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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8143Conicor. Lib. V.

58[Figure 58]

Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
11f extra S L, & c. Ad vitandam confuſionem figuræ, & prolixitatem demonſtrationis
appoſui duas figuras, in quibus duo caſus ĳſdem caracteribus notantur, itaque abſq;
nouo labore, ſi inſpiciatur ſecunda figura, ĳſdem verbis prioris caſus, oſtendetur ca-
ſus ſecundus.

Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, & c. Pars ſecun-
22g da huius propoſitionis innuitur tantummodo pauciſsimis verbis; quare maioris cla-
ritatis gratia integram demonſtrationem hìc afferre libuit.

Demonſtratio ſecundæ partis.

PROPOSITIONIS LI.

Eſto E D æqualis trutinæ H: Dico ex concurſu E vnicum tantùm breui-
ſecantem ramum duci poſſe.

In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
E D æqualis H; ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
rum E D I, B G I) eſt, vt G F ad F D, & componendo D G ad G I eſt, vt eadem G D
ad D F; ideoque I G æqualis eſt D F, ſeu A C ſemierecto; igitur B I eſt breuiſsima.

338. huius.

Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & in-
fra in ſecunda) occurrente axi in R, & ducta K M perpendiculari ad axim, quæ eum
ſecet in M, & tangentem O B in P. Quoniam (vt dictum eſt) O F ſecatur

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