Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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[Figure 81]
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[Figure 82]
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[Figure 83]
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<
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">Sint duo priſmata ae, af, quorum eadem baſis quadri
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latera abcd:
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ſitq;
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priſmatis ae altitudo eg; & priſmatis
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af altitudo fh. </
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<
s
id
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s.000518
">Dico priſma ae ad priſma af eam habere
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proportionem, quam eg ad fh. </
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<
s
id
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s.000519
">iungatur enim ac: & in
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unoquoque priſmate duo priſmata intelligantur, quorum
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baſes ſint triangu
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la abc, acd. </
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<
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id
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s.000520
">habe
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bunt duo priſma
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te in eadem baſi
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lb
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abc conſtituta,
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lb
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proportionem
<
expan
abbr
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eã
">eam</
expan
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dem, quam ipſo
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rum altitudines e
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g, fh, ex iam de
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monſtratis. </
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<
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id
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s.000521
">& ſi
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militer alia duo,
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quæ ſunt in baſi a
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marg62
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c d. </
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<
s
id
="
s.000522
">quare totum priſma ae ad priſma af eandem propor
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tionem habebit, quam altitudo eg ad fh altitudinem. </
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>
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lb
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<
s
id
="
s.000523
">Quòd cum priſmata ſint pyramidum tripla, & ipſæ pyrami
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des, quarum eadem eſt baſis quadrilatera, & altitudo priſ
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matum altitudini æqualis, eam inter ſe proportionem ha
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bebunt, quam altitudines.</
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12. quinti</
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<
s
id
="
s.000525
">Si uero priſmata baſes æquales habeant,
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expan
abbr
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nõ
">non</
expan
>
eaſdem, ſint
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lb
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duo eiuſmodi priſmata ae, fl: & ſit baſis priſmatis ae qua
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drilaterum abcd; & priſmatis fl quadrilaterum fghk. </
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>
<
lb
/>
<
s
id
="
s.000526
">Dico priſma ae ad priſma fl ita eſſe, ut altitudo illius ad
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huius altitudinem. </
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>
<
s
id
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s.000527
">nam ſi altitudo ſit eadem,
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expan
abbr
="
intelligãtur
">intelligantur</
expan
>
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marg63
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duæ pyramides abcde, fghkl. </
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<
s
id
="
s.000528
">quæ
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expan
abbr
="
ĩtcrſe
">interſe</
expan
>
æquales
<
expan
abbr
="
erũt
">erunt</
expan
>
,
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lb
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cum æquales baſes, & altitudinem eandem habeant. </
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>
<
s
id
="
s.000529
">quare
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marg64
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& priſmata ae, fl, quæ ſunt
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abbr
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harũ
">harum</
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>
pyramidum tripla, æqua
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lia ſint neceſſe eſt. </
s
>
<
s
id
="
s.000530
">ex quibus perſpicue conſtat
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abbr
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propoſitũ
">propoſitum</
expan
>
. </
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<
s
id
="
s.000531
">Si uero altitudo priſmatis fl ſit maior, à priſmate fl ab
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ſcindatur priſma fm, quod æque altum ſit,
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atq;
">atque</
expan
>
ipſum ae. </
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