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

Conicor. Lib. VII. guli ex ſumma extremorum, vel intermediorum in differentiam mini-
morum ſegmentorum, ſcilicet ex G A cum H E in E A.

322.1.

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Quia duplum rectanguli G A H cum duplo rectanguli G A E æquatur duplo
rectanguli ſub G A in H E, addito cõmuniter duplo rectanguli H E A erit du-
plum rectanguli G E H æquale duplo rectanguli G A H cum duplo rectanguli ex
ſumma G A, H E in E A; & addito communi quadrato G H, erit duplum
rectanguli G E H cum quadrato G H, ſcilicet duo quadrata ex G E, & ex E
H, erunt æqualia illis om-
nibus ſpatijs, ſcilicet duplo
rectanguli ex ſumma G A,
H E in E A cum duplo re-
ctanguli G A H ſimul cum
quadrato ex G H: ſed duplo
rectanguli G A H cum quadrato G H æqualia ſunt duo quadrata ex G A,
& ex A H, ergo duo quadrata ex G E, & ex E H æqualia erunt quadratis ex
G A, & ex A H cum duplo rectanguli ex G A; & H E in E A, quod erat
oſtendendum.

322.1.

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323. LEMM A XII.

IN hyperbola, cuius axis A C, erectus A F, præſectæ C G, H A,
centrum D, atque diameter I L, eiuſque erectus I K, & latus
C E, pariterque altera diameter Q P, cuius erectus P R, & latus
C O: dico quod duplum rectanguli ex G E cũ O H in H E à duobus
quadratis ex G E, & ex E H; nec non quadrata Q P, & P R late-
rum figuræ diametri Q P à quadratis ex L I, & ex I K, vel ex C A,
& ex A F, vna deficiunt, aut vna æqualia ſunt, vel vna exce-
dunt.

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