Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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11072Apollonij Pergæi

Patet ex hoc, quod ſi producantur ex duo-
11d

91[Figure 91] bus punctis contactus in ellipſi perpendiculares
E M, A L; & fuerit E M minor, exempli gra-
tia, tunc tangens educta ab eius extremitate,
quæ eſt in ſectione, minor quoque eſt, & c. Si
enim ex punctis E, A contactuum in ellipſi ducan-
tur ad axim minorem K C perpendiculares E M,
& A L ſecantes eum in M, & L, fueritque E M
minor, quàm A L, tunc quidem punctum E magis
recedit à vertice B axis maioris, quàm punctum
A; & propterea, ex præmiſſa 70. huius libri, erit
tangens E F minor, quàm A F. Expungo deter-
minationem ab aliquo incaute additam (quæ eſt in
ſectione) manifeſtum enim eſt ducinon poſſe contin-
gentem ellipſim à perpendicularis termino M in axi minori poſito, ſed à termi-
no E in ſectionis peripheria conſtituto.

SECTIO DVODECIMA

Continens XXIX. XXX. XXXI.

Propoſ. Appollonij.

Q Vælibet linea recta A E D tangens fectionem aliquam A
F B in A extremitate lineæ breuiſſimæ A C eſt perpeudi-
cularis ſuper illam, nẽpe D A C eſt angulus rectus.
Et ſi fuerit perpendicularis ſuper illam vtique tanget ſectio-
nem.

Alioquin producatur perpendicu-
22a

92[Figure 92] laris C E ſuper A D, erit A C maior,
quàm E C, ergo maior eſt, quàm F
C; ſed eſt minor, cũ ſit minor, quàm
C F, quod eſt abſurdum. Igitur an-
gulus D A C, eſt rectus, quod erat
oſtendendum.

Si verò fuerit D A C rectus, erit
33b A D tangens, alioquin ſit tangens A
G; ergo C A G erit rectus, ſed erat
C A D rectus, quod eſt abſurdum;
ergo A D eſt tangens, & hoc erat
probandum.

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