Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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225187Conicor. Lib. VI. T ſimilia, pariterque triangula S R K, & Q E Z inter ſe ſimilia; ideoque erit
L B ad B T vt V X ad X H, pariterque Q E ad E Z erit vt S R ad R K;
erat autem prius V X ad X H, vt S R ad R K; igitur L B ad B T eandem
proportionem habebit, quàm Q E ad E Z; & propterea circa roctos angulos B,
E, figuræ ſectionum ſimiles erunt inter ſe. Quod erat oſtendendum.

Notæ in Propoſit. XVI.

ERgo M A ad A P eſt vt O C ad C Q, & angulus O æqualis eſt M,
11a oſtendetur (vt diximus in 11. ex 6.) quod, & c. Sequitur enim ex
æqualitate ordinata, quod M A ad A P eandem proportionem habet, quàm O C
ad C Q, cumque ſint duo ſegmenta parabolica H A G, & K C I, quorũ diame-
tri A M, & C O efficiunt cum baſibus G H, & K I angulos M, & O æquales
inter ſe (cum ſint æquales angulis R A L, & S C N æqualibus à contingentibus

253[Figure 253] verticalibus parallelis baſibus, & à diametris contentis) atque abſcißa M A ad
latus rectum A P eandem proportionem habet, quàm altera abſcißa O C ad C Q
latus rectum alterius ſectionis; igitur duo ſegmenta H A G, & K C I ſimilia
22Lem. 6.
huius. ſunt inter ſe.

Et quia G M poteſt A P in A M, & ſimiliter I O poteſt C Q in C
33b O; ergo P A ad G M eſt, vt C Q ad I O, & G M ad M A eſt, vt I O
ad O C; quia duo ſegmenta ſunt ſimilia, & E A ad A M, eſt vt F C ad
C O; & c. Senſus huius textus confuſi, talis eſt. Quia ſegmenta H A G, &
44Defin. 7.
huius. K C I ſimilia ſupponuntur erit A M ad M G, vt C O ad O I, & quadratum
A M ad quadratum M G erit vt quadratum C O ad quadratum O I; eſt verò
5511. lib. 1. rectangulum P A M æquale quadrato G M; pariterque rectangulum Q C O eſt
æquale quadrato I O; igitur quadratum A M ad rectangulum P A M eandem
proportionem habet, quàm quadratum C O ad rectangulum Q C O; & propte-
rea M A ad A P eandem proportionem habebit, quàm C O ad C Q; ſed prius
oſt enſa fuit P A ad A E, vt Q C ad C F; igitur ex æquali ordinata erit M

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