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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226188Apollonij Pergæi ad A E, vt O C ad C F, ſuntque anguli E, & F æquales, vt dictum eſt. Et
hoc erat propoſitum.

Notæ in Propoſit. XVII.

DEinde ſint ſectiones hyperbolicæ, aut ellipticæ, & reliqua in ſuo
11a ſtatu, & c. Ideſt. Supponantur ſectiones hyperbolicæ, vel ellipticæ A B,
& C D ſimiles inter ſe, ſcilicet figuræ axium V B, & γ D ſint ſimiles inter ſe,
atque à verticibus A, & C duarum diametrorum A M, & C O ductæ ſint re-

254[Figure 254] ctæ lineæ contingentes A E, & C F, efficientes cum axibus angulos A E B, &
C F D æquales, ſintque H G, & K I ordinatim ad diametros applicatæ, ſcili-
cet æquidiſtantes contingentibus verticalibus; & habeat abſciſſa M A ad portio-
nem contingentis A E eandem proportionem, quàm abſcißa O C habet ad por-
tionem contingentis C F; Dico ſegmenta H A G, & K C I ſimlia eſſe inter ſe.

Ergo Y c C ſimile eſt V a A, & c. Quoniam duæ ordinatim ad axes ap-
22b plicatæ A a, & C c perpendiculares ſunt ad axes, erunt in triangulis A a E,
& C c F duo anguli a, & c recti: atque ex hypotheſi duo reliqui anguli E, &
F æquales quoque ſunt; igitur tertius angulus a A E æqualis eſt tertio angulo c
C F, cumque in duobus triangulis V A E, atque γ C F ab eorum verticibus A,
& C ducuntur ad baſes V E, & γ F duæ rectæ lineæ A a, & C c continentes
cum baſibus angulos æquales, nempe rectos, & rectangulum V a E ad quadra-
tum a A eandem proportionem habet, quàm rectangulum γ c F ad quadratum
c C, vt in textu oſtenſum eſt: atq; duo anguli a A E, & c C F æquales oſten-
33ex 37.
lib. 1. ſi ſunt inter ſe; igitur erunt triangula V A E, & γ C F ſimilia inter ſe; ergo
44Propoſ. 6
præmiſſ. angulus V æqualis eſt angulo γ, atque angulus E A V æqualis erit angulo F

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