Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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023/01/031.jpg
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Itaque ſolidi parallelepipedi y
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centrum grauitatis eſt in
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linea
<
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ſolidi u
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centrum eſt in linea
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& ſolidi sz in li
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nea
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m, quæ quidem lineæ axes ſunt, cum planorum oppo
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ſitorum centra coniungant. </
s
>
<
s
id
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s.000285
">ergo magnitudinis ex his ſoli
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dis compoſitæ centrum grauitatis eſt in linea
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m, quod ſit
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<
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; & iuncta
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">θ</
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o producatur: à puncto autem h ducatur h
<
foreign
lang
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">α</
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>
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ipſi mk æquidiſtans, quæ cum
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o in
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grc
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conueniat. </
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>
<
s
id
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s.000286
">triangu
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lum igitur ghk ad omnia triangula gzr,
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foreign
lang
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grc
">β</
foreign
>
t, t
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lang
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grc
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>
x, x
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foreign
lang
="
grc
">δ</
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>
k,
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k
<
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lang
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grc
">δ</
foreign
>
y, yu, us, s
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lang
="
grc
">α</
foreign
>
h eandem habet proportionem, quam hm
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lb
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ad mq ; hoc eſt, quam
<
foreign
lang
="
grc
">μθ</
foreign
>
ad
<
foreign
lang
="
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">θλ·</
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>
nam ſi hm,
<
foreign
lang
="
grc
">μθ</
foreign
>
produci in
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lb
/>
telligantur, quouſque coeant; erit ob linearum qy, mk æ
<
lb
/>
quidiſtantiam, ut hq ad qm, ita
<
foreign
lang
="
grc
">μλ</
foreign
>
ad ad
<
foreign
lang
="
grc
">λθ·</
foreign
>
& componen
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lb
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do, ut hm ad mq, ita
<
foreign
lang
="
grc
">μθ</
foreign
>
ad
<
foreign
lang
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">θλ.</
foreign
>
</
s
>
<
s
id
="
s.000287
"> linea uero
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foreign
lang
="
grc
">θ</
foreign
>
o maior eſt,
<
lb
/>
<
arrow.to.target
n
="
marg40
"/>
<
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/>
quàm
<
foreign
lang
="
grc
">θλ·</
foreign
>
habebit igitur
<
foreign
lang
="
grc
">μθ</
foreign
>
ad
<
foreign
lang
="
grc
">θλ</
foreign
>
maiorem proportio
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/>
nem, quàm ad
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">θ</
foreign
>
o. </
s
>
<
s
id
="
s.000288
">quare triangulum etiam ghk ad omnia
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lb
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iam dicta triangula maiorem
<
expan
abbr
="
proportionẽ
">proportionem</
expan
>
habebit, quàm
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lb
/>
<
foreign
lang
="
grc
">μθ</
foreign
>
ad
<
foreign
lang
="
grc
">θ</
foreign
>
o. </
s
>
<
s
id
="
s.000289
">ſed ut
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
ghk ad omnia triangula, ita
<
expan
abbr
="
to-tũ
">to
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lb
/>
tum</
expan
>
priſma afad omnia priſmata gzr, r
<
foreign
lang
="
grc
">β</
foreign
>
t, t
<
foreign
lang
="
grc
">γ</
foreign
>
x, x
<
foreign
lang
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grc
">δκ, κδ</
foreign
>
y,
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yu, us, s
<
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">α</
foreign
>
h: quoniam enim ſolida parallelepipeda æque al
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/>
ta, eandem inter ſe proportionem habent, quam baſes; ut
<
lb
/>
ex trigeſimaſecunda undecimi elementorum conſtat. </
s
>
<
s
id
="
s.000290
">ſunt
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/>
<
arrow.to.target
n
="
marg41
"/>
<
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/>
autem ſolida parallelepipeda priſmatum triangulares ba
<
lb
/>
<
arrow.to.target
n
="
marg42
"/>
<
lb
/>
ſes habentium dupla: ſequitur, ut etiam huiuſmodi priſ
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lb
/>
mata inter ſe ſint, ſicut eorum baſes. </
s
>
<
s
id
="
s.000291
">ergo totum priſma ad
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lb
/>
omnia priſmata maiorem proportionem habet, quam
<
foreign
lang
="
grc
">μθ</
foreign
>
<
lb
/>
<
arrow.to.target
n
="
marg43
"/>
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/>
ad
<
foreign
lang
="
grc
">θ</
foreign
>
o: & diuidendo ſolida parallelepipeda y
<
foreign
lang
="
grc
">γ,</
foreign
>
u
<
foreign
lang
="
grc
">β,</
foreign
>
sz ad o
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lb
/>
mnia priſmata proportionem habent maiorem, quàm
<
foreign
lang
="
grc
">μ</
foreign
>
o
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lb
/>
ad o
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foreign
lang
="
grc
">θ</
foreign
>
. </
s
>
<
s
id
="
s.000292
">fiat
<
foreign
lang
="
grc
">ν</
foreign
>
o ad o
<
foreign
lang
="
grc
">θ,</
foreign
>
ut ſolida parallelepipeda y
<
foreign
lang
="
grc
">γ,</
foreign
>
u
<
foreign
lang
="
grc
">β,</
foreign
>
sz ad
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lb
/>
omnia priſmata. </
s
>
<
s
id
="
s.000293
">Itaque cum à priſmate af, cuius
<
expan
abbr
="
cẽtrum
">centrum</
expan
>
<
lb
/>
grauitatis eſt o, auferatur magnitudo ex ſolidis parallelepi
<
lb
/>
pedis y
<
foreign
lang
="
grc
">γ,</
foreign
>
u
<
foreign
lang
="
grc
">β,</
foreign
>
sz conſtans: atque ipſius grauitatis centrum
<
lb
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ſit
<
foreign
lang
="
grc
">θ·</
foreign
>
reliquæ magnitudinis, quæ ex omnibus priſmatibus
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lb
/>
conſtat, grauitatis centrum erit in linea
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foreign
lang
="
grc
">θ</
foreign
>
o producta: &
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in puncto
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">f</
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>
, ex octava propoſitione eiusdem libri </
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>
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