Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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134FED. COMMANDINI t u, x y ipſi g h æquidiſtare. Et quoniam triangula, quæ
fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, &
ſimilia
triangulo K m h:
habebit triangulum K m h ad triangulũ
1119. ſexti K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
ſed _K_ h poſita eſt quadrupla ipſius k y. ergo triangulum
κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
ad quatuor triangula k δ y, y u,
u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
eſt quam h K ad κ y:
& ſimiliter eandem habere demonſtra
bitur trian-
gulum κ m g
triãgula K δ
x, x γ t, t β r,
r z g.
quare
222. uel 121
quinti.
totum trian
gulum K g h
angula g z r,
r β t, t γ x, x δ
_K_, K δ y, y u,
u s, s α h ita
erit, ut h κ a d
k y, hoc eſt
q.
Si igitur in
triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
ſcripta eſt in g h K triangulo:
& per lineas ſibi reſp onden-
tes plana ducantur:
totum priſma a f diuiſum eritin tria
ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
les &
ſimiles ipſis parallelogrammis y γ, u β, s z: & in octo
priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h:
quorum
item baſes æquales, &
ſimiles ſunt dictis triangulis; altitu-
do autem in omnibus, totius priſmatis altitudini æ qualis.