;&yuml;&eth;&ucirc; &auml;&euml;&yuml; &ograve;&icirc;&divide;&aring;&ecirc;
&acirc;&iacute;&aring; C , &egrave; &iuml;&icirc;&euml;&thorn;&ntilde;&agrave; &auml;&euml;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde; C . (&Egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml; &iuml;&icirc;&iacute;&yuml;&ograve;&egrave;&aring; &egrave;&iacute;&acirc;&aring;&eth;&ntilde;&egrave;&egrave;
&icirc;&ograve;&iacute;&icirc;&ntilde;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C , &igrave;&icirc;&aelig;&iacute;&icirc; &egrave;&iacute;&agrave;&divide;&aring; &ntilde;&ecirc;&agrave;&ccedil;&agrave;&ograve;&uuml;, &divide;&ograve;&icirc; lp &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&ograve;&ntilde;&yuml; &egrave;&iacute;&acirc;&aring;&eth;&ntilde;&egrave;&aring;&eacute; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;, &iuml;&icirc;&ntilde;&ograve;&eth;&icirc;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&agrave;&ecirc; &iacute;&agrave; &auml;&egrave;&agrave;&igrave;&aring;&ograve;&eth;&aring; &iacute;&agrave; &icirc;&ograve;&eth;&aring;&ccedil;&ecirc;&aring; p0 p, &atilde;&auml;&aring; p0 &ouml;&aring;&iacute;&ograve;&eth;
&icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C .)
&Oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; 4.5. &Iuml;&eth;&icirc;&acirc;&aring;&eth;&uuml;&ograve;&aring;, &divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &ograve;&icirc;&divide;&ecirc;&egrave; q &egrave; r &euml;&aring;&aelig;&agrave;&ograve; &iacute;&agrave; &iuml;&icirc;&euml;&yuml;&eth;&aring; lp ,
&ograve;&icirc; &iuml;&icirc;&euml;&yuml;&eth;&ucirc; lq &egrave; lr &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ograve;&ntilde;&yuml; &acirc; &ograve;&icirc;&divide;&ecirc;&aring; p. (&Iacute;&agrave;&iuml;&eth;&egrave;&igrave;&aring;&eth;, &igrave;&icirc;&aelig;&iacute;&icirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&ograve;&uuml;
&ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave; &egrave;&iacute;&acirc;&aring;&eth;&ntilde;&egrave;&egrave;.)
&Yacute;&ograve;&icirc; &oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; &iuml;&icirc;&ccedil;&acirc;&icirc;&euml;&yuml;&aring;&ograve; &auml;&icirc;&icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&uuml; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&oacute;&thorn; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml; &auml;&euml;&yuml; &ograve;&icirc;&divide;&aring;&ecirc; &acirc;&iacute;&oacute;&ograve;&eth;&egrave; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C (&egrave;&ccedil; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &ecirc;&agrave;&ntilde;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&aring; &iacute;&aring; &iuml;&eth;&icirc;&acirc;&aring;&auml;&frac14;&oslash;&uuml;) &egrave; &auml;&euml;&yuml; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &iacute;&aring; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&egrave;&otilde; C . &Auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &iuml;&oacute;&ntilde;&ograve;&uuml; &ograve;&aring;&iuml;&aring;&eth;&uuml; &ograve;&icirc;&divide;&ecirc;&agrave; p &euml;&aring;&aelig;&egrave;&ograve; &acirc;&iacute;&oacute;&ograve;&eth;&egrave;.
