Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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culi, uel ellipſes cd, ef ab ad circulum, uel ellipſim ab. </
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<
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id
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s.000702
">In
<
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telligatur pyramis q baſim habens æqualem tribus rectan
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gulis ab, ef, cd; & altitudinem
<
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abbr
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eãdem
">eandem</
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, quam fruſtum ad. </
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<
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/>
<
s
id
="
s.000703
">intelligatur etiam conus, uel coni portio q, eadem altitudi
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ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus ab,
<
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ef, cd æqualis. </
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>
<
s
id
="
s.000704
">poſtremo intelligatur pyramis alb, cuius. </
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>
<
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<
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id
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s.000705
">baſis ſit rectangulum mnop, & altitudo eadem, quæ fru
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ſti:
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expan
abbr
="
itemq,
">itemque</
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>
intelligatur conus, uel coni portio alb, cuius
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lb
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baſis circulus, uel ellipſis circa diametrum ab, & eadem al
<
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/>
<
arrow.to.target
n
="
marg86
"/>
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titudo. </
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<
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id
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s.000706
">ut igitur rectangula ab, ef, cd ad rectangulum ab,
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ita pyramis q ad pyramidem alb; & ut circuli, uel ellip
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ſes ab, ef, cd ad ab circulum, uel ellipſim, ita conus, uel co
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ni portio q ad conum, uel coni portionem alb. </
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>
<
s
id
="
s.000707
">conus
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igitur, uel coni portio q ad conum, uel coni portionem
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alb eſt, ut pyramis q ad pyramidem alb. </
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>
<
s
id
="
s.000708
">ſed pyramis
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lb
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alb ad pyramidem agb eſt, ut altitudo ad altitudinem, ex
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20. huius: & ita eſt conus, uel coni portio alb ad conum,
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uel coni portionem agb ex 14. duodecimi elementorum,
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& ex iis, quæ nos demonſtrauimus in commentariis in un
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decimam de conoidibus, & ſphæroidibus, propoſitione
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quarta. </
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>
<
s
id
="
s.000709
">pyramis autem agb ad pyramidem cgd propor
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tionem habet compoſitam ex proportione baſium & pro
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lb
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portione altitudinum, ex uigeſima prima huius: & ſimili
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ter conus, uel coni portio agb ad conum, uel coni portio
<
lb
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nem cgd proportionem habet
<
expan
abbr
="
compoſitã
">compoſitam</
expan
>
ex eiſdem pro
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portionibus, per ea, quæ in dictis commentariis demon
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ſtrauimus, propoſitione quinta, & ſexta: altitudo enim in
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utriſque eadem eſt, & baſes inter ſe ſe eandem habent pro
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portionem. </
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>
<
s
id
="
s.000710
">ergo ut pyramis agb ad pyramidem cgd, ita
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eſt conus, uel coni portio agb ad agd conum, uel coni
<
lb
/>
portionem: & per
<
expan
abbr
="
conuerſionẽ
">conuerſionem</
expan
>
rationis, ut pyramis agb
<
lb
/>
ad
<
expan
abbr
="
ſruſtũ
">fruſtum</
expan
>
à pyramide abſciſſum, ita conus uel coni portio
<
lb
/>
agb ad fruſtum ad. </
s
>
<
s
id
="
s.000711
">ex æquali igitur, ut pyramis q ad fru
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/>
ſtum à pyramide abſciſſum, ita conus uel coni portio q ad </
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