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


SI mutuo ſe ſecuerint in circulo duæ lineæ A B, C D, (ſed
non in centro) ad angulos rectos, vtique duo arcus A D,
C B ſunt æquales duobus arcubus A C, D B.

Educamus diametrum E F parallelam ipſi A B, quæ ſecet C D biſa-
riam in G, erit E C æqualis ipſi E D; & quia tam arcus E D F, quam
E C F eſt ſemicirculus, & arcus
E D æqualis arcui E A cum
arcu A D, erit arcus C F cum
duobus arcubus E A, A D æ-
qualis ſemicirculo, & arcus E
A æqualis arcui B F, ergo ar-
cus C B cum arcu A D æqualis
eſt ſemicirculo, & remanent duo
arcus E C, E A nempe arcus A
C cum arcu D B æquales illi,
& hoc eſt quod voluimus.




SI fuerit circulus A B C, & D A tangens illum, & D B ſe-
cans illum, & D C etiam tangens, & educta fuerit C E
parallela ipſi D B, & iuncta fuerit E A ſecans D B in F, & educta fuerit ex F perpendicularis F G ſuper C E; vtique bifa-
riam ſecabit illam in G.

Iungamus A C, & quia D A eſt tangens, & A C ſecans circulum
erit angulus D A C æqualis angulo cadenti in alterno ſegmento A C


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