&Iuml;&eth;&icirc;&acirc;&aring;&auml;&frac14;&igrave; &auml;&acirc;&aring; &iuml;&eth;&yuml;&igrave;&ucirc;&aring; &divide;&aring;&eth;&aring;&ccedil; p &egrave; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&egrave;&igrave; &divide;&aring;&eth;&aring;&ccedil; q &egrave; r &egrave;&otilde; &iuml;&icirc;&euml;&thorn;&ntilde;&agrave;. &Ograve;&icirc;&atilde;&auml;&agrave; &iuml;&icirc;&euml;&yuml;&eth;&agrave; &ograve;&icirc;&divide;&ecirc;&egrave; p &yacute;&ograve;&icirc;, &iuml;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&thorn;, &iuml;&eth;&yuml;&igrave;&agrave;&yuml;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&agrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; q &egrave; r, &iuml;&eth;&egrave;&divide;&frac14;&igrave;
&icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&aring; &iacute;&aring; &ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&ograve; &icirc;&ograve; &acirc;&ucirc;&aacute;&icirc;&eth;&agrave; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;.
&Oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; 4.6. &Icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&aring; &iuml;&icirc;&euml;&thorn;&ntilde; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &iacute;&aring; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&thorn;&ugrave;&aring;&eacute; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;
C.
&Ouml;&aring;&iacute;&ograve;&eth; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C &yacute;&ograve;&icirc; &aring;&auml;&egrave;&iacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &ograve;&icirc;&divide;&ecirc;&agrave;, &icirc;&ntilde;&ograve;&agrave;&acirc;&oslash;&agrave;&yuml;&ntilde;&yuml; &aacute;&aring;&ccedil; &iuml;&icirc;&euml;&yuml;&eth;&ucirc;, &iacute;&icirc; &igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&ecirc;&agrave;&ccedil;&agrave;&ograve;&uuml;,
&divide;&ograve;&icirc; &iuml;&icirc;&euml;&yuml;&eth;&icirc;&eacute; &ouml;&aring;&iacute;&ograve;&eth;&agrave; &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &oacute;&auml;&agrave;&euml;&frac14;&iacute;&iacute;&agrave;&yuml; &iuml;&eth;&yuml;&igrave;&agrave;&yuml;. &Ecirc;&agrave;&ecirc; &egrave; &eth;&agrave;&iacute;&uuml;&oslash;&aring;, &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&aring; p &iacute;&agrave;
&iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; z = 1 &ntilde;&icirc;&iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&igrave; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; P &acirc; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&oacute;&thorn; &divide;&aring;&eth;&aring;&ccedil; &iacute;&agrave;&divide;&agrave;&euml;&icirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;
&egrave; &ograve;&icirc;&divide;&ecirc;&oacute; p. &Ograve;&icirc;&atilde;&auml;&agrave; &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; l &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; z = 1 &aacute;&oacute;&auml;&oacute;&ograve; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&icirc;&acirc;&agrave;&ograve;&uuml; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; L &acirc;
&iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&aring;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&agrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &iacute;&agrave;&divide;&agrave;&euml;&icirc; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve; &egrave; &iuml;&eth;&yuml;&igrave;&oacute;&thorn; l. &Aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &oacute;&auml;&agrave;&euml;&frac14;&iacute;&iacute;&agrave;&yuml; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; &yacute;&ograve;&icirc; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; z = 0. &Ograve;&aring;&iuml;&aring;&eth;&uuml; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&oacute;&thorn; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml; &igrave;&icirc;&aelig;&iacute;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&uuml; &ograve;&agrave;&ecirc;: &iuml;&eth;&yuml;&igrave;&icirc;&eacute;
P &iuml;&icirc;&ntilde;&ograve;&agrave;&acirc;&egrave;&igrave; &acirc; &ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&egrave;&aring; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; L, &iuml;&aring;&eth;&iuml;&aring;&iacute;&auml;&egrave;&ecirc;&oacute;&euml;&yuml;&eth;&iacute;&oacute;&thorn; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; P . &Ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &acirc; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&egrave;
&Egrave;&Ntilde;&times;&Egrave;&Ntilde;&Euml;&Egrave;&Ograve;&Aring;&Euml;&Uuml;&Iacute;&Agrave;&szlig; &Atilde;&Aring;&Icirc;&Igrave;&Aring;&Ograve;&ETH;&Egrave;&szlig;: &Igrave;&Aring;&Ograve;&Icirc;&Auml; &Oslash;&Agrave;&Euml;&szlig; &Egrave; &Oslash;&Oacute;&Aacute;&Aring;&ETH;&Ograve;&Agrave;
11
&ntilde; &aring;&auml;&egrave;&iacute;&egrave;&divide;&iacute;&icirc;&eacute; &ntilde;&ocirc;&aring;&eth;&icirc;&eacute; x2 + y 2 + z 2 = 1 &iuml;&eth;&yuml;&igrave;&agrave;&yuml; P &egrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&uuml; L &auml;&agrave;&auml;&oacute;&ograve; &auml;&acirc;&agrave; &iuml;&icirc;&euml;&thorn;&ntilde;&agrave; &egrave; &yacute;&ecirc;&acirc;&agrave;&ograve;&icirc;&eth;,
&ntilde;&icirc;&icirc;&ograve;&acirc;&aring;&ograve;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;.
