Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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5120DE IIS QVAE VEH. IN AQVA. pla. ex quo fit ut pr, rh, fg inter ſe ſint æquales; itémq; æquales
rg
, pf.
eſt enim pg utrique r p, gf communis. Quoniam igitur
hb
ad bg est, ut
31[Figure 31] gb ad bf;
per c
uerſionem
ratio-
mis
erit b h ad
h
g, ut b g ad gf.
eſt autem q h ad
h
b, ut h o ad gb.

nam
ex 35 primi
libri
conicorum,
cum
linea qm
tingat
ſectionem
in
punctom;
erút
h
b, bq æquales;

&
gh ipſius h b
dupla
.
ergo ex æ-
quali
q h ad hg,
ut
ho ad g f;
hoc
eſt
ad hr:
& per
mutando
q h ad
h
o, ut g h ad h r.

rurſus
per conuerſionem rationis h q ad qo, ut h g ad g r;
hoc eſt
p
f:
& propterea ad ipſam cn, quod demonstrandum fuerat.

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