Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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habeat circulus, uel ellipſis gh ad aliud ſpacium, in quo u:
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& in cit culo, uel ellipſi plane deſcribatur rectilinea figura,
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ita ut
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tãdem
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relinquãtur
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portiones minores ſpacio u, quæ
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ſit opgqrsht:
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deſcriptaq;
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ſimili figura in oppoſitis pla
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nis cd, fe, per lineas ſibi ipſis reſpondentes plana
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abbr
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ducãtur
">ducantur</
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. </
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<
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id
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">Itaque cylindrus, uel cylindri portio diuiditur in priſma,
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cuius quidem baſis eſt figura rectilinea iam dicta, centrum
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que grauitatis punctum K: & in multa ſolida, quæ pro baſi
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bus habent relictas portiones, quas nos ſolidas portiones
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appellabimus. </
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<
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">cum igitur portiones ſint minores ſpacio
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u, circulus, uel ellipſis gh ad portiones maiorem propor
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tionem habebit, quàm linea mk ad Kl. </
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">fiat nk ad Kl, ut
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circulus uel ellipſis gh ad ipſas portiones. </
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s.000341
">Sed ut circulus
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uel ellipſis gh ad figuram rectilineam in ipſa deſcri
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ptam, ita eſt cylindrus uel cylindri portio ce ad priſma,
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quod rectilineam figuram pro baſi habet, & altitudinem
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æqualem; id, quod infra demonſtrabitur. </
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">crgo per conuer
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ſionem rationis, ut circulus, uel ellipſis gh ad portiones re
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lictas, ita cylindrus, uel cylindri portio ce ad ſolidas por
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tiones, quate cylindrus uel cylindri portio ad ſolidas por
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tiones eandem proportionem habet, quam linea nk ad k
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& diuidendo priſma, cuius baſis eſt rectilinea figura ad ſo
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lidas portiones eandem proportionem habet, quam nl ad
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lk & quoniam a cylindro uel cylindri portione, cuius gra
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uitatis centrum eſt l, aufertur priſma baſim habens rectili
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neam
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abbr
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figurã
">figuram</
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, cuius
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abbr
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centrũ
">centrum</
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>
grauitatis eſt K: reſiduæ magnitu
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dinis ex ſolidis portionibus
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abbr
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cõpoſitæ
">compoſitæ</
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grauitatis
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abbr
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cẽtrũ
">centrum</
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>
erit
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in linea kl protracta, & in puncto n; quod eſt
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abſurdũ
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. </
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quitur ergo, ut
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cẽtrum
">centrum</
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grauitatis cylindri; uel cylindri por
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tionis ſit
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abbr
="
punctũ
">punctum</
expan
>
k. </
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<
s
id
="
s.000344
">quæ omnia
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demonſtrãda
">demonſtranda</
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>
propoſuimus.</
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4. huius</
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<
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">At uero cylindrum, uel cylindri
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portionẽ
">portionem</
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ce
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ad priſma, cuius baſis eſt rectilinea figura in ſpa
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cio gh deſcripta, & altitudo æqualis; eandem </
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