Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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FI, ad omnia quadrata circuli, vel ellipſis, CFEH, eſſe
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vt cylindricum ſub, MI, & </
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<
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">portione, TCFE Y, vna cum,
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{1/6}, cubi, TY, pro circulo, pro ellipſi verò, vna cum ſæpius
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dicta parte cubi, TY, vel parallelepipedi ſub, RV, & </
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bo, RZ, ad, {2/3}, parallelepipedi ſub, AD, & </
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mo, AQ, ideſt, in circulo ad, {1/6}, cubi, FH.</
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">quadrata figurę, LCFE G, demptis omnibus quadra-
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tis trilineorum, CLT, YGE, ad omnia quadrata, AG, ſunt vt cy-
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lindricus ſub, MI, & </
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<
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">portione, TCFE Y, vna cum, {1/6}, cubi, TY,
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pro circulo, pro ellipſi verò, vna cum ſæpius dicta parte cubi, TY.
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</
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">vel dicti parallelepipedi, ad parallelepipedum ſub, LA, & </
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logrammo, AG; </
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AQ, ſunt vt quadratum, AL, ad quadratum, AD, .</
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P, communi altitudine, vt parallelepipedum ſub, PA, & </
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to, AL, ad parallelepipedum ſub, PA, & </
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vt parallelepipedum ſub, LA, & </
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lelepipedum ſub, DA, & </
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">parallelogrammo, AQ, omnia autem qua-
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drata, AQ, omnium quadratorum circuli, vel ellipſis, CFEH, ſunt
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huius.</
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ſexquialtera .</
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lelogrammo, AQ, ad eiuſdem, {2/3}, ergo ex æquali omnia quadrata
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figuræ, LCFE G, demptis ommbus quadratis trilineorum, CLT,
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YGE, ad omnia quadrata circuli, vel ellipſis, CFEH, erunt vt
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cylindricus ſub, MI, & </
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<
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">portione, TCFEY, vna cum, {1/6}, cubi, T
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Y, pro circulo, pro ellipſi verò, vna cum ſæpius dicta parte cubi, T
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Y, vel parallelepipedi ſub, RV, & </
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pipedi ſub, AD, & </
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cubi, AD, vel cubi, FH, quod oſtendere opus erat.</
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">SIparallelogrammo ſit inſcripta figura quæcunque, ita ta-
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men, vt, ſumpto vno laterum parallelogrammi pro re-
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gula, &</
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">, ductis vtcunque ipſiregulæ parallelis intra paralle-
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logrammum, earum quælibet, vel tota ſit intra figuram in-
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ſcriptam, vel eiuſdem aliqua parte extra figuram exiſtente,
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ac ad vnum laterum parallelogrammi terminante, ad latus
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eiuſdem parallelogrammi prædicto oppoſitum terminet alia
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portio eiuſdem, regulæ æquidiſtantis, ſint autem duæ </
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