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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CONICORUM LIBER IV. 77 et ducta AA producatur; secabit igitur sectiones in alio atque alio puncto. secet in N, M; itaque rectae a Z Sid Nf M ductae sectiones contingent [prop. I], et eodem modo, quo antea, erit [III, 39; Eucl. Y, 16] KZ, prop- propter alteram sectionem S^ \AZ— SK : ter alteram autem ISIA : AZ = SH : HZ] quod fieri non potest. ergo sectio opposita non concurret. XLIX. Si byperbola alteram oppositarum contingens in alio quoque puncto cum ea concurrit, sectio ei opposita cum altera oppositarum in pluribus punctis non concurret quam in uno. sint oppositae ABr, EZHj et byperbola AAF in A contingat, in F autem secet, sitque EZ® sectioni AAF opposita. dico, eam cum altera oppositarum in pluribus punctis non concurrere quam in uno. nam si fieri potest, concurrat in duobus E, Z, ducaturque EZ, et per A sectiones contingens ducatur AK, aut igitur parallelae sunt aut non parallelae. prius parallelae sint, et diametrus rectam EZ in duas partes aequales diuidens ducatur; ea igitur per A ueniet et diametrus erit sectionum coniugatarum [II, 34]. per r rectis AK, EZ parallela ducatur FAAB-^ ea igitur sectiones in alio atque alio puncto secabit. erit igitur [I def. 4] in altera FA == AA, in reliqua autem FA = AB. boc uero fieri non potest. AK, EZ igitur parallelae ne sint, sed in K concurrant, et FA rectae AK parallela ducta cum EZ in N concurrat, AB autem rectam EZ in duas par-
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CONICORUM LIBER IV. 77<br />
et ducta AA producatur; secabit igitur sectiones in<br />
alio atque alio puncto. secet in N, M; itaque rectae<br />
a Z Sid Nf M ductae sectiones contingent [prop. I],<br />
et eodem modo, quo antea, erit [III, 39; Eucl. Y, 16]<br />
KZ, prop-<br />
propter alteram sectionem S^ \AZ— SK :<br />
ter alteram autem ISIA : AZ = SH :<br />
HZ] quod fieri<br />
non potest. ergo sectio opposita non concurret.<br />
XLIX.<br />
Si byperbola alteram oppositarum contingens in<br />
alio quoque puncto <strong>cum</strong> ea concurrit, sectio ei opposita<br />
<strong>cum</strong> altera oppositarum in pluribus punctis<br />
non concurret quam in uno.<br />
sint oppositae ABr, EZHj et byperbola AAF in<br />
A contingat, in F autem secet, sitque EZ® sectioni<br />
AAF opposita. dico, eam <strong>cum</strong> altera oppositarum<br />
in pluribus punctis non concurrere quam in uno.<br />
nam si fieri potest, concurrat in duobus E, Z,<br />
ducaturque EZ, et per A sectiones contingens ducatur<br />
AK,<br />
aut igitur parallelae sunt aut non parallelae.<br />
prius parallelae sint, et diametrus rectam EZ in<br />
duas partes aequales diuidens ducatur; ea igitur per A<br />
ueniet et diametrus erit sectionum coniugatarum [II, 34].<br />
per r rectis AK, EZ parallela ducatur FAAB-^ ea<br />
igitur sectiones in alio atque alio puncto secabit. erit<br />
igitur [I def. 4] in altera FA == AA, in reliqua autem<br />
FA = AB. boc uero fieri non potest.<br />
AK, EZ igitur parallelae ne sint, sed in K concurrant,<br />
et FA rectae AK parallela ducta <strong>cum</strong> EZ<br />
in N concurrat, AB autem rectam EZ in duas par-
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