Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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producta, AC, vſq; </
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in, O, portio igi-
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tur circuli, CAV
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N, ad portionem
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circuli, DAEGO,
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habet rationem
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compoſitá ex ea,
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quam habet por-
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1. 1.</
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tio, CAVN, ad
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portionem, OAE
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">Coroll. 2.
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3. huius.</
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G, ideſt ex ratio-
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ne quadrati, VA,
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Elem.
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7. huius.</
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ad quadratum, A
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E, & </
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">ex ratione
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portionis, OAEG, ad portionem, DAEGO, ideſt ex r@tione cir-
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cumferentiæ, EGO, ad circumferentiam, EGD, ideſt ex ratione,
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VA, ad, AE, duæ autem rationes quadrati, VA, ad qua lratum, A
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E, & </
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<
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">ipſius, VA, ad, AE, componunt rationem cubi, VA, ad cu-
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bum, AE, ergo portio, CAVN, ad portionem, DAEGO, erit vt
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cubus, VA, ad cubum, AE, ſunt autem ſpatia, AXC, AXCD, ter-
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tiæ partes dictarum portionum, ergo ſpacium, AXC, ad ſpatium,
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AXCD, erit vt cubus, VA, ad cubum, AE, quoderat oſtenden-
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dum.</
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">COmpræhenſum ſpatium ſub ſpirali, q æ eſt minor
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ea, quæ ſub prima reuolutione fit, nec abet termi-
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num initium ſpiralis, & </
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">rectis, quæ à terminis ipſius in ſpi-
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ralis initium ducuntur, ad ſectorem habentem radium æ-
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qualem maiori earum, quæ à termino ad initium ſpiralis
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ducuntur, arcum verò, qui intercipitur inter duas rectas
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ſecundum eaſdem partes ſpiralis, habet eandem rationem,
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quam rectangulum compræhenſum ſub rectis à terminis
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in principium ſpiralis ductis, vna cum. </
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quo maior dictarum linearum ſuperat minotẽ, ad quadra-
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tum maioris linearum à terminis ad initium ſpiralis coniũ-
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ctarum.</
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