Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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eani proportionem habeat, quam a b c d fruſtum ad por-
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tionem a g d; </
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<
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xml:space
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</
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<
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<
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xml:space
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">componendo K l ad 1 h proportionem eandem,
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quam portio conoidis b gc ad a g d portionem. </
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<
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">20. I. coni
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corum.</
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niam quadratum b f ad quadratum a e, hoc eſt quadratum
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b c ad quadratum a d eſt, ut linea f g ad g e: </
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<
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xml:space
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">erunt duæ ter-
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tiæ quadrati b c ad duas tertias quadrati a d, ut h g ad g _k_:
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</
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<
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xml:space
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<
s
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xml:space
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">ſi à duabus tertiis quadrati b c demptæ fuerint duæ ter-
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tiæ quadrati a d: </
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<
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">erit diuidẽdo id, quod relinquitur ad duas
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tertias quadrati a d, ut h k ad k g. </
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<
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xml:space
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">Rurſus duæ tertiæ quadra
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ti a d ad duas tertias quadrati b c ſunt, ut _k_ g ad g h: </
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<
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xml:space
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<
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xml:space
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tertiæ quadrati b c ad tertiã partẽ ipſius, ut g h ad h f. </
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<
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ex æ quali id, quod relinquitur ex duabus tertiis quadrati
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b c, demptis ab ipſis quadrati a d duabus tertiis, ad tertiã
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partem quadrati b c, ut _k_ h ad h f: </
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<
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<
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">ad portionem eiuſdẽ
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tertiæ partis, ad quam unà cum ipſa portione, duplam pro
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portionem habeat eius, quæ eſt quadrati b c ad quadratũ
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a d, ut K 1 ad 1 h. </
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<
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xml:space
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">habet enim _K_l ad 1 h ean dem proportio-
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nem, quam conoidis portio b g c ad portionem a g d: </
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tio autem b g c ad portionem a g d duplam proportionem
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habet eius, quæ eſt baſis b c ad baſim a d: </
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<
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b c ad quadratum a d; </
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dempto a d quadrato à duabus tertiis quadrati b c, erit id,
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quod relin quitur unà cum dicta portione tertiæ partis ad
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reliquam eiuſdem portionem, ut el ad 1 f. </
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<
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">Cum igitur cen-
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trum grauitatis fruſti a b c d ſit l, à quo axis e f in eam, quã
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diximus, proportionem diuidatur; </
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<
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">conſtat uerũ eſſe illud,
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quod demonſtrandum propoſuimus.</
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GRAVITATIS SOLIDORVM.</
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