Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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H, NOS, ſit autem, veluti in anteced. </
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logrammum, FC, cuius oppoſita latera, FD, EC, ſint ad axim,
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vel diametrum, AV, in eadem productam, órdinatim applica@a,
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0413-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0413-01
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erunt, DC, FE, ipſi, AV, ęqui
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diftantes, ſint earum portiones
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inter aſymptotos concluſæ, H
<
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S, NY, regula ſit, AV. </
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<
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ergo omnia quadrata, FC, ad
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omnia quadrata figuræ, FAD
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CVE, ideſt figuræ concluſæ in-
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ter latera, FE, DC, & </
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<
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tarum ſectionum portiones in-
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ter eadem manentes, quę ſunt,
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FAD, EVC, eſſe, vt quadratũ,
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DC, vel, FE, ad quadratum,
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AV, cum {1/3}. </
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<
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xml:space
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">quadrati, HS, vel,
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NY. </
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<
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">Per puncta ergo, O, V,
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ducantur, XL, VP, ad ipſam,
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AV, ordinatim applicatæ, erit
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igitur, XL, ſecunda diameter,
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&</
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<
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">, VP, tanget ſectionem, EV
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C. </
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<
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">Quoniam ergo rectangulum, HCS, æquatur quadrato. </
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<
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">OV,
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ideſt quadrato, LP, rectangulum verò, HCS, æquatur rectangu-
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<
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xlink:label
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note-0413-01
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xlink:href
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xml:space
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">II. Secun.
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Con.</
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lo, LSC, bis vna cum quadrato, SC, ideò, rectangulum, LSC, bis
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vna cum quadrato, SC, erit æquale quadrato, LP; </
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<
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">eodem pacto
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ſi intelligamus ipſi, LC, æquidiſſantem vtcunq; </
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<
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">ductam intra pa-
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rallelogrammum, OP, viq; </
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<
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">ad ſectionem, VC, productam, oſten-
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demus rectangulum bis ſub eius portionibus inter, OL, OS, & </
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ter, OS, & </
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<
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xml:space
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">ſectionem, VC, concluſis, vna cum quadrato eius, quę
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inter, OS, & </
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<
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">ſectionem, VC, clauditur, æquari quadrato eius, quę
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manet inter, OL, VP, & </
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<
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patebit tandem rectangula ſub trianguio, LOS, & </
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<
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">figura, OVCS,
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bis ſumpta, vna cum omnibus quadratis figuræ, CVCS, æquari
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omnibus quadratis, OP, regula, AV, iam ſuppoſita, quia ergo
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<
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omnia quadrata, CO, ad omnia quadrata, OP, ſunt vt quadratũ,
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ZO, ad quadratum, OV, ideò pam
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teron @ a quadrata, OC, ad
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rectangula ſub triangulo, LOS, & </
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<
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">figura, OVCS, bis, vna cum om-
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nibus quadratis figuræ, OVCS, erunt vt quadratum, ZO, ad qua-
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dratum, OV; </
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<
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<
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">Inſuper omnia quadrata, CO, ad omnia quadrata parallelogrã-
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mi, SO, ſi compleretur, eſſent vt quadiatum, CL, ad </
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