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave;, &divide;&ograve;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&aring; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&icirc;&eacute; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave; &auml;&icirc;&ntilde;&euml;&icirc;&acirc;&iacute;&icirc; &iuml;&aring;&eth;&aring;&iacute;&icirc;&ntilde;&egrave;&ograve;&ntilde;&yuml;
&iacute;&agrave; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&eacute; &ntilde;&euml;&oacute;&divide;&agrave;&eacute; (&egrave; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &auml;&agrave;&aelig;&aring; &ntilde;&ograve;&agrave;&iacute;&icirc;&acirc;&egrave;&ograve;&ntilde;&yuml; &iuml;&eth;&icirc;&ugrave;&aring;). &Auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &acirc;
&ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring;, &egrave;&ccedil; &euml;&thorn;&aacute;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&icirc;&acirc;&aring;&ntilde;&ograve;&egrave; &auml;&acirc;&aring; &ecirc;&agrave;&ntilde;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&otilde; (&acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&icirc;&acirc;&iuml;&agrave;&auml;&agrave;&thorn;&ugrave;&egrave;&otilde;) &ecirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;, &egrave; &euml;&thorn;&aacute;&agrave;&yuml; &iuml;&eth;&yuml;&igrave;&agrave;&yuml; &acirc;&ntilde;&aring;&atilde;&auml;&agrave; &iuml;&aring;&eth;&aring;&ntilde;&aring;&ecirc;&agrave;&aring;&ograve; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;
&acirc; &auml;&acirc;&oacute;&otilde; &ograve;&icirc;&divide;&ecirc;&agrave;&otilde; (&acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&icirc;&acirc;&iuml;&agrave;&auml;&agrave;&thorn;&ugrave;&egrave;&otilde; &egrave;&euml;&egrave; &aacute;&aring;&ntilde;&ecirc;&icirc;&iacute;&aring;&divide;&iacute;&icirc; &oacute;&auml;&agrave;&euml;&frac14;&iacute;&iacute;&ucirc;&otilde;). &Iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute;
&igrave;&icirc;&aelig;&iacute;&icirc; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&uuml; &iuml;&icirc;&euml;&yuml;&eth;&oacute; &auml;&euml;&yuml; &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave;, &egrave; &iuml;&icirc;&euml;&thorn;&ntilde; &auml;&euml;&yuml; &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;.
