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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254216Apollonij Pergæi B cadit inter verticem G, & punctum

293[Figure 293] C eiuſdem parabolæ G C; igitur Z B
K ordinatim applicata ad diametrum
G I neceßario ſecabit diametrum G I
intra ſectionem in Z, & producta
occurret K N extra eandem in K.
Non ſecus oſtendetur, quod E N I or-
dinatim applicatæ ad diametrum H
N, punctum N cadit intra, & I ex-
tra eandem ſectionem H E, & pro-
pterea recta C H minor erit, quàm K
N, ſeu B E ei æqualis in parallelo-
grammo E K; pariterque Z I, ſeu ei
æqualis B E minor erit, quàm G V.
Cadat poſtea L M extra duas diame-
tros ad eaſdem partes. Quoniam in parallelogrammo L S latera L O, M S æqua-
lia ſunt; eſtque S R maior quàm M S, ſeu quàm O L; ergo (vt in prima parte
huius propoſitionis oſtenſum eſt) rectangulum M S R, ſeu rectangulum ſub S V,
& latere recto G F maius erit quadrato L O, ſeu rectãgulo O G F, & propterea
11II. lib. I. S V maior erit, quàm O G, & addita communi O V; erit O S, ſeu ei æqualis
L M, in parallellogrammo L S, maior quàm G V. Quod erat oſtendendum.

Idem omnino verificari in ellipſibus demonſtrari facile poſſet, quod breuitati
22SCHO-
LIVM. ſtudens libens omitto.

Si fuerint duæ quælibet coniſectiones A B C, D E F æquales, & ſi-
33PROP. 5.
Addit. miles ad eaſdemque partes cauæ, quarum diametri B H, E I (æquè in-
clinatæ ad ordinatim ad eas applicatas) æquidiſtantes ſint inter ſe, vel
congruentes; & ducantur quælibet rectæ lineæ A D, K L à ſectionibus
interceptæ, parallelæ rectæ lineæ B E vertices coniungenti: erunt illæ
æquales inter ſe.

Si enim hoc verum non eſt,

294[Figure 294] ſit A D ſi fieri pote@t maior,
aut minor, quàm B E, & ſe-
t@tur A R æqualis B E: pa-
tet punctum R cadere intra,
aut extra ſectionem D E (ſed
in eius plano cum ſectiones in
eodem plano exiſtant) iungan-
turque rectæ lineæ A B, E
R, quæ æquales erunt, & pa-
rallelæ inter ſe, cum ſint con-
iungentes æqualium, & æqui-
diſtantium B E, & A R. Po-
ſtea ducatur A H ordinatim
applicata ad diametrum B H efficiens abſcißam H B; ſeceturque abſciſſa E I in
altera ſectione æqualis B H; iunganturque H I, I D, & I R. Et quoniam B

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