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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142104104 Apollonij Pergæi nem: Dico, quod circumpherentia Z γ ſecat tangentem rectam lineam
x A, & coniſectionem B G in puncto A.

Quoniam perpendicularis D E ponitur ma-

127[Figure 127] ior trutina L; ergo quilibet ramus D A cadit
1151. 52.
huius. ſupra breuiſsimam ex puncto A ad axim B E
ductam: efficit vero breuiſsima cum tangente
A x angulum rectum; ergo angulus D A x eſt
2229. 30.
huius. acutus; & propterea recta A x cadit intracir-
culum A Z; ſed A x cadit extra coniſectio-
3335. 36.
Lib. 1. nem B A, quàm contingit; ergo circumferen-
tia Z A cadit extra ſectionem B A, & extra
tangentem A x: poſtea ducatur quilibet ramus
D G infra ramum D A ſecans circumferentiã
circuli in r: & quia ramus D A propinquior
eſt vertici B, quàm D G, erit D A minor,
4464. 65.
huius. quàm D G; eſtque D γ æqualis D A (cum ſint ambo radĳ eiuſdem circuli) ergo
D γ minor erit, quàm D G: & propterea quodlibet punctum γ peripheriæ cir-
cularis infra punctum A poſitum cadet intra coniſectionem B G; & ideo cir-
cumferentia Z A γ ſecat tangentẽ, & coniſectionẽ in A, quod erat propoſitum.

Iſdem poſitis, ſit perpendicularis D E æqualis Trutinæ L, & ſit D
55PR. 10.
Addit. A ſingularis ille ramus breuiſecans, qui ex concurſu D ad ſectionem
B G duci poteſt; perficiaturque conſtructio, vt antea factum eſt; Dico,
6651. 52.
huius. circulum Z A γ ſecare coniſectionem in A, & contingere rectam Ax.

Ducatur quilibet ramus D F ſupra breuiſe-

128[Figure 128] cantem D A, ſecans circuli peripheriam in Z,
& quilibet alius ramus D G infra D A ſecans
eandem peripheriam in γ. Et quia ex con-
curſu D ad ſectionem B G vnicus tantum bre-
77Ibidem. uiſecans D A duci poteſt; igitur ramus D F
propinquior vertici B minor eſt remotiore D
8867. huius. A, & D A propinquior vertici B minor eſt
remotiore D G: ſuntque rectæ D Z, D γ æ-
quales eidem D A (cum ſint radĳ eiuſdem,
circuli) ergo D Z maior eſt, quàm D F, &
D γ minor, quàm D G; & propterea quodli-
bet punctum Z circuli ſupra A ſumptum ca-
dit extra coniſectionem B F A, & quodlibet
infimum punctum γ eiuſdem circuli cadit intra eandem coniſectionem A G;
quapropter circumferentia circuli Z A γ ſecat coniſectionem B A G in A. Po-
ſtea quia recta A x contingens ſectionem in A perpendicularis eſt ad breuiſe-
cantem D A, cum I A ſit breuiſsima; igitur recta linea x A, quæ perpendicu-
9929. 30.
huius. laris eſt ad radium D A, continget circulum Z Y γ. Quapropter circulus Z
A γ ſecant coniſectionem B A G in A, & tangit eandem rectam lineam A x,
quàm contingit ſectio conica B A G, & in eodem puncto A, quod erat oſtendendũ.

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