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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11779Conicor. Lib. V. (qui eſt D B) cadit ſupra breuiſsimam ex puncto I ad axim ductam, quæ per-
1151. 52.
huius. pendicularis eſt ad tangentem L I H, & propterea angulus D I L, verticem
2229. 30.
huius. A reſpiciens erit acutus, & conſequens angulus D I H obtuſus.

LEMMA XI.

Iiſdem poſitis, ſi à concurſu D duo breuiſecantes D C, D B ad ſe-
ctionem A B duci poſſunt; Dico, quod quilibet ramus ſecans D I poſi-
tus ſupra breuiſecantem D B vertici proximiorem, vel infra infimum
breuiſecantem D C, efficit cum recta L I H tangente ſectionem in I an-
gulum D I L, reſpicientem verticem A, acutum, & conſequentem D
I H obtuſum, & quilibet ramus D O inter breuiſecantes poſitus efficit
cum recta G O N ſectionem tangente in O angulum D O G verticem
reſpicientem obtuſum, conſequentem vero D O N acutum.

Quia (ex conuerſa propoſitione 51. & 52. huius) perpendicularis D E mi-
3351. 52.
huius. nor eſſe debet Trutina F, & propterea quilibet ramus D I ſupra breuiſecantem
D B, vel infra breuiſecãtem D C cadit ſupra breuiſsimam ex puncto I ad axim
4429. 30.
huius. ductam, cum qua contingens L I angulum rectum conſtituit; ergo angulus D I
L verticem reſpiciens, eſt acutus, & conſequens D I H obtuſus; Similiter qui-
libet ramus D O inter breuiſecantes poſitus cadit infra breuiſsimam ex puncto
O ad axim ductam, & cum illa ſectionem contingens G O efſicit angulos rectos,
55Ibidem. igitur angulus D O G verticem reſpiciens, eſt obtuſus, & conſequens D O N
acutus.

Notæ in Propoſ. LXIV.
& LXV.

ANtea Apollonius docuit qui nam rami ab origine ad coniſectionem ducti
eſſent minimi, & quo ordine reliqui rami ſe ſe excederent, modo agit
de ramis axim ſecantibus à concurſu ductis, & quærit qui minimus, & qui
maximus ſit, & quo ordine diſponantur.

Producamus perpendicularem D E ſuper axim, & c. Si nullus ramus
66a breuiſecans à concurſu D ad ſectionem A C duci poteſt; Dico, quod ramus ter-
minatus D A eſt minimus omnium ramorum ſecantium D B, D C, & propin-
quiores vertici A minores ſunt remotioribus; ducatur D E perpendicularis ad
axim eum ſecans in E, & reperiatur Trutina F. Et ſiquidem D A non eſt
minor quolibet alio ramo ſecante D B infra ipſum poſito erit æqualis, aut maior
illo; ſitque prius D A æqualis D B, ſi fieri poteſt, & ex puncto A verticis du-
catur A G perpendicularis ad axim A E, quæ continget ſectionem in A, pari-
7717. lib. 1.
32. pr. terque ducatur recta A H perpendicularis ad ramum A D inclinatum ad axim;

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