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

Apollonij Pergæi permutando vt prius, idem quadratum A C ad quadratum ex Q P R, maiorem
proportionem habebit, quàm ad quadratum ex C A F, ſeu ex L I K, & pro-
pterea ſumma Q P R minor erit, quàm C A F, vel L I K, quæ erat oſten-
denda.

317. Notæ in Propoſit. XXXVIII. XXXIX.

QVia axis C A minor non eſt triente eius erecti A F, eſtq; H A ad A G vt C A
ad A F, ergo H A æqualis, aut maior eſt parte tertia ipſius A G; & A H
æqualis, aut maior erit, quàm ſemiſſis ipſius H G differentiæ illa-
rum, eſtque G H ſecta bifariam in D, ergo H A æqualis, aut maior erit,
quàm D H, eſtque H E maior quàm H A, ergo pariter H E maior eſt, quàm
D H, quare rectangulum ſub E D A in A H maius erit quadrato D A, atque
ſumma laterum figuræ L I K maior, quàm ſumma laterum figuræ axis C A F.

317.1.

0368-01
Lem. 6.
Lem. 9.

Similiter quia H M maior eſt, quàm H E, erit quoque H M maior, quàm
D H, & propterea ex lemma 6. & 9. ſumma Q P R maior erit, quàm ſum-
ma L I K.

318. Notæ in Propoſit. XXXX.

QVia C A minor eſt triente ipſius A F, eſtque H A ad A G vt C A ad A
F, ergo H A minor eſt tertia parte ipſius A G, & minor ſemiſſe diffe-

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