Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
nea h m ad li-
Figure: /permanent/library/4E7V2WGH/figures/0050-01 not scanned
[Figure 30]
neam fc.
at uero
ut h m ad f c, ita
o h ad a f:
& ut
quadratum h m
ad quadratú g l,
ita linea h b ad
b g;
hoc est b g
ad b f.
ex quibus
ſequitur o h ad
a f ita eſſe, ut b g
ad b f:
& permu
tando oh ad b g,
ut a f ad f b.
ſed
eſt a f dupla ip-
ſius fb:
ſunt eni
a b, b f æquales
ex 35 primi libri
conicorum.
ergo
&
h o ipſius g b
eſt dupla.
quod demonſtrare oportebat.

LEMMA IIII.

Iiſdem manentibus, & à puncto m ducta m q uſque
ad diametrum, quæ ſectionem in puncto m conting at;
Dico h q ad q o eandem proportionem habere, quam
habet g h ad c n.
F_IAT_ enim h r æqualis g f. & cumtriangula a f c, o p n ſimi
lia ſint, &
p n ſit æqualis f c; eodem modo demonſtrabimus p o, f a
inter ſe æquales eſſe.
quare p o ipſius f b dupla erit. Sed eſt h o du
pla g b.
ergo & reliqua p h reliquæ f g; uidelicet ipſius r h eſt du-

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