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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13193Conicor. Lib. V. reſpicientem verticem C concurſui propinquiorem: & quilibet. ramus E
L inter breuiſecantem G E, & axim maiorem poſitus efficit cum tan-
gente L M angulum E L M reſpicientem eundem verticem A acu-
tum.

116[Figure 116]

Ducatur E F perpendicularis ad axim maiorem, eum ſecans inter verticem
c, & centrum D in F, & ex concurſu axis minoris B H, & breuiſsimæ G E,
scilicet ex H ducantur rectæ H K, & H L; pariterque ex punctis, K, & L
ducantur ad axim maiorem A C lineæ breuiſsimæ K N, L O, ei occurrentes in
N, & O. Luoniam (ex præmiſſo Lemmate 8.) à concurſu H ducitur ramus
H K inter breuiſecantes H B, H G interceptus; ergo H K cadit infra breuiſ-
ſimam K N ad partes verticis C; eſt vero angulus N K P rectus à tangente,
1129. 30.
huius.& breuiſsima contentus; ergo angulus H K P erit acutus, cum H K cadat in-
ter N K, & tangentem K P; cadit vero E K infra ramum H K verſus C; igi-
tur angulus E K P reſpiciens verticem C proximiorem concurſui E erit acutus.

Similiter (ex eodem Lemmate 8.) quia ramus H L ducitur inter breuiſecan-
tem H G, & verticem A à concurſu E remotiorem, cadet ipſe ſupra breuiſsimã
22Ibidem. L O, eſtque angulus O L M ad partes verticis A rectus; ergo H L M acutus erit,
cumque E L cadat ſupra H L verſus A; igitur angulus E L M, verticem A re-
motiorem reſpiciens, erit acutus, quod erat oſtendendum.

Si à concurſu E non exiſtente ſuper recto ellipſis A C, producatur vni-
33a cus ramus ſecans ipſam A C, vt E G, cuius ſegmentum G I, & A C ſit
breuiſsimum, vel duo breuiſecantes; vtique maximus ſecantium ramorum
egredientium ex illo concurſu, eſt breuiſecans, qui rectum ſectionis ab-
ſcindit, nempe E G, & c. Textum mendoſum ſic reſtituendum cenſeo. Si

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