Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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eſſe, vt parallelepipedum ſub baſi quadrato, AE, altitudine autem,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0229-01
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EX, ad parallelepipedum ſub baſi quadrato, AM,
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altitudine, MX. </
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">Nam omnia quadrata portionis,
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">Ex antec.</
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BAF, ad omnia quadrata circuli, vel ellipſis, A
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CND, ſunt vt parallelepipedum ſub baſi quadra-
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to, AE, altitudine, EX, ad parallelepipedum ſub
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baſi quadrato, AN, altitudine, NX, item om-
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nia quadrata circuli, vel ellipſis, ACND, ad om-
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note-0229-02
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note-0229-02a
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">Ex antec.</
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nia quadrata portionis, CAD, ſunt vt parallele-
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pipedum ſub baſi quadrato, AN, altitudine, N
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X, ad parallelepipedum ſub baſi quadrato, AM,
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altitudine, MX, ergo ex æquali omnia quadrato portionis, BAF,
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ad omnia quadrata portionis, CAD, erunt vt parallelepipedum ſub
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baſi quadrato, AE, altitudine, EX, ad parallelepipedum ſub baſi
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quadrato, AM, altitudine, MX, quod erat oſtendendum.</
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">ADato circulo, vel ellipſi portionem abſcindere per li-
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neam ad eiuſdem axim, vel diametrum ordinatim ap-
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plicatam, cuiusomnia quadrata ad omnia quadrata trian-
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guli in eadem baſi, & </
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">altitudine cum ipſa portione, habeant
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rationem datam; </
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">oportet autem hanc eſſe maiorem ſexqui-
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altera, exiſtente regula ipſa ordinatim applicata.</
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">Sit circulus, vel ellipſis, ADME, axis, vel diameter, AM, cen-
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trum, F, oportet igitur ad ipſum axim, vel diametrum, lineam or-
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fig-0229-02
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xlink:href
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fig-0229-02a
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number
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141
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<
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0229-02
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0229-02
"/>
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dinatim applicare, quæ ab ipſo circulo,
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vel ellipſi abſcindat, portionem, cuius
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omnia quadrata (regula ipſa applicata)
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ad omnia quadrata trianguli in eadem
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baſi, & </
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tionem datam; </
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">hanc dico prius oporte-
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re eſſe maiorem ſexquialtera, nam cu-
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iuslibet abſciſſæ portionis (vt oſtenſum
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eſt) omnia quadrata ad omnia quadrata
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trianguli in eadem baſi, & </
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cum ipſa ſunt, vt compoſita ex dimidia
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totius axis, vel diametri, & </
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reliquæ portionis, ad axim, vel diame-
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trum reliquæ portionis, & </
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