Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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tu, xy ipſi gh æquidiſtare. </
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<
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">Et quoniam triangula, quæ
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fiunt à lineis Ky, yu, us, sh æqualia ſunt inter ſe, & ſimilia
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triangulo Kmh: habebit triangulum Kmh ad
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triangulũ
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K
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y duplam proportionem eius, quæ eſt lineæ kh ad Ky. </
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lb
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<
s
id
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s.000281
">ſed Kh poſita eſt quadrupla ipſius ky. </
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>
<
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id
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s.000282
">ergo triangulum
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kmh ad triangulum K
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foreign
lang
="
grc
">δ</
foreign
>
y
<
expan
abbr
="
eãdem
">eandem</
expan
>
proportionem habebit,
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lb
/>
quam ſexdecim ad
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expan
abbr
="
unũ
">unum</
expan
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: & ad quatuor triangula k
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grc
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y, yu,
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us, s
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">α</
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h habebit eandem, quam ſexdecim ad quatuor, hoc
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eſt quam hK ad ky: & ſimiliter eandem habere demonſtra
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bitur trian
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gulum kmg
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ad quatuor
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/>
<
expan
abbr
="
triãgula
">triangula</
expan
>
K
<
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grc
">δ</
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x, x
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t, t
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r,
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rzg. </
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<
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id
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">quare
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totum trian
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gulum Kgh
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ad omnia tri
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angula gzr,
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r
<
foreign
lang
="
grc
">β</
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t, t
<
foreign
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="
grc
">γ</
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>
x, x
<
foreign
lang
="
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">δ</
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>
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/>
K, K
<
foreign
lang
="
grc
">δ</
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>
y, yu,
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us, s
<
foreign
lang
="
grc
">α</
foreign
>
h ita
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erit, ut hk ad
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ky, hoc eſt
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ut hm ad m
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q. </
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>
<
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id
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">Si igitur in
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triangulis abc, def deſcribantur figuræ ſimiles ei, quæ de
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ſcripta eſt in ghK triangulo: & per lineas ſibi reſponden
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tes plana ducantur: totum priſma af diuiſum erit in tria
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lb
/>
ſolida parallelepipeda y
<
foreign
lang
="
grc
">γ,</
foreign
>
u
<
foreign
lang
="
grc
">β,</
foreign
>
sz, quorum baſes ſunt æqua
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les & ſimiles ipſis parallelogrammis y
<
foreign
lang
="
grc
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>
u
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foreign
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grc
">β,</
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sz: & in octo
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priſmata gzr, r
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grc
">β</
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t, t
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grc
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x, x
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grc
">δ</
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>
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/>
K, k
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grc
">δ</
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y, yu, us, s
<
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">α</
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>
h: quorum
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item baſes æquales, & ſimiles ſunt dictis triangulis; altitu
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do autem in omnibus, totius priſmatis altitudini </
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