Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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nium linearum figurę, GOQ, hac lege producta, complectetur eas,
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quæ de ip. </
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<
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">a manent in figuris iam diſpoſitis, ergo omnes lineæ figu-
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ræ, GOQ, ſic productæ complectentur omnes lineas figurarum ſic
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diſpoſitarum, ergo erunt ad illas ſimul ſumptas, vt totum ad partem,
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nam illæ in his reperientur, & </
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<
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">aliquid amplius, ergo erunt illis ma-
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iores, omnes lineę autem figurarum ſic diſpoſitarum ſunt non mino-
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res omnibus lineis figuræ, EAG, ex qua deſumptæ ſunt, ergo om-
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nes lineę figurę, GOQ, ſic productæ ſunt, vt effectæ fuerint maio-
<
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res omnibus lineis figurę, EAG; </
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<
s
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xml:space
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">eodem pacto oſtendemus nos poſ-
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ſe vice verſa iſtas illis efficere maiores, ergo omnes lineæ figurarum,
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EAG, GOQ, ſumptæ cum regulis vtcumque ſuppoſitis, cuiuſuis
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">Diffin. 4.
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1.5. Elem.</
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ſint altitudinis ſumptę iux-
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ta eaſdem regulas, ſunt
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magnitudines inter ſe ra-
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tionem habentes, quod ſi
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ſubter rectam, HQ, ad-
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huc eſſent portiones con-
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ſideratarum à nobis figu-
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rarum, EAG, GOQ, eo-
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dem modo oſtenderemus omnes lineas earundem ſumptas, cum ijſ-
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dem regulis eſſe magnitudines rationem inter ſe habentes, vnde inte-
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grarum figurarum omnes lineę eſſent magnitudines inter ſe rationem
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habentes, quod in fig. </
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<
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">In ſiguris autem ſolidis conſimiliter procedemus; </
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<
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xml:space
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">nam ſi in ſupe-
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riori figura intellexerimus, EAG, GOQ, eſſe figuras ſolidas, & </
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pro rectis lineis æquidiſtantibus intellexerimus plana æquidiſtantia,
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vt pro rectis, EG, GQ, plana, EG, GQ, quibus plana, LM, N
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S, ſint æquidiſtanter ducta, ſumptis pro regulis planis, EG, GQ,
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ijſque in directum ſibi conſtitutis.</
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<
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">ita vt iaceant regulæ in eodem
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plano, oſtendemus nos poſſe ita producere omnia plana ſolidæ figu-
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ræ, GOQ, vt eadem complectantur omnia plana figuræ, EAG,
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(ſi ſint eiuſdem altitudinis dictæ figuræ) integræ exiſtentis, vel (ſi
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non ſint) diuiſæ in figuras ſolidas, ex. </
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<
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">EBDG, BAD, ſic di-
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ſpoſitas, vt baſes, ſiue regulę iaceant in eodem plano, & </
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<
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">ita, vt om-
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nia plana dictarum ſigurarum ſolidarum, vel ſint intra oppoſita pla-
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na dictas figuras tangentia, vel nihil eorum extra, vnde omnia pla-
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na figuræ ſolidæ, GOQ, ſic producta fient totum, & </
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eiſdem captæ in figura ſolida, EAG, integra, vel diuiſa, vt dictum
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eſt.</
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<
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">omnia plana figuræ, EAG, fient pars omnium planorum fi-
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guræ, GOQ, ſic productorum, nam hæc in illis tota reperientur,
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& </
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<
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">aliquid amplius, vnde omnia plana figuræ, GOQ, ſic producta
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erunt, vt effecta ſint maiora omnibus planis figuræ, EAG; </
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