Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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23
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eſt ſolidi gm altitudo ad oe altitudinem ſolidi mc, uel
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abbr
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quã
">quam</
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axis kq ad ql axem. </
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<
s
id
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s.000470
">Si uero axis kl non ſit perpendicularis
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ad planum baſis; ducatur a puncto k ad idem planum per
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pendicularis kr,
<
expan
abbr
="
occurrẽs
">occurrens</
expan
>
plano mnop in s. </
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>
<
s
id
="
s.000471
">ſimiliter
<
expan
abbr
="
de-mõſtrabimus
">de
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lb
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monſtrabimus</
expan
>
ſolidum gm ad
<
expan
abbr
="
ſolidũ
">ſolidum</
expan
>
mc ita eſſe, ut axis kq
<
lb
/>
ad axem ql. </
s
>
<
s
id
="
s.000472
">Sed ut Kq ad ql, ita ks altitudo ad altitudi
<
lb
/>
<
arrow.to.target
n
="
marg52
"/>
<
lb
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nem sr; nam lineæ Kl, Kr à planis æquidiſtantibus in eaſ
<
lb
/>
dem proportiones ſecantur. </
s
>
<
s
id
="
s.000473
">ergo ſolidum gm ad ſolidum
<
lb
/>
mc
<
expan
abbr
="
eandẽ
">eandem</
expan
>
proportionem habet, quam altitudo ad
<
expan
abbr
="
altitudinẽ
">altitu
<
lb
/>
dinem</
expan
>
, uel quam axis ad axem. </
s
>
<
s
id
="
s.000474
">quod
<
expan
abbr
="
demõſtrare
">demonſtrare</
expan
>
oportebat.</
s
>
</
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type
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margin
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<
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id
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s.000475
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id
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25 undeci
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lb
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mi.</
s
>
</
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<
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type
="
margin
">
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s
id
="
s.000476
">
<
margin.target
id
="
marg51
"/>
<
expan
abbr
="
ſextĩ
">ſextim</
expan
>
.</
s
>
</
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type
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margin
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id
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s.000477
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17. unde
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cimi</
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<
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">
<
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id
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s.000478
">THEOREMA XV. PROPOSITIO XIX.</
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>
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type
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<
s
id
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">Solida parallelepipeda in eadem baſi, uel in
<
lb
/>
æqualibus baſibus conſtituta eam inter ſe propor
<
lb
/>
tionem habent, quam altitudines: & ſi axes ipſo
<
lb
/>
rum cum baſibus æquales angulos contineant,
<
lb
/>
eam quoque, quam axes proportionem
<
expan
abbr
="
habebũt
">habebunt</
expan
>
.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000480
">Sint ſolida parallelepipeda in
<
expan
abbr
="
eadẽ
">eadem</
expan
>
baſi
<
expan
abbr
="
cõſtituta
">conſtituta</
expan
>
abcd,
<
lb
/>
abef: & ſit ſolidi abcd altitudo minor: producatur au
<
lb
/>
tem planum cd adeo, ut ſolidum abef ſecet; cuius ſectio
<
lb
/>
<
figure
id
="
id.023.01.053.1.jpg
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xlink:href
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number
="
44
"/>
<
lb
/>
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arrow.to.target
n
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marg53
"/>
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ſit gh. </
s
>
<
s
id
="
s.000481
">
<
expan
abbr
="
erũt
">erunt</
expan
>
ſoli
<
lb
/>
da abcd, abgh
<
lb
/>
in eadem baſi,
<
lb
/>
& æquali altitu
<
lb
/>
dine inter ſe æ
<
lb
/>
qualia. </
s
>
<
s
id
="
s.000482
">
<
expan
abbr
="
Quoniã
">Quoniam</
expan
>
<
lb
/>
igitur ſolidum
<
lb
/>
abef ſecatur
<
lb
/>
plano baſibus
<
lb
/>
<
expan
abbr
="
æquidiſtãte
">æquidiſtante</
expan
>
, erit
<
lb
/>
<
arrow.to.target
n
="
marg54
"/>
<
lb
/>
ſolidum ghef
<
lb
/>
adipſum abgh </
s
>
</
p
>
</
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>
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>
</
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>
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