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

0154-01

Ergo quadratum I C æquale eſt duplo trianguli N F M cum duplo
trianguli D I N, & c. Quoniam quadratum I C æquale eſt duplo trianguli I
C F, ſeu duplo trianguli I F E vna cum duplo trianguli E F C; eſtque duplum
trianguli E D M æquale duplo trianguli E C F; igitur quadratum I C æquale
eſt duplo trianguli I F E vna cum duplo trianguli E M D: ijs vero triangulis
æquatur duplum trianguli N F M vna cum duplo trianguli D I N; igitur qua-
dratum I C æquale eſt duplo trianguli N F M vna cum duplo trianguli D I N: eſt vero quadratum I D æquale duplo trianguli D I N; igitur exceſſus quadrati
I C ſupra quadratum I D eſt triangulum N F M bis ſumptum; ſcilicet exem-
plar applicatum ad latus tranſuerſum D C.

131.1.

e

132. SECTIO DECIMASEPTIMA
Continens XIX. XX. XXI. XXII. XXIII.
XXIV. & XXV. Propoſ. Apollonij.

PROPOSITIO XIX.

SI menſura E C ſumatur in axe minori ellipſis A B C, ſitque
maior comparata; erit maximus omniũ ramorũ egredientiũ
ex ſua origine, vt E F, E B, E G; & maximo propinquior,
maior erit remotiore, nempe E F, quàm E B, & E B, quàm E G.

132.1.

a

Coniungamus rectas A G, G B, B F,
F C; & ſecetur C H æqualis compara-
tæ: iungãturque F H, H B, H G.

132.1.

0154-02
b

Et quoniam H C maior eſt, quàm H
F, (16. 17. 18. ex 5.) erit angulus H C
F minor, quàm H F C; & ideo multo
minor erit, quàm E F C, quare E C
maior eſt, quàm E F: & ſic conſtat, quod
E F maior ſit, quàm E B, & E B, quàm
E G, & E G, quàm A E; quod erat
oſtendendum.

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