Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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<
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">SI duæ rectæ lineæ ducantur, quarum altera parabolam
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tangat, altera verò axi, vel diametro parabolæ æqui-
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diſtanter ducta eandem ſecet, in idem punctum concurren-
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tes: </
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<
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">Omnia quadrata parallelogrammi, regula tangente,
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erunt ſexcupla omnium quadratorum trilinei ſub dictis tan-
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gente, & </
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comprehenſi.</
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<
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">Sit ſemiparabola, ACB, quam tangat lineæ, AD, & </
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<
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cto, A, ducta, AB, axis, vel diameter, integræ parabolæ, dein-
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de agatur vtcunque, DC, parallela axi, vel diametro, AB, ſecans
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curuam parabolæ in, C, & </
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<
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">occurrens tangenti, AD, in, D, duca-
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tur tandem à puncto, C, ipſi, AD, æquidiſtans, CB, ſecans, AB,
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in, B, regula autem ſit, AD. </
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<
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0343-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0343-01
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grammi, AC, eſſe omnium quadratorum
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trilinei, ADC, ſexcupla: </
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<
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quadrata, AC, ad rectangula ſub, AC,
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26. l. 2.</
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& </
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ſemiparabolam, ABC, .</
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<
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.</
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<
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">omnia autem quadrata, AC,
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ad omnia quadrata ſemiparabolę ABC,
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ſunt dupla .</
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<
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<
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23. l. 2.</
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drata, AC, ad reſiduum demptis omni-
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bus quadratis ſemiparabolæ, ABC, à re-
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ctangulis ſub, AC, & </
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<
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ſemiparabola, ABC, & </
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<
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cuplaideſt vt 6. </
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<
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niam verò omnia quadrata, AC, ad omnia quadrata ſemipara-
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bolæ, ABC, ſum vt 6. </
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<
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<
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">vt dictum eſt, ideò omnia quadrata,
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AC, ad omnia quadrata ſemiparabolæ, ABC, cum rectangulis
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bis ſub ſemiparabola, ABC, & </
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<
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">ergo ad reliquum ſcilicet ad omnia quadrata trilinei, ADC, omnia
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quadrata, AC, erunt vt 6. </
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<
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<
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quod oſtendere oportebat.</
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