Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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uel coni portionis axis à centro grauitatis ita diui
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ditur, ut pars, quæ terminatur ad uerticem reli
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quæ partis, quæ ad baſim, ſit tripla.</
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<
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id
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">Sit pyramis, cuius baſis triangulum abc; axis de; & gra
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uitatis centrum K. </
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<
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id
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s.000574
">Dico lineam dk ipſius Ke triplam eſſe. </
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<
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id
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s.000575
">trianguli enim bdc centrum grauitatis ſit punctum f;
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abbr
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triã
">trian</
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>
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guli adc
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abbr
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centrũ
">centrum</
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>
g; & trianguli adb ſit h: & iungantur af,
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b g, ch. </
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>
<
s
id
="
s.000576
">Quoniam igitur
<
expan
abbr
="
centrũ
">centrum</
expan
>
grauitatis pyramidis in axe
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arrow.to.target
n
="
marg66
"/>
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/>
<
expan
abbr
="
cõſiſtit
">conſiſtit</
expan
>
:
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expan
abbr
="
ſuntq;
">ſuntque</
expan
>
de, af, bg, ch
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expan
abbr
="
eiuſdẽ
">eiuſdem</
expan
>
pyramidis axes: conue
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/>
nient omnes in
<
expan
abbr
="
idẽ
">idem</
expan
>
<
expan
abbr
="
punctũ
">punctum</
expan
>
k, quod eſt grauitatis centrum. </
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>
<
lb
/>
<
s
id
="
s.000577
">Itaque animo concipiamus hanc pyramidem diuiſam in
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/>
quatuor pyramides, quarum baſes ſint ipſa pyramidis
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/>
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number
="
57
"/>
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/>
triangula; &
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emph
type
="
ul
"/>
axis
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emph.end
type
="
ul
"/>
pun
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/>
ctum k quæ quidem py
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lb
/>
ramides inter ſe æquales
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ſunt, ut
<
expan
abbr
="
demõſtrabitur
">demonſtrabitur</
expan
>
. </
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>
<
lb
/>
<
s
id
="
s.000578
">Ducatur
<
expan
abbr
="
enĩ
">enim</
expan
>
per lineas
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lb
/>
dc, de planum
<
expan
abbr
="
ſecãs
">ſecans</
expan
>
, ut
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lb
/>
ſit ipſius, & baſis abc
<
expan
abbr
="
cõ
">com</
expan
>
<
lb
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munis ſectio recta linea
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cel:
<
expan
abbr
="
eiuſdẽ
">eiuſdem</
expan
>
uero &
<
expan
abbr
="
triã-guli
">trian
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lb
/>
guli</
expan
>
adb ſit linea dhl. erit linea al æqualis ipſi
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lb: nam centrum graui
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tatis trianguli conſiſtit
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in linea, quæ ab angulo
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ad dimidiam baſim per
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ducitur, ex tertia deci
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ma Archimedis. </
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>
<
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<
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id
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s.000579
">quare
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triangulum acl æquale
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eſt triangulo bcl: & propterea pyramis, cuius baſis trian
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gulum acl, uertex d, eſt æqualis pyramidi, cuius baſis bcl
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<
arrow.to.target
n
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marg69
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triangulum, & idem uertex. </
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>
<
s
id
="
s.000580
">pyramides enim, quæ ab
<
expan
abbr
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eodẽ
">eodem</
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