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

Apollonij Pergæi Simili modo oſtendetur quod I K minor ſit, quam P R: etenim ſi pona-
tur linea f æqualis ſummæ M G, G E: cum G E non ſit maior duplo E
H, & f maior ſit duplo G E; igitur f in E H maius eſt quadrato G E. Poſtea oſtendetur (quemadmodum antea dictum eſt) quod M H ad H
E, nempe M H in H A ad E H in H A minorem proportionem habet
quàm quadratum M G ad quadratum G E; & permutando M H in H A
ad quadratum M G, ſeu quadratum A C ad quadratum P R(15. ex 7.) minorem proportionem habebit, quàm E H in H A ad quadratum G E,
nempe quàm quadratum A C ad quadratum I K: & propterea A C ad
P R minorem proportionem habebit, quàm ad I K; ideoquè I K minor
eſt, quàm P R: & pariter P R minor, quàm S Z.

301.1.

0353-01
0354-01

302. PROPOSITIO XXXV. &
XXXVI.

S It poſtea A C minor dimidio A F; erit A G maior duplo A H, & ideo H G maior eſt, quàm H A: ponatur iam H M æqualis H G,
ducaturque ad axim perpendicularis N M ; iungaturque N C, & educa-
tur diameter P Q parallela N C. Et quia M H medietas eſt ipſius M G,
erit P Q dimidium ipſius P R (6. ex 7.) Inter duas diametros P Q, A C
ducatur diameter I I. , & C B ei parallela, & ad axim perpendicularis
B E. Quoniam M H in H E minus eſt quadrato H G; addito communi

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