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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185147Conicor. Lib. VI. ſectioni A C; quia ſi eſſet æqualis illi, facta ſuperpoſitione, ſibi mutuò
congruerent, & caderent puncta E, F, L, I, ſuper B, C, G, K, & eſſet
F I æqualis C G, atque E L æqualis B K; ideoque quadratũ F I ad qua-
dratum E L eſſet, vt D I ad D L (19. ex 1.) eſſetque quadratum C G
1120. lib. 1. ad quadratum K B, vt A G ad K A, quod eſt abſurdum; quia illius pro-
portio ad iſtam eſt, vt H G in G A ad H K in K A (20. ex 1.) Igitur
2221. lib. 1 ſectio parabolica non eſt æqualis ſectioni hyperbolæ, nec ſectio aliqua.
æqualis eſt ſectioni, quæ non ſit eiuſdem generis; Et hoc erat oſten-
dendum.

PROPOSITIO VI.

QVælibet duæ ſectiones A B C, & D H F, quarum portio
33a vnius ſuperpoſita portioni alterius congruit, ſunt æquales
inter ſe.

192[Figure 192]

Alioquin congruat portio B C portio-

193[Figure 193] ni E F, at non cadat portio A B ſuper
D E, ſed cadat in ſitu E G, & educamus
lineam tangentem duas ſectiones in H, &
4434. lib. 1. educamus E I, D G F parallelas tangen-
ti; & ex H ad ſemipartitionem ipſius E I
ducatur H K, quæ occurrat D F in L.
Et quia H L ſecat bifariam lineam paral-
lelam tangenti ab eius termino ductæ;
ergo eſt diameter vniuerſæ ſectionis (5.
557. lib. 2. ex 2.) quare bifariam ſecat vnamquan-
que ex D F, G F, & fiet D L æqualis G
L, quod eſt abſurdum: igitur ſectio A B
C tota congruit ſectioni D H F. Quod
erat oſtendendum.

PROPOSITIO VII.

DVæ ordinationes axis in qualibet coniſectione abſcindunt
66a à ſectione ex vtraque parte axis duas portiones, quarum
ſi vna alteri ſuperponatur ſibi mutuò congruent, nec congruunt
alicui aliæ portioni ſectionis.

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