&Iuml;&icirc;&euml;&yuml;&eth;&iacute;&agrave;&yuml; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml; &iuml;&icirc;&ccedil;&acirc;&icirc;&euml;&yuml;&aring;&ograve; &ograve;&agrave;&ecirc;&aelig;&aring; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&egrave;&ograve;&uuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&oacute;, &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&oacute;&thorn; &ecirc; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&aring;. &Agrave; &egrave;&igrave;&aring;&iacute;&iacute;&icirc;, &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&egrave;&igrave; &acirc;&ntilde;&aring; &ecirc;&agrave;&ntilde;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&aring;
&ecirc; &auml;&agrave;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&aring; Q &egrave; &acirc;&icirc;&ccedil;&uuml;&igrave;&frac14;&igrave; &egrave;&otilde; &iuml;&icirc;&euml;&thorn;&ntilde;&agrave;. &Icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml;, &iuml;&icirc;&euml;&thorn;&ntilde;&agrave; &aacute;&oacute;&auml;&oacute;&ograve; &euml;&aring;&aelig;&agrave;&ograve;&uuml;
&iacute;&agrave; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc;&icirc;&iacute;&egrave;&ecirc;&aring; (&ntilde;&igrave;. [1, &Ograve;&aring;&icirc;&eth;&aring;&igrave;&agrave; 3.5]), &ecirc;&icirc;&ograve;&icirc;&eth;&oacute;&thorn; &igrave;&ucirc; &egrave; &iacute;&agrave;&ccedil;&icirc;&acirc;&frac14;&igrave; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&eacute; &ecirc; Q &egrave; &icirc;&aacute;&icirc;&ccedil;&iacute;&agrave;&divide;&egrave;&igrave; &divide;&aring;&eth;&aring;&ccedil; Q∗ . &Egrave;&ccedil; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&yuml; &ntilde;&eth;&agrave;&ccedil;&oacute; &ntilde;&euml;&aring;&auml;&oacute;&aring;&ograve;,
&divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; Q &ecirc;&agrave;&ntilde;&agrave;&euml;&agrave;&ntilde;&uuml; &iuml;&eth;&yuml;&igrave;&icirc;&eacute;, &ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; Q∗ &aacute;&oacute;&auml;&aring;&ograve; &ntilde;&icirc;&auml;&aring;&eth;&aelig;&agrave;&ograve;&uuml; &iuml;&icirc;&euml;&thorn;&ntilde; &yacute;&ograve;&icirc;&eacute;
&iuml;&eth;&yuml;&igrave;&icirc;&eacute;. &Ecirc;&eth;&icirc;&igrave;&aring; &ograve;&icirc;&atilde;&icirc;, &egrave;&ccedil; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&yuml; &ograve;&agrave;&ecirc;&aelig;&aring; &ntilde;&euml;&aring;&auml;&oacute;&aring;&ograve;, &divide;&ograve;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave;, &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml;
&ecirc; Q∗ , &ntilde;&icirc;&acirc;&iuml;&agrave;&auml;&agrave;&aring;&ograve; &ntilde; Q.
&Oacute;&iuml;&eth;&agrave;&aelig;&iacute;&aring;&iacute;&egrave;&aring; 4.7. &Iuml;&oacute;&ntilde;&ograve;&uuml; Q &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;, &ecirc;&icirc;&iacute;&ouml;&aring;&iacute;&ograve;&eth;&egrave;&divide;&iacute;&agrave;&yuml; &ntilde;
&acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&eacute; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;&thorn; C (&iuml;&icirc; &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&yuml;&euml;&agrave;&ntilde;&uuml; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&agrave;&yuml; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml;). &Iuml;&eth;&icirc;&acirc;&aring;&eth;&uuml;&ograve;&aring;, &divide;&ograve;&icirc; Q∗ &ograve;&icirc;&aelig;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;, &egrave; &divide;&ograve;&icirc; Q∗ &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&ograve;&ntilde;&yuml; &egrave;&ccedil; Q
&egrave;&iacute;&acirc;&aring;&eth;&ntilde;&egrave;&aring;&eacute; &icirc;&ograve;&iacute;&icirc;&ntilde;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; C . &Iuml;&eth;&egrave;&acirc;&aring;&auml;&egrave;&ograve;&aring; &iuml;&eth;&egrave;&igrave;&aring;&eth; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; Q,
&ograve;&agrave;&ecirc;&icirc;&eacute; &divide;&ograve;&icirc; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave; Q∗ &iacute;&aring; &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&uuml;&thorn;.
