Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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omnium quadratorum, CMH, & </
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rum, CMH, vel, CBM, &</
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<
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">, MEF, ſunt autem omnia quadrata
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trianguli, CEG, æqualia omnibus quadratis, AF, cum omnibus
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quadratis triangulorum, CBM, MEF, ergo hæc erunt quadrupla
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omnium quadratorum triangulorum, CBM, MEF, & </
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omnia quadrata, AF, eruntillorum tripla,
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ſunt autem omnia quadrata, AG, ad om-
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nia quadrata, AF, vt quadratum, GE, ad
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quadratum, EF, ideſt quadrupla .</
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<
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</
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">& </
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<
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">omnia quadrata, AF, ſunt omnium
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quadratorum triangulorum, BMC, ME
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F, tripla, ergo omnia quadrata, AG, e-
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runt duodecupla omnium quadratorum
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triangulorum, BMC, MEF, & </
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omnia quadrata, AF, vt 12. </
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<
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<
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nia quadrata, AG, ad omnia quadrata, A
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F, cum omnibus quadratis triangulorum, CBM, MEF, erunt vt
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12. </
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">cum omnibus quadra-
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tis triangulorum, CBM, MEF, æqualia omnibus quadratis trian-
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guli, CEG, vel, AEC, vt oſtenſum eſt, ergo omnia quadrata, A
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G, ad omnia quadrata trianguli, CEG, vel, AEC, ſunt vt 12. </
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ad 4. </
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<
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">_H_Inc patet, ſi ducamus intra parallelogrammum, AG, æquidiftan-
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tem ipſi, EG, vtcunque, RV, ſec antem, CE, in, T, &</
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<
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in, S, quod veluti oſtendimus, RV, æquari vni maximarum abſciſſarum.
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</
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<
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">CG, dum, EG, eſt æqualis ipſi, GC, ita namc oſtendemus quadratum,
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RV, æquari quadrato vnius maxim trum abſciſſarum, CG, & </
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<
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tum, TV, æquari quadrato vnius omnium abſciſſarum, CG, ideſt qua-
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drato, VC; </
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<
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">quadratum verò, RT, æquari quadrato @nius reſiduarum
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omnium abſciſſirum, CG, ideſt quadrato, VG, vnde concludemus om-
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nia quadrata, AG, regula, EG, æquari quadratis maximarum abſciſ-
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ſarum, CG, & </
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<
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">omnia quadrata triangult, CEG, æquari quadratis om-
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nium abſciſſarum, CG, & </
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<
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">omnia quadrata trianguli, AEC, æquari
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quadratis reſiduarum omnium abſciſſarum, CG, & </
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">rectangula ſub tri-
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angulis, AEC, CEG, æquari rectangu is ſub omnibus abſctſſis, & </
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ſiduis omnium abſciſſarum, CG, ita ſumptis, vt quoduts rectangulum
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intelligatur ſub vna abſciſſirum, & </
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<
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mus omnia quadrata, AG, tripla eſſe omnium quadratorum </
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