Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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NX, & </
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demus?</
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">? omnia quadrata parallelogrammi, SF, ad om-
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nia quadrata fruſti hyperbolæ, HDFG, eſſe vt rectangu-
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lum, OEN, ad rectangulum ſub, OE, &</
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<
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ctangulo ſub compoſita ex. </
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<
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</
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<
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">Omnia verò quadrata trianguli, DMF, ad omnia quadra-
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ta eiuſdem fruſti, HDFG, eſſe vt rectangulum, OEN, ad
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rectangulum ſub, OE, & </
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<
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ſub compoſita ex, NX, & </
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<
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<
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">per ipſum regulæ,
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DF, parallela ducatur, LK, curuam hyp rbolicam in, I, ſecans;
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Eſt ergo quadratum, EF, vel quadratum,
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LK, ad quadratum, LI, vt rectangulum,
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OEN, adrectangulum, OLN; </
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<
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parallelogrammum, MF, in eadem baſi, & </
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altitudine cum figura, MGFE, punctum,
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L, ſumptum eſt vt cunque, perq; </
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<
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gulæ, DF, ducta parallela, LK, repertum
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eſt, vt quadratum, KL, ad quadratum, LI,
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ita eſſe rectangulum, OEN, ad rectangulũ,
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OLN; </
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<
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">quatuor ergo ordinum magnitudi-
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nes conſtructæ iuxta has quatuor inuentas
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magnitudines proportionales, erunt quoq;
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</
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<
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omnia quadrata figuræ, MGFE, quæ ſunt
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magnitudines primi, & </
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<
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<
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26. l. 2.</
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ſecundam .</
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<
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<
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rectangula ſub maximis abſciſſarum, EM, adiuncta, MO, & </
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maximis abſciſſarum, EM, adiuncta, MN, ad rectangula ſub om-
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nibus abſciſsis, EM, adiuncta, MO, & </
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adiuncta, MN, quæ ſunt magnitudines tertij, & </
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collectæ iuxta tertiam, & </
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OLN; </
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<
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MO, & </
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ſciſsis, EM, adiuncta, MO, & </
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<
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l. 2.</
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recti vel eiuſdem obliqui tranſitus ſumptis, ſunt, vt rectangulum,
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OEN, ad rectangulum ſub, OE, &</
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compoſita ex {1/2}. </
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ta, MF, ad omnia quadrata figuræ, GMEF, vel horum quadru-
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pla .</
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