&Egrave;&ccedil; &iuml;&aring;&eth;&aring;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&iacute;&ucirc;&otilde; &acirc;&ucirc;&oslash;&aring; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&icirc;&eacute; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave; &ntilde;&eth;&agrave;&ccedil;&oacute; &acirc;&ucirc;&ograve;&aring;&ecirc;&agrave;&aring;&ograve;
&ograve;&agrave;&ecirc;&icirc;&aring; &ntilde;&euml;&aring;&auml;&ntilde;&ograve;&acirc;&egrave;&aring; (&iuml;&icirc;&euml;&aring;&ccedil;&iacute;&icirc;&aring; &auml;&euml;&yuml; &eth;&aring;&oslash;&aring;&iacute;&egrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &Oslash;&ograve;&aring;&eacute;&iacute;&aring;&eth;&agrave;). &Iuml;&icirc;&euml;&yuml;&eth;&iacute;&agrave;&yuml; &auml;&acirc;&icirc;&eacute;-
&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&uuml; &auml;&euml;&yuml; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc; &iuml;&aring;&eth;&aring;&ntilde;&ograve;&agrave;&acirc;&euml;&yuml;&aring;&ograve; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml;
&ntilde; &iuml;&eth;&yuml;&igrave;&icirc;&eacute; &egrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; &iuml;&eth;&icirc;&otilde;&icirc;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute;. &Iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring; κ &ecirc;&agrave;&ntilde;&agrave;&iacute;&egrave;&yuml; &ntilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;&icirc;&eacute; &ntilde;&egrave;&igrave;&igrave;&aring;&ograve;&eth;&egrave;&divide;&iacute;&icirc; &icirc;&ograve;&iacute;&icirc;&ntilde;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&icirc;&eacute; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave;. &Icirc;&ograve;&ntilde;&thorn;&auml;&agrave;
&ntilde;&euml;&aring;&auml;&oacute;&aring;&ograve; &oacute;&ograve;&acirc;&aring;&eth;&aelig;&auml;&aring;&iacute;&egrave;&aring;, &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&aring; &igrave;&ucirc; &egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&icirc;&acirc;&agrave;&euml;&egrave; &acirc; &iuml;&eth;&aring;&auml;&ucirc;&auml;&oacute;&ugrave;&aring;&igrave; &eth;&agrave;&ccedil;&auml;&aring;&euml;&aring;: &aring;&ntilde;&euml;&egrave;
κ = m&micro; + nν , &ograve;&icirc; &icirc;&aacute;&yuml;&ccedil;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc; m = n. &Ecirc;&eth;&icirc;&igrave;&aring; &ograve;&icirc;&atilde;&icirc;, &iuml;&icirc;&euml;&oacute;&divide;&agrave;&aring;&igrave; &ograve;&agrave;&ecirc;&icirc;&eacute; &eth;&aring;&ccedil;&oacute;&euml;&uuml;&ograve;&agrave;&ograve;.
&Iuml;&eth;&aring;&auml;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&aring; 4.8. &Auml;&euml;&yuml; &ecirc;&agrave;&aelig;&auml;&icirc;&atilde;&icirc; k = 0, 1,. . . , 5, &divide;&egrave;&ntilde;&euml;&icirc; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;,
&iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; k &ograve;&icirc;&divide;&aring;&ecirc; &iacute;&agrave; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; (5 − k) &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &eth;&agrave;&acirc;&iacute;&icirc;
&divide;&egrave;&ntilde;&euml;&oacute; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; (5 − k) &ograve;&icirc;&divide;&aring;&ecirc; &egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; k
&iuml;&eth;&yuml;&igrave;&ucirc;&otilde;.
&Auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &ograve;&icirc;&atilde;&icirc;, &divide;&ograve;&icirc;&aacute;&ucirc; &ntilde;&divide;&egrave;&ograve;&agrave;&ograve;&uuml;, &ntilde;&ecirc;&agrave;&aelig;&aring;&igrave;, &divide;&egrave;&ntilde;&euml;&icirc; &ecirc;&icirc;&iacute;&egrave;&ecirc;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &iuml;&yuml;&ograve;&egrave; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &igrave;&ucirc; &iacute;&agrave;&eacute;&auml;&frac14;&igrave; &divide;&egrave;&ntilde;&euml;&icirc; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&otilde; &ecirc;&icirc;&iacute;&egrave;&ecirc;. &Auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&aring; &ecirc;&icirc;&iacute;&egrave;&ecirc;&egrave;
&aacute;&oacute;&auml;&oacute;&ograve; &iuml;&eth;&icirc;&otilde;&icirc;&auml;&egrave;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &iuml;&icirc;&euml;&thorn;&ntilde;&agrave; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &divide;&aring;&eth;&aring;&ccedil; &iuml;&yuml;&ograve;&uuml; &ograve;&icirc;&divide;&aring;&ecirc;. &Ntilde;&euml;&aring;&auml;&icirc;&acirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &aring;&ntilde;&ograve;&uuml; &eth;&icirc;&acirc;&iacute;&icirc; &icirc;&auml;&iacute;&agrave; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&agrave;&yuml; &ecirc;&icirc;&iacute;&egrave;&ecirc;&agrave;, &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&agrave;&yuml;&ntilde;&yuml; &iuml;&yuml;&ograve;&egrave; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde;
&iuml;&eth;&yuml;&igrave;&ucirc;&otilde;.
&Egrave;&ntilde;&iuml;&icirc;&euml;&uuml;&ccedil;&oacute;&yuml; &iuml;&eth;&aring;&auml;&euml;&icirc;&aelig;&aring;&iacute;&egrave;&aring; 4.8 &egrave; &icirc;&ograve;&acirc;&aring;&ograve;&ucirc; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde; 4.2 &egrave; 4.3, &igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&eth;&agrave;&ccedil;&oacute; &eth;&aring;&oslash;&egrave;&ograve;&uuml;
&icirc;&ntilde;&ograve;&agrave;&acirc;&oslash;&egrave;&aring;&ntilde;&yuml; &auml;&acirc;&aring; &ccedil;&agrave;&auml;&agrave;&divide;&egrave; (&auml;&euml;&yuml; k = 1 &egrave; k = 3).
&Acirc;&iacute;&egrave;&igrave;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&eacute; &divide;&egrave;&ograve;&agrave;&ograve;&aring;&euml;&uuml;, &acirc;&icirc;&ccedil;&igrave;&icirc;&aelig;&iacute;&icirc;, &ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&euml;, &divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave; &eth;&aring;&oslash;&agrave;&ograve;&uuml; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &auml;&euml;&yuml; k = 3 &ograve;&aring;&igrave; &aelig;&aring;
&igrave;&aring;&ograve;&icirc;&auml;&icirc;&igrave;, &divide;&ograve;&icirc; &egrave; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; 4.3 &ograve;&icirc; &aring;&ntilde;&ograve;&uuml; &egrave;&ntilde;&ecirc;&agrave;&ograve;&uuml; &divide;&egrave;&ntilde;&euml;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &iuml;&eth;&icirc;&otilde;&icirc;&auml;&yuml;&ugrave;&egrave;&otilde; &divide;&aring;&eth;&aring;&ccedil; &auml;&agrave;&iacute;&iacute;&oacute;&thorn; &ograve;&icirc;&divide;&ecirc;&oacute;
