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

Apollonij Pergæi minimo remotiore minor eſt. Quadratum autem menſuræ mi-
nus eſt quadrato cuiuslibet rami aſſignati (4) in parabola qui-
dem quadrato ſuæ abſciſſæ (5) & in hyperbola (6) & ellipſi
exemplari applicato ad abſciſſam illius rami.

37. PROPOSITIO IV.

SIt ſectio A B C, & axis eius C E, & inclinatus, ſiue tranſuerſa D C
centrum G, atque erectum C F, & ex C E ſecetur C I æqualis C H
(quæ ſit ſemiſſis erecti) & ex puncto
originis I educantur rami I B perpen-
dicularis, & I K, I L, I A, & per H, I
in hyperbola, & ellipſi ducatur H I P,
& per H, G recta H G T, ad quam ex
A, B, K, L extendantur A P E T, B I S,
K N R, L M O Q perpendiculares ſuper
C E. Dico, quod C I, comparata mi-
nor eſt, quam I L, & I L, quam I K, & I K,
quam I B, & maximus
ramorum in ellipſi eſt
I D, & quod quadra-
tum menſuræ I C mi-
nus eſt quadrato I L,
in parabola quidem
quadrato C M, & in
hyperbola, & ellipſi
exemplari applicato
ad C M. Quoniam in
parabola L M poteſt
duplum M C in C H, nempè C I (12. ex primo) & quadratum I L ęqua-
le eſt aggregato duorum quadratorum L M, & M I, quadratum itaque L
I æquale eſt quadrato M I, & M C in C I bis, quæ ſunt æqualia duobus
quadratis C I, M C. Quadratum igitur C I minus eſt quadrato L I qua-
drato ipſius M C, quæ eſt eius abſciſſa, & pariter oſtendetur, quod qua-
dratum C I minus eſt quadrato I K quadrato N C, & minus quadrato I
B quadrato C I, & minus quadrato A I quadrato E C.

37.1.

0046-01
a

38. PROPOSITIO V. & VI.

AT verò in hyperbola, & ellipſi producantur ex Q, O, H lineæ pa-
rallelæ ipſi M C, & quia I C ex hypotheſi æqualis eſt H C, erit I
M æqualis M O, quadratum itaque I M duplum eſt trianguli I M O, & quadratum L M duplum eſt trapezij C M Q H (prima ex 5.) ergo quadra-

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