Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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HR, ad quadratum, SX, & </
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<
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xml:space
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<
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">AVO, quæ eſt compoſita pariter ex duabus .</
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<
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<
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xml:space
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CV, ad, VO, & </
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<
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xml:space
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">ex ea, quam habet, BV, ad, VA, vt autem, BV,
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ad, VA, ſic eſt, ſumpta, OV, communi altitudine, rectangulum,
<
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BVO, ad rectangulum, AVO, quodſerua. </
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<
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xml:space
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">Sumatur nunc harum
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rationum componentium ea, quam habet quadratu, HR, ad qua-
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dratum, SX, quæ eſt eadem el, quam habet quadratum, HV, ad
<
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<
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xlink:label
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note-0397-02
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xlink:href
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xml:space
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quadratum, VS, quia verò rectangulum, HSR, cum quadrato, SV,
<
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xml:space
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eſt æquale quadrato, HV, ideò quadratum, VS, eſt exceſſus, quo
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quadratũ, HV, ſuperat rectang. </
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<
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<
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<
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">HSR, eſt
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æquale quadrato, EO, ideò, vt quadratum, HV, ad rectaugulum,
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<
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HSR, ita erit idem quadratum, HV, ad quadratum, EO, & </
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<
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erit quadratum, VC, ad quadratum, CO, quia triangula, CEO,
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CHV, ſunt ſimilia, ergo, per conuerſionem rationis, quadratum,
<
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HV, ad exceſſum ſui ſuper quadratum, EO, .</
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<
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<
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">ad quadratum, VS,
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erit vt quadratum, VC, ad exceſſum ſui ſuper quadratum, CO, .</
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<
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</
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<
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<
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gulum ſemel ſub, BO, OV, cum quadrato, OV, .</
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<
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<
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rectangul@, BVO; </
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<
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">erit ergo, vt quadratum, HV, ad quadratum,
<
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VS, ita quadratum, CV, ad rectangulum, BVO, hæc ergo ratio,
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quam nempè habet quadratum, CV, ad rectangulum, BVO, ſum-
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pta vice eius, quam habet quadratum, HV, ad quadratum, VS,
<
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vel quadratum, HR, ad quadratum, SX, (quæ erat vna rationum
<
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componentium) componit rationem omnium quadratorum triã-
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guli, HCR, ad omnia quadrata hyperbolæ, SOX, ſimul ſumpta
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cum ea, quam habet rectangulum, BVO, ad rectangulum, AVO,
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& </
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<
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xml:space
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">cum ea, quam habet, CV, ad, VO; </
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<
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xml:space
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">harum autem trium rationũ
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componentium ea, quam habet quadiatum, CV, ad rectangulum,
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BVO, & </
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<
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xml:space
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">quam habet hoc rectangulum, BVO, ad rectangulum,
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AVO, componunt rationem quadrat, CV, ad rectangulum, AV
<
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O, illas ergo tres in has duas rationes reiolutas habemus .</
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<
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<
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quam habea quadratum, CV, ad rectangulum, AVO, & </
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<
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">in eam,
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quam habet, CV, ad, VO, porro iſtæ duæ rationes componunt
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rationem parallelepipedi ſub, CV, & </
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<
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ad parallelepipedum ſub, OV, & </
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<
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pipedi ſub, AV, & </
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<
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<
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<
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quadrato, OV, cum cubo, OV, i. </
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<
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<
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quadrato, OV, cum cubo, OV; </
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<
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HCR, ad omnia quadrata hyperbolæ, SOX, erunt vt cubus, CV,
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ad parallelepipedum ter ſub, CO, & </
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<
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V, quod oſtendere opus erat.</
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