12
&Acirc;&agrave;&euml;&aring;&iacute;&ograve;&egrave;&iacute;&agrave; &Ecirc;&egrave;&eth;&egrave;&divide;&aring;&iacute;&ecirc;&icirc;
&egrave; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ugrave;&egrave;&otilde;&ntilde;&yuml; &auml;&acirc;&oacute;&otilde; &auml;&agrave;&iacute;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;, &ograve;&icirc; &iuml;&icirc;&euml;&oacute;&divide;&egrave;&ograve;&ntilde;&yuml; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &auml;&acirc;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; (&agrave; &iacute;&aring; &divide;&aring;&ograve;&ucirc;&eth;&aring;, &ecirc;&agrave;&ecirc;
&auml;&icirc;&euml;&aelig;&iacute;&icirc; &aacute;&ucirc;&ograve;&uuml; &egrave;&ccedil; &iuml;&icirc;&euml;&yuml;&eth;&iacute;&icirc;&eacute; &auml;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&ntilde;&ograve;&egrave;). &Auml;&aring;&euml;&icirc; &acirc; &ograve;&icirc;&igrave;, &divide;&ograve;&icirc; &iacute;&aring;&auml;&icirc;&ntilde;&ograve;&agrave;&thorn;&ugrave;&egrave;&aring; &auml;&acirc;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;
&iacute;&agrave; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;&eacute; &iuml;&euml;&icirc;&ntilde;&ecirc;&icirc;&ntilde;&ograve;&egrave; &iuml;&eth;&icirc;&ntilde;&ograve;&icirc; &iacute;&aring; &acirc;&egrave;&auml;&iacute;&icirc;. &Auml;&aring;&eacute;&ntilde;&ograve;&acirc;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;, &eth;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&egrave;&igrave; &ntilde;&aring;&igrave;&aring;&eacute;&ntilde;&ograve;&acirc;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;, &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&aring; &ecirc;&agrave;&ntilde;&agrave;&thorn;&ograve;&ntilde;&yuml;, &ntilde;&ecirc;&agrave;&aelig;&aring;&igrave;, &auml;&acirc;&oacute;&otilde; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&iacute;&ucirc;&otilde; &iuml;&eth;&yuml;&igrave;&ucirc;&otilde;. &Icirc;&iacute;&icirc; &ntilde;&icirc;&ntilde;&ograve;&icirc;&egrave;&ograve; &egrave;&ccedil; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;
&auml;&acirc;&oacute;&otilde; &ograve;&egrave;&iuml;&icirc;&acirc;: (x−a)2 +(y−a)2 = a2 &egrave; (x+a)2 +(y−a)2 = a2 , &atilde;&auml;&aring; a &iuml;&agrave;&eth;&agrave;&igrave;&aring;&ograve;&eth;. &Iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &aring;&ntilde;&euml;&egrave; &igrave;&ucirc;
&auml;&icirc;&iuml;&oacute;&ntilde;&ecirc;&agrave;&aring;&igrave; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &acirc;&aring;&ugrave;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&ucirc;&aring; &ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&agrave;&eth;&agrave;&igrave;&aring;&ograve;&eth;&agrave; a, &ograve;&icirc; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &iuml;&aring;&eth;&acirc;&icirc;&atilde;&icirc; &ograve;&egrave;&iuml;&agrave; &iacute;&egrave;&ecirc;&icirc;&atilde;&auml;&agrave;
