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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10264Apollonij Pergæi

Notæ in Propoſit. LIX. LXII. & LXIII.

E T lineis, atque ſignis eodem ſtatu manentibus, & c. Ideſt punctum
11a C extra, aut intra ſectionem ponatur, dummodo non ſit in axi, ducaturq;
C E perpendicularis ad axim, ſecans eum in E, & vt latus tranſuerſum ad re-
ctum, ita ſiat D F ad F E, atque C L ad L E, & per L producatur O L M pa-
rallela A I, & per F ducatur F M G parallela C E, quæ ſecet O M in M, & per
C deſcribatur hyperbole H C B circa aſymptotos G M O, quæ in ellipſi per eius
224. lib. 2. centrum D tranſibit, & ideo eam ſecabit ſicuti oſtenſum eſt in 56. huius.

81[Figure 81]

Eo quod O M parallela axi D A inclinato ſubtendit, & c. Quoniam
33b in hyperbola O M parallela axi ſecat vtrãque linearum continentium angulum,
qui deinceps eſt ei, qui hyperbolen continet ſectioni occurret, & producta ſectio-
4411. lib. 2. nem A B ſecabit, & ideo O M cadit intra ſectionem A B, atque hyperbole A B
producta ſemper magis, ac magis recedit tum ab M O parallela axi, cum ab M
G parallela tangenti verticali, & ſectio H C B, & asymptoti O M G ad ſe ip-
5514. lib. 2. ſas jemper propius accedunt, igitur ſectiones A B, B C conueniunt; ſecent ſe
ſe in B, & ducamus per B, C lineam occurrentem axi in I, ipſi M O in O, &
M G in G.

Et quia B O æqualis eſt ipſi C G, & c. Cum lineæ rectæ O M, O G ſe ſe-
66c cantes in O, ſecentur à parallelis E C, K B, F G proportionaliter, erit O N
æqualis M L, ſicuti O B æqualis erat C G, & O L, æqualis erit N M, ſicuti
O C æqualis erat B G, cumque triangula O C L, & I C E ſint ſimilia propter
778. lib. 2. parallelas O L, I E, erit O L ad E I, vt L C ad C E; eſt vero M N, ſeu F
K æqualis ipſi L O, igitur F K ad E I eſt, vt L C ad E C, ſed ex conſtru-
ctione erat D F ad F E, vt C L ad L E, ſciluet vt latus tranſuerſum ad
rectum; ergo antecedentes ad ſummas terminorum in hyperbola, & ad
88Lem. 1.

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