Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ad ſibi ſimilare genitum ex triangulo, DBF, iuxta communem re-
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gulam, DF.</
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cunque conois byperbolica, im cuius baſi ſit cylindrus, & </
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<
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& </
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<
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xml:space
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">circa eundem axem, vel diametrum ſecetur planis baſi æquidiſtan-
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tibus, quibus pariter ſecentur cylindrus, & </
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<
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ſolidis figuræ ſimiles baſi, ideò omnia plana eorundem regula baſi erũt
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">_45. l. 1._
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_Elicitur ex_
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_45. l. 1. pſo_
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_Conoide_
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_Hyperb. &_
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_ex Cor. 3_
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_34. l. 2. pro_
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_Cylindro._
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_& Cono-_</
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omnes figuræ ſimiles dictorum ſolidorum, in quibus ſi ducatur pla-
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num per axem, producet in ipſis figuras genitrices earundem, nempè
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parallelogrammum in cylindro, hyperbolam in conoide, & </
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gulum in cono, dicta autem ſolida erunt ſimilaria genita ex his figu.
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</
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<
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">ris genitricibus iuxta communem regulam ipſam baſim, & </
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<
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ratio nota erit, quia ſcimus quam rationem habeant inter ſe omnia
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quadrata dictarum genitricium figurarum, regula baſi. </
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ſimiliter pro ſequentibus memoria teneantùr, in quibus ſiet noſtrum
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ſolitum exemplum per reuolutionem ſigurarum circa ſuos axes, Vt
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habeamus omnes figuras ſimiles genitorum ſolidorum, quæ ſint circuli
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diametros in figuris genitricibus, quibus ſint erecti, ſitas habentes,
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licet eadem Verificentur ſſumptis non axibus, ſed tantum diametris,
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Vt alibi pluriés repetitum eſt, ex dictis autem infraſcripta habentur
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Corollaria.</
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rallelogrammum, AF, circam manentem axim, BE, vt fiat
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ex parallelogrammo, AF, cylindrus, A
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F, ex hyperbola, DBF, conois, DBF,
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& </
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ligitur ergo cylindrum, AF, ad conoidé,
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DBF, eſſe vt, OE, ad compoſitam ex,
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NB, & </
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">BE, conoidem autem, DBF,
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ad conum, DBF, eſſe vt compoſitam
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ex ſexquialtera, OB, & </
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</
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genita ex eiſdem figuris .</
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grammo, AF, hyperbola, DBF, & </
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gulo, DBF, iuxta communem regulam,
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DF, vt ſupra dictum eſt, quę declarare oportebat.</
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