Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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AH, CONICORUM LIBER IV. 85 Aj A sectiones contingentes ducantur A&^ SJ, ducaturque A^y et per E rectae AJ parallela ducatur EBFy a ® autem secunda diametrus oppositarum ducatur ®KA^)\ ea igitur in K rectam AA in duas partes aequales secabit [II, 39]. itaque etiam utraque EBj EF in A in binas partes aequales secta est [I def. 4]. quare BA = AF'^ quod fieri non potest. ergo in alio puncto non concurrent. LIII. Si hyperbola alteram oppositarum in duobus punctis contingit, sectio ei opposita cum altera oppositarum non concurret. sint oppositae AAB^Ej et hyperbola AF sectionem AAB m duobus punctis A, B contingat, sitque sectioni AF opposita Z. dico, Z cum E non concurrere. nam si fieri potest, in E concurrat, et ab A^ B sectiones contingentes ducantur AHj HBj et ducatur AB ei EHf quae producatur; sectiones igitur in alio atque alio puncto secabit. uelut sit EHrA0. quoniam igitur AH^ HB contingunt, et AB puncta contactus coniungit, in alteris sectionibus coniugatis erit EH in alteris autem ®E : = '. &^ ®E'.EH=®r'.rH 1) Aiit cum Comin. &A K scribendum aut figura cum Halleio mutanda (in fig. codicis F, B permutatae sunt). sed omnino liaec demonstratio minus recte expressa est.
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