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