Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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76ARCHIMEDIS
Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
ipſis ſectionibus in eandem proportionem ſecari.
eſt enim
diuidendo, conuertendoque cm ad mb, &
cf ad fb, ut
ce ad ea.
LEMMA III.
Sed & illud constare potest; lineas, quæ in portioni-
bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
les angulos contineant, ab ipſis ſimiles quoque portiones
abſcindere:
hoc eſt, ut in propoſita figura, portiones h b c,
m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
ſimiles eſſe.
D_ividantvr_ enim ch, cm bifariam in punctis p q: & per
ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes.
erit portio-
nis b s c diameter p s, &
portionis m u c diameter q u. Itaque fiat
ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
quæ ſit s x:
& ut quadratum c t ad quadratum c q, ita fiat f o ad
u y.
iam exijs
47[Figure 47] quæ demóſtra
uimus in com-
mentarijs in
quartam pro-
poſitioné.
Ar-
chrmedis de co
noidibus, &

ſphæroidibus,
patet quadra-
tum c p æqua-
le eſſe rectan-
gulo p s x:

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