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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158120Apollonij Pergæi

Nam ſi coniungamus A G, B G, B F,

150[Figure 150]11b F C, & c. Ideſt; ſecetur C H æqualis com-
paratæ, ſeu ſemiſsi lateris recti axis A C;
quia menſura E C ſuppoſita eſt maior compa-
rata, erit quoque E C maior, quàm C H, &
propterea recta linea E F cadet infra H F;
ideoque angulus C F E maior erit angulo C
F H: eadem ratione angulus F B E maior
erit angulo F B H, atque angulus B F E mi-
nor erit angulo B F H, & ſic de reliquis,
cumque C H ſit æqualis comparatæ, & ſit
maior C D ſemiße axis recti minoris, omnium ramorum ex origine H ad elli-
2216. 17. 18.
huius. pſim C F B G, cadentium maximus erit H C; & propterea H C maior erit,
quàm H F, & in triangulo H F C angulus H F C oppoſitus maiori lateri ma-
ior erit angulo C; eſtque oſtenſus angulus E F C maior angulo H F C; igitur
in triangulo C E F erit angulus C F E maior angulo F C E; & propterea ra-
mus E C maior erit, quàm E F: ſimili modo, quia ramus H F propinquior ma-
33Ibidem. ximo maior eſt remotiore H B, erit angulus H F B minor angulo H B F: ideo-
que angulus E F B, pars minoris, adbuc minor erit angulo E B F, maiorem
excedente; & propterea in triangulo E F B erit ramus E F propinquior maxi-
mo E C, maior remotiore E B, & c.

Notæ in Propoſit. XX. XXI. XXII.

SI vero fuerit menſura I C minor comparata, quæ ſit C F, nempe ſe-
44a miſſe erecti, & maior dimidio recti E C, & origo ſit in recto, aut in
eius productione, vt in I; tunc maximus ramorum egredientium ex origi-
ne, vt I A, I B, I K, I H eſt cuius inuerſi proportio E G (poſt abſolu-
tionem figuræ cum perpendicularibus, & lineis præcedentibus) ad ab-

151[Figure 151] ſciſſam eius potentialis ex menſura cum origine, vt I G eſt, vt propor-
tio figuræ recti, vt D C ad erectum illius, & quadratum eius, nẽpe

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