Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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habeat circulus, uel ellipſis g h ad aliud ſpacium, in quo u:
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<
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xml:space
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">in circulo, uel ellipſi plane deſcribatur rectilinea figura,
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ita ut tãdem relinquãtur portiones minores ſpacio u, quæ
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ſit o p g q r s h t: </
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xml:space
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">ſimili figura in oppoſitis pla-
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nis c d, f e, per lineas ſibi ipſis reſpondentes plana ducãtur. </
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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: </
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<
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xml:space
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">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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">cum igitur portiones ſint minores ſpacio
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u, circulus, uel ellipſis g h ad portiones maiorem propor-
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tionem habebit, quàm linea m k ad K l. </
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<
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circulus uel ellipſis g h ad ipſas portiones. </
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uel ellipſis g h ad figuram rectilineam in ipſa deſcri-
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ptam, ita eſt cylindrus uel cylindri portio c e ad priſma,
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quod rectilineam figuram pro baſi habet, & </
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æqualem; </
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">id, quod infra demonſtrabitur, ergo per conuer
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ſionem rationis, ut circulus, uel ellipſis g h ad portiones re
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lictas, ita cylindrus, uel cylindri portio c e ad ſolidas por-
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tiones, quare cylindrus uel cylindri portio ad ſolidas por-
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tiones eandem proportionem habet, quam linea n k a d _k_
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& </
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">diuidendo priſma, cuius baſis eſt rectilinea figura ad ſo-
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lidas portiones eandem proportionem habet, quam n lad
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1 _k_. </
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<
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<
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xml:id
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xml:space
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">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 figurã, cuius centrũ grauitatis eſt _K_: </
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dinis ex ſolidis portionibus cõpoſitæ grauitatis cẽtrũ erit
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in linea k l protracta, & </
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quitur ergo, ut cẽtrum grauitatis cylindri; </
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">uel cylin dri por
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tionis ſit punctũ k. </
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<
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">At uero cylindrum, uel cylindri portionẽ ce
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ad priſma, cuius baſis eſt rectilinea figura in ſpa-
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cio g h deſcripta, & </
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<
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