Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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hos circulos eſſe ſimiles iuxta meam definitionem ſimilium plana-
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rum figurarum, & </
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<
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">ductarum oppoſitarum tangentium in-
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cidentes eſſe ipſas diametros, AC, OQ, quæ etiam de ſemicirculis
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verificantur. </
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">Diametri ergo, AC, OQ, diuidantur fimiliter ad ean-
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dem partem in punctis, E, M, à quibus vſque ad circumferentiam
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ducantur ipſæ, EB, MN, parallelæ dictis tangentibus, quæ cum
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ad angulos rectos diametros diuidant, etiam ipſę, BE, NM, erunt
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<
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0090-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0090-01
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illis perpendiculares, igitur quadratum,
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BE, erit ęquale rectangulo, AEC, ſi-
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cuti quadratum, NM, æquale rectan-
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gulo, OMQ, rectangulum autem, A
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EC, ad quadratum, EC, eſt vt, AE,
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ad, EC, ideſt vt, OM, ad, MQ, ideſt
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">1. Sex. El.</
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vt rectangulum, OMQ, ad quadratum,
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MQ, ideſt vt quadratum, NM, ad qua-
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dratum, MQ, ergo quadratum, BE,
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ad quadratum, EC, eſt vt quadratum,
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NM, ad quadratum, MQ, (quæ au-
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tem hic ſupponuntur, vel petantur ex
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Eucl. </
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<
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<
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">vel ex ſequenti meo lib.
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">8. Lib. 2.
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ſequen.
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vel 20.
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Sex. El.</
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in quo, quæ hic aſſumuntur indepen-
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denter ab hoc Lemmate demonſtratur)
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ergo, BE, ad, EC, erit vt, NM, ad,
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MQ, permutando, BE, ad, NM, e-
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rit vt, EC, ad, MQ, vel vt, AC, ad, OQ, igitur, quæ æquidi-
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ſtant ipſis tangentibus, FA, HO, & </
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<
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vtcumque diuidunt ipſas, AC, OQ, & </
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">iacent inter ipſas, & </
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">circui-
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tus ſemicirculorum, ABC, ONQ, ad eandem partem, eodem or-
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dine ſumptæ, ſunt vt ipſæ, AC, OQ, quæ dictis tangentibus inci-
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<
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">Defin. 10.</
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dunt ad eundem angulum ex eadem parte, quęideò ſunt earum inci-
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dentes, ergo ſemicirculi, ABC, ONQ, ſunt figuræ planæ fimiles
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ſuxta meam definitionem, quarum & </
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">oppoſitarum tangentium, quę
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ab extremitate diametrorum ducuntur, incidentes ſunt ipſi diame-
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tri; </
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<
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">ſic etiam patebit ſemicirculos, ADC, OZQ, necnon circu-
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los, AC, OQ, eſſe ſimiles, iuxta eandem definitionem; </
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dendum erat.</
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">POſitis infraſcriptis definitionibus ſimilium cylindro-
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rum, & </
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">conorum, ſequitur definitio generalis, quam
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de ſimilibus ſolidis ipſe attuli.</
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