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

Apollonij Pergęi ius eſt quadrato N O, & qua-
dratum S T maius quadrato V
X ; ideoquè quando axis A C
maior eſt, quàm Q R, crit dia-
meter I L maior eius coniugata
N O, & S T maior quàm V X. Pari ratione, quandò axis A C
minor eſt, quàm Q R erit H A
minor, quàm A G, & H E mi-
nor, quàm E G, atque H M mi-
nor, quàm M G : & propterea
in ſecunda hyperbola, & ſecun-
da ellipſi etiam diameter I L
minor erit, quàm N O, & S T
minor erit quàm V X. Idem,
contingit in reliquis diametris,
dummodò in ellipſi cadant inter
A, & a, nam a b eſt ęqualis
ſuę coniugatę e d: & vltra pũ-
ctum a ad partes Q diametri
cadentes minores ſunt ſuis coniugatis in prima ellipſi, & maiores in ſecunda,
cum propinquiores ſint axi Q R.

295.1.

0345-03
Defin. 1.
huius.
Prop. 7.
huius.
0346-01

Si verò fuerit vnus duorum axium in hyperbola aut ellipſi maior, tunc
eius homologa diameter coniugata maior eſt, & c. Non nulla in hoc texta
deficiunt; non enim omnes diametri in ellipſi ſunt inęquales vt in Lemmate I. oſtenſum eſt, & ideo textus corrigi debuit.

295.1.

a

296. Notę in Propoſit. XXI.

ET conuenient duo puncta H, & G in puncto D ; eritque A C ad Q
R, vt A D ad ſe ipſam, ſiue vt A C ad ſe ipſam, & c. Quia qua-
dratum A C ad quadratum Q R eſt
vt C G ad G A, & vt quadratum,
I L ad quadratum N O, ita eſt H E
ad E G, nec non quadratum S T ad
quadratum V X eſt vt H M ad M G; ſed quandò axium quadrata ſunt inter
ſe ęqualia, tunc quidem pręſecta C G,
ſeu H A ęqualis eſt interceptę G A, & terminus G, ſeu H cadit in cẽtro D; & ideo H E vel D E ęqualis eſt E G vel
E D : pariterq; H M ęqualis eſt M G: quarè coniugatarũ diametrorũ quadra-
ta ęqualia ſunt inter ſe; & etiã tranſ-
uer ſa latera ſuis erectis ęqualia erunt.

296.1.

b
0346-02
Defin. 1.
Prop. 7.
huius.

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