Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

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224. PROPOSITIO XXI.

SInt poſtea duæ illæ ſectiones hyperbolicæ, & ellipticæ ſi-
miles, & earum centra T, X (remanentibus lineis, & ſi-
gnis, vt prius) & ducantur duæ contingentes V e, & Y f.

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Quoniam B G ad B I ſuppoſita eſt, vt H E ad E K, & pariter G B ad
B L, vt H E ad E M; ergo ex æqualitate, & per conuerſionem rationis
B L ad L I eſt vt E M ad M K; & propter ſimilitudinem duarum ſectio-
num N L ad A I nempe L O ad O I eſt, vt M P ad D K, nempe M Q
ad Q K, & antecedentes ad ſummas vel differentias terminorum, ſcilicet
O L ad L I eandem proportionem habebit, quàm Q M ad M K, & ex
æqualitate O L ad L B erit, vt Q M ad M E, ſed B L ad L N eſt, vt E
M ad M P, cum ex ſuppoſitione ſectiones ſint ſimiles; ergo O L ad L N
eſt, vt Q M ad M P; ſuntque L, M duo anguli recti: ergo anguli O, Q,

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