&iacute;&aring; &iuml;&eth;&icirc;&eacute;&auml;&oacute;&ograve; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; (x0 , y0 ), &oacute; &ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&ucirc; &egrave;&igrave;&aring;&thorn;&ograve; &eth;&agrave;&ccedil;&iacute;&ucirc;&aring; &ccedil;&iacute;&agrave;&ecirc;&egrave;, &agrave; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave;
&acirc;&ograve;&icirc;&eth;&icirc;&atilde;&icirc; &ograve;&egrave;&iuml;&agrave; &divide;&aring;&eth;&aring;&ccedil; &ograve;&icirc;&divide;&ecirc;&oacute; &ntilde; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&agrave;&igrave;&egrave; &icirc;&auml;&iacute;&icirc;&atilde;&icirc; &ccedil;&iacute;&agrave;&ecirc;&agrave;. &Aring;&ntilde;&euml;&egrave; &aelig;&aring; &auml;&icirc;&iuml;&oacute;&ntilde;&ograve;&egrave;&ograve;&uuml; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&aring;
&ccedil;&iacute;&agrave;&divide;&aring;&iacute;&egrave;&yuml; &iuml;&agrave;&eth;&agrave;&igrave;&aring;&ograve;&eth;&agrave; a, &ograve;&icirc; &divide;&aring;&eth;&aring;&ccedil; &ecirc;&agrave;&aelig;&auml;&oacute;&thorn; &ograve;&icirc;&divide;&ecirc;&oacute; (x0 , y0 ), &ograve;&agrave;&ecirc;&oacute;&thorn; &divide;&ograve;&icirc; x0 6= 0 &egrave; y0 6= 0, &iuml;&eth;&icirc;&eacute;&auml;&oacute;&ograve;
&eth;&icirc;&acirc;&iacute;&icirc; &auml;&acirc;&aring; &icirc;&ecirc;&eth;&oacute;&aelig;&iacute;&icirc;&ntilde;&ograve;&egrave; &ecirc;&agrave;&aelig;&auml;&icirc;&atilde;&icirc; &ograve;&egrave;&iuml;&agrave;. &Ograve;&agrave;&ecirc;&egrave;&igrave;&egrave; &aelig;&aring; &agrave;&euml;&atilde;&aring;&aacute;&eth;&agrave;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&igrave;&egrave; &eth;&agrave;&ntilde;&ntilde;&oacute;&aelig;&auml;&aring;&iacute;&egrave;&yuml;&igrave;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc;
&iuml;&eth;&icirc;&acirc;&aring;&eth;&egrave;&ograve;&uuml;, &divide;&ograve;&icirc; &egrave; &acirc; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;&otilde; 4.1 &egrave; 4.2 &igrave;&ucirc; &iacute;&egrave;&ecirc;&agrave;&ecirc;&egrave;&otilde; &ecirc;&icirc;&igrave;&iuml;&euml;&aring;&ecirc;&ntilde;&iacute;&ucirc;&otilde; &eth;&aring;&oslash;&aring;&iacute;&egrave;&eacute; &iacute;&aring; &oacute;&iuml;&oacute;&ntilde;&ograve;&egrave;&euml;&egrave;.
&Ntilde;&iuml;&egrave;&ntilde;&icirc;&ecirc; &euml;&egrave;&ograve;&aring;&eth;&agrave;&ograve;&oacute;&eth;&ucirc;
[1] &Agrave;&ecirc;&icirc;&iuml;&yuml;&iacute; &Agrave;. &Acirc;., &Ccedil;&agrave;&ntilde;&euml;&agrave;&acirc;&ntilde;&ecirc;&egrave;&eacute; &Agrave;. &Agrave;., &Atilde;&aring;&icirc;&igrave;&aring;&ograve;&eth;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&aring; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave; &ecirc;&eth;&egrave;&acirc;&ucirc;&otilde; &acirc;&ograve;&icirc;&eth;&icirc;&atilde;&icirc; &iuml;&icirc;&eth;&yuml;&auml;&ecirc;&agrave;,
&Igrave;&Ouml;&Iacute;&Igrave;&Icirc;, 2007
[2] S. L. Kleiman, Chasles's enumerative theory of conics: a historical introduction, Studies in
Algebraic Geometry, Studies in Math., 20, Math. Assoc. Amer., Washington, D. C, 1980, pp.
117138
[3] S. L. Kleiman and Dan Laksov, Schubert calculus, The American Mathematical Monthly,
79, No. 10, (1972), pp. 1061-1082