Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Conicor. Lib. VI. H O cadent puncta T, & V infra centrum L; & P vlterius tendit quàm Q ad
partes, eiuſdem centri L. igitur in tali caſit quatuor æquidiſtantium duæ P E,
T X vlterius tendent ad partes centri, & asymptoti L M, quàm duæ aliæ æqui-
diſtantes Q F, V Z. Quando verò B E, & C F cadunt vltra centra H, & L in productionibus æquidiſtantium asymptotorum G H, K L: quia N P cadit
ſupra, & L f infra centrũ H, ergo in parallelogrammo P f recta N f, ſeu ei æ-
qualis L P maior erit quàm N H: facta autem fuit L T æqualis H N; igitur
L T minor eſt, quàm L P; Eadem ratione L V minor erit, quàm L Q, at-
que P vlterius tendit quàm Q ad partes centri L, & ab ijſdem punctis caden-
tibus ſupra centrum L in productione asymptoti K L ducuntur quatuor rectæ
lineæ inter ſe æquidiſtantes vſque ad hyperbolen D Z; igitur duæ P E, T X vl-
terius tendunt ad partes centri, vel asymptoti L M, quàm duæ Q F, V Z. Secetur poſtea P a æqualis N B, atque Q b æqualis O C. Et quia T X æqua-
lis oſtenſa fuit N B erit P a æqualis ipſi T X; eſtque P E maior quàm T X; propterea quod illa vlterius tendit ad partes cẽtri L, quàm T X; igitur P E ma-
ior erit, quàm P a, & earum differentia erit E a. Simili modo oſtendetur Q
b æqualis V Z, & minor quàm Q F, quarum differentia F b: cumque Q P
æqualis ſit ipſi N O, propterea quod ſunt latera oppoſita eiuſdem parallelogram-
mi; igitur T V, quæ oſtenſa fuit æqualis O N erit quoque æqualis Q P, & sũ-
pta communiter Q T erit Q V æqualis T P, atque à terminis æqualium ſeg-
mentorum eiuſdem asymptoti L K ducuntur vſque ad hyperbolen E Z quatuor
rectæ lineæ inter ſe æquidiſtantes, & earum binæ P E, T X vlterius tendunt
ad partes centri, & asymptoti L M, quàm binæ Q F, V Z; igitur differentia
priorum, ſcilicet E a maior erit poſteriorum differentia F b; eſtque B a æqua-
lis N P, propterea quod æqualibus N B, & P a ponitur communiter B P; pa-
riterque O Q æqualis eſt C b; ſuntque N P, & O Q æquales inter ſe, nempe
latera oppoſita eiuſdem parallelogrammi; igitur B a, & C b æquales ſunt inter
ſe: ijs verò adduntur exceßus inæquales E a, F b efficietur E B vlterius ten-
dens ad partes asymptoti H I maior, quàm F C. Quod erat primum.

234.1.

0250-02
Def. add.
Def. add.
0251-01
Ibidem.
Coroll.
Propoſ. 2.
addit.
Propoſ. 2.
addit.

Tertio ijſdem poſitis N E, O F ſint parallelæ alicui rectæ lineæ H g diuidẽti
angulum L H G, & propterea extensæ productionem asymptoti M L ſecabunt,

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