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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182144Apollonij Pergæi ad D K, & propterea etiam conſequentes A I, & D K æquales ſunt inter ſe,
& compræhendunt angulos rectos A, & D; ergo ſiguræ G A I, & H D K ſimi-
les ſunt inter ſe, & æquales.

Notæ in Propoſit. IV.

I Am ergo demonſtratum eſt, quod duo

186[Figure 186] vertices tympani ſunt ſimiles, & æqua-
les, & inclinatus communis inter vtrum-
que verticem (16. ex 1.) ergo figura eſt
communis, & c. Hæc propoſitio eſt veluti Co-
rollarium primæ partis ſecundæ propoſitionis in
qua oſtenſum eſt, quod ſi duæ hyperbolæ habue-
rint axium ſiguras æquales, & ſimiles, erunt
quoque ſectiones ipſæ æquales, & congruentes;
habent verò ſectiones oppoſitæ A B, & D E
(quæ vocantur Vertices Tympani ab Arabico
interprete) figuras D A H, & A D I axis D
A æquales, & ſimiles (vt in 14. primi libri
demonſtrauit Apollonius); ergo ſectiones oppo-
ſitæ æquales erunt inter ſe, & congruentes.

Notæ in Propoſit. X.

SImiliter conſtat, quod ſi potentes contineant cum ſuis abſciſſis angu-
los equales obliquos, iudicium eſt, quod memorauimus in ſectioni-
11a bus, & c. Senſus huius propoſitionis talis eſt. In duabus ſectionibus conicis, ſi
cum earum diametris ordinatim applicatæ contineant angulos æquales, non re-
ctos, & earum latera recta ſint æqualia in parabolis, in reliquis verò ſectioni-

187[Figure 187] bus latera recta, & tran-
ſuerſa æqualia, itaut figuræ
ipſæ æquales ſint; erunt ſe-
ctiones ipſæ inter ſe æqua-
les: & è conuer ſo, ſi ſectio-
nes æquales fuerint, habe-
bunt latera æqualia earum
diametrorum, cum quibus
ordinatim applicatæ angulos
æquales, non rectos continent.

Demonſtrationes non apponuntur ab Apollonio, quia ĳſdem verbis omnino in
eiſdem figuris ab ſolui poßunt. Sint enim primo duæ parabolæ A B, & C D, at-
que earum diametri A G, & C H efficiant æquales angulos F, & E, cum ordi-
natim ductis D F, & B E, ſintque latera recta A I, C N æqualia.

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