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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Educamus inter P Q, A C diametrum I L, & educamus C B ei æ-
quidiſtantem
, &
perpendicularem B E, & ſecemus E l æqualem E A
erit
ſumma ipſarum G E, &
E H æqualis C l; eſtque H E minor quam
M
H, quæ quarta pars eſt ipſius C m;
ergo ſumma ipſarum M G, H E
in
M H quater ſumptum minus eſt quadrato C m:
auferatur communi-
ter
M G, H E in M E quater ſumptum remanebit quadruplum ſummæ
M
G, H E in H E minus quàm quadratum C l (quia M G, H E ſimul
ſumptæ
, nempe M C vna cum A E in M E quater ſumptum æquale eſt
quadrato
l m;
quod eſt duplum M E, & aggregatum C E, A E, nem-
pe
C l in l m bis ſumptum ) igitur aggregatum M G, &
H E in M E
quater
ſumptum ad aggregatum M G, H E in H E quater ſumptum, nẽ-
pe
G E ad H E maiorem proportionem habebit, quàm ad quadratum l
C
.
& componendo M H ad H E, ſeu M H in H A ad E H in H A
habebit
maiorem proportionem, quàm M G, H E in M E quater ſum-
ptum
cum quadrato l C (quæ æqualia ſunt quadrato C m) ad quadra-
tum
l C:
& permutando erit M H in H A ad quadratum C m, nempe
ad
quadratum ſummæ ipſarum M G, &
M H, ſeu quadratum A C ad
quadratum
ſummæ ipſarum P Q, P R (17.
ex 7.) maiorem proportio-
nem
habebit, quàm E H in H A ad quadratum l C (quod eſt æquale
quadrato
ſummæ ipſarum G E, E H ) quod erit vt quadratum A C ad
quadratum
aggregati ipſarum I L, I K:
quapropter A C ad duo latera
figuræ
P Q maiorem proportionem habet, quàm ad duo latera figuræ I
L
.
Et propterea duo latera figuræ P Q minora ſunt, quàm duo latera
432[Figure 432]

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