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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12183Conicor. Lib. V. ſunt D A V, D L G, D B I, D Q O, D C P, oſtenſus eſt ramus D A minor
quàm D B, & D B propinquior vertici A, minor ramo D C remotiore.

Notæ in Propoſ. LXVII.

POſtea repetamus figuram vtrã-

102[Figure 102]11a que hyperboles, & c. Lego;
Repetamus figuras paraboles, & hy-
perboles, & ſupponantur denuo eædem
lineæ æductæ ex concurſu D ad ſectio-
nem; & perpendicularis D E, atque
Trutina F, & omnium ramorum ſe-
cantium vnicus tantummodo D B ſit
breuiſecans.

Et illi propinquiores ſint maio-
22b res remotioribus, & c. Sed mendo-
sè; legi debet: Et illi propinquiores
ſint minores remotioribus.

Quia educitur ex D vnus tantum breuiſecans, & c. Legi debet. Quia
33Conuerſ.
51. 52.
huius.44c educitur ex concurſu D vnus tantum breuiſecans, erit menſura E A maior di-
midio erecti, & D E perpendicularis ad axim æqualis erit Trutinæ F.

Inde conſtat D G maiorem eſſe, quàm D A, & c. Quia ex concurſu D
55d ad ſectionem A C vnicus ramus D B breuiſecans ſupponitur igitur omnes rami
cadentes inter A, & B præter infimum D B conſtituunt cum tangentibus ſectio-
nem, ab eorum terminis ductis, angulos reſpicientes verticem A acutos; & pro-
66Lem. 10. pterea ramus terminatus D A minor eſt quolibet ramo D G infra ipſum, & ſu-
pra ramum D B poſito; atque ramus D G minor eſt quolibet alio à vertice re-
77Coro 11.
64. 65.
huius. motiore ducto ex D ad peripheriam A B. Dico iam, quod ramus D B maior
eſt quolibet ramo D G, poſito infra verticem A, & ſupra breuiſecantem D B;
Si enim hoc verum non eſt, erit D B æqualis, aut minor, quàm D G, & tunc
ducto quolibet ramo D H ad ſectionem G B infra ramum D G, erit D H re-
88Ibidem. motior à vertice A maior propinquiore D G, & propterea ramus D B adhuc
minor erit ramo D H.

Ergo D M nempe D I, & c. Quia D M, vt remotior à vertice A, eſt ma-
99e ior, quàm propinquior D H eſt vero D L, atque D I æqualis D M cum ſint
1010Ibidem. radĳ eiuſdem circuli; ergo D I portio maior eſt, quàm totum D H, quod eſt
abſurdum; quare D B maior eſt quolibet ramo D G infra verticem A, & ſu-
pra ramum D B poſito; & propterea D B multo maior erit, quàm D A.

Ergo D N minor eſt, quàm D C, & c. Dubitare quis poſſet, an ramus
1111f D N, quia propinquior eſt vertici A ſit minor remotiore ramo D C, vt in pro-
poſitione 64. & 65. verificabatur; & ratio eſt, quia hypotheſes ſunt diuerſæ,
nam ibi nullus ramus breuiſecans à concurſu D ad ſectionem A C duci poſſe
ſupponebatur, in hac vero propoſitione 67. ponitur vnicus breuiſecans D B, at
ſcrupulus omnis tolletur, ſi dicatur, non quidem ex propoſitionibus 64. & 65.
ſed ex demonſtratione ibi allata, ſeu ex Corollario in fine notarum

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