Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEO METRIÆ
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ra bolæ, AQG, habent rationem compoſitam ex ea, quam habent
<
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omnia quadrata, DPG, ad omnia quadrata, DG, ideſt ex ratione
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compoſitę ex {1/2}. </
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<
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<
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<
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">ex ea, quam habent om-
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nia quadrata, DG, ad omnia quadrata, AG, .</
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<
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<
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">ex ratione paralle-
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lepipedi ſub, DP, & </
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<
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">quadrato, PG, ad parallel epipedum ſub, AQ,
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& </
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<
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">quadrato, QG, & </
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<
s
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">tandem ex ea, quam habent omnia quadrata,
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A G, ad omnia quadrata ſemiparabolæ, AQG, .</
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<
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<
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">ex ratione paral-
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lelepipedi ſub, AQ, & </
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<
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">quadrato, QG, ad eiuſdem dimidium: </
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x1. l. 2.</
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autem rationes parallelepipedi ſub, DP, & </
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<
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">quadrato, PG, ad paral-
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lelepipedum ſub, AQ, & </
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<
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">quadrato, QG, & </
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<
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">ratio huius ad eiuſdem
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">21. huius.</
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dimidium, conſiciunt rationem parallelepipedi ſub, DP, & </
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<
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to, PG, ad {1/2}. </
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<
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<
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">quadrato, QG, ergo om-
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l. 1.</
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nia quadrata, D & </
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">G, ad omnia quadrata ſemiparabolæ, AQG, ha-
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bent rationem compoſitam ex ratione rectæ compoſitæ ex {1/3}. </
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<
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{1/2}. </
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<
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">PG, ad, ZP, & </
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<
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">ex ratione parallelepipedi ſub, DP, & </
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<
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P G, ad {1/2}. </
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<
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<
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">quadrato, QG, vt dictum eſt.</
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<
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">Inſuper omnia quadrata trilinei, AXG, ad omnia quadrata trili-
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nei, DEG, habent rationem compoſitam ex ratione omnium qua-
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dratorum, AXG, ad omnia quadrata, AG, .</
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<
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<
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tione {1/6}. </
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<
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<
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lelepipedum, & </
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<
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quadrata, DG, .</
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<
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<
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<
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">quadrato, QG, ad
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parallelepipedum ſub, DP, & </
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<
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">quadrato, PG, quæ duæ rationes cõ-
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ficiunt rationem {1/6}. </
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<
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<
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">quadrato, QG, ad pa-
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rallelepipedum ſub, DP, & </
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<
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<
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omnium quadratorum, DG, ad omnia quadrata trilinei, DEG, .</
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</
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ex ea, quam habet, ZP, ad reſiduum, ab eadem, ZP, demptis {2/3}. </
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<
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<
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cum {1/6}. </
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<
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">PG, ergo omnia quadrata trilinei, AXG, ad omnia quadra-
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ta trilinei, DEG, habent rationem compoſitam ex ea, quam habet
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{1/6}. </
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<
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<
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ſub, DP, & </
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<
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<
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duum, demptis ab ea {2/3}. </
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<
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<
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<
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<
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verſus, AX, cui occurrat in, C, omnia quadrata trilinei,
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D GP, ad omnia quadrata figuræ, CAZP, demptis omni-
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bus quadratis trilinei, ACD, habere rationem compoſitam
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ex ea, quam habet compoſita ex {1/3}. </
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<
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ex ratione parallelepipedi ſub, DP, & </
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<
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