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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140102Apollonij Pergæi periaturque Trutina K minoris, vel maioris menſuræ F B: dico perpen-
dicularem C F minorem eſſe Trutina K.

Secentur primo in parabola abciſsæ B H, & B N æquales trienti exceſſus inæ-
qualium menſurarum ſupra ſemierectum (vt præcipitur in propoſitione 51. hu-
ius) manifeſtum eſt, abſciſſam B N minorem eſſe ipſa B H, quando B F minor
eſt, quàm B E, & maior, quando B F ſuperat ipſam B E; eo quod eorum tri-
plæ, vna cum ſemierecto, ideſt menſura B F minor fuerat in primo caſu, &
maior in ſecundo, quàm menſura B E.

In hyperbola vero, & ellipſi fiat proportio rectæ H L ad ſemiaxim tranſuer-
11Lem. 7.
huius. ſum L B ſubtriplicata eius, quàm inuerſæ L E ſegmentum L G homologum la-
teri tranſuerſo habet ad ſemiaxim tranſuerſum (ex præſcripto propoſit. 52. &
53. huius) pariterque fiat proportio N L ad L B ſubtriplicata eius quàm inuer-
ſæ minoris L F in primo caſu, & maioris in ſecundo, ſegmentum homologum
lateri tranſuerſo habet ad L B.

125[Figure 125]

Quoniam in primo caſu maius ſegmentum G L ad eandem L B habet maio-
rem proportionem, quàm minus ſegmentum ex L F diſſectum; igitur earum;
ſubtriplicatæ proportiones inæquales erunt, videlicet H L ad L B maiorem pro-
portionem habebit, quàm N L ad ipſam L B, & propterea H L maior erit,
quàm N L, & ablata communi L B, erit H B abſciſſa maioris menſuræ ma-
ior, quàm N B abſcißa menſuræ minoris. Similiter oſtendetur in ſecundo ca-
ſu, quod abſciſſa N B maioris menſuræ maior eſt, quàm B H. Oſtendedum
modo eſt, perpendicularem C F in vtroque caſu minorem eſſe trutina K; Si
2251. 52.
huius. enim hoc verum non eſt, ſi fieri poteſt, ſit C F maior trutina K; igitur ex con-
curſu C ad ſectionem B A nullus ramus breuiſecans duci poteſt, quod eſt contra
hypotheſim; erat enim A I breuiſsima; quare C F non erit maior trutina K.
Sit ſecundo C F æqualis K, ſi fieri poteſt, ergo ramus principalis C O ductus
legibus propoſit. 51. 52. huius cui competit trutina K erit breuiſecans ſin-
gularis eorum, qui ad ſectionem duci poſſunt, nec vllus alius, præter C O, bre-
uiſecans erit: cadit vero ramus C A infra, vel ſupra ramum C O, propterea
quod abſciſſæ B H, & B N inæquales oſtenſæ ſunt; igitur ramus C A diuerſus
à breuiſecante ſingulari C O non erit breuiſecans, quod eſt contra hypotheſin;

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