Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Table of contents

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[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
[481.] THEOREMA XLI. PROPOS. XLIII.
Page: 357 (337)
[482.] THEOREMA XLII. PROPOS. XLIV.
Page: 358 (338)
[483.] THEOREMA XLIII. PROP. XLV.
Page: 358 (338)
[484.] THEOREMA XLIV. PROP. XLVI.
Page: 359 (339)
[485.] THEOREMA XLV. PROP. XLVII.
Page: 360 (340)
[486.] THEOREMA XLVI. PROPOS. XLVIII.
Page: 361 (341)
[487.] THEOREMA XLVII. PROPOS. XLIX.
Page: 362 (342)
[488.] THEOREMA XLVIII. PROPOS. L.
Page: 364 (344)
[489.] THEOREMA XLIX. PROPOS. LI.
Page: 365 (345)
[490.] SCHOLIVM.
Page: 365 (345)
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            lelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8316" xml:space="preserve">dicti, ſpatijs, ideò omnia quadrata, AF,
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            ad omnia quadrata figuræ, CBHF, demptis omnibus quadratis
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            trilinei, BGE, erunt vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8317" xml:space="preserve">quadrato, H
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            F, ad reſiduum, dempta ſexta parte parallelepipedi ſub, BI, vel, C
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            E, exceſſu, BG, ſuper, EF, & </s>
            <s xml:id="echoid-s8318" xml:space="preserve">ſub quadrato, IE, à parallelepipedo
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            ſub, BG, & </s>
            <s xml:id="echoid-s8319" xml:space="preserve">dictis ſpatijs .</s>
            <s xml:id="echoid-s8320" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8321" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8323" xml:space="preserve">re-
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            ctangulo ſub ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8324" xml:space="preserve">ſub, GF.</s>
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        <div xml:id="echoid-div815" type="section" level="1" n="482">
          <head xml:id="echoid-head502" xml:space="preserve">THEOREMA XLII. PROPOS. XLIV.</head>
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            <s xml:id="echoid-s8326" xml:space="preserve">INeadem figura Prop. </s>
            <s xml:id="echoid-s8327" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8328" xml:space="preserve">ducta intra fruſtum parabolæ,
              <lb/>
            EBHF, recta, VR, parallela baſi, HM, oſtendemus
              <lb/>
            omnia quadrata figuræ, CBHF, ad omnia quadrata figu-
              <lb/>
            ræ, CBRV, eſſe vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8329" xml:space="preserve">his ſpa-
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            tijs .</s>
            <s xml:id="echoid-s8330" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8331" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8332" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8333" xml:space="preserve">rectangulo ſub
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            ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8334" xml:space="preserve">ſub, GF, ad parallelepipedum ſub, B
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            S, & </s>
            <s xml:id="echoid-s8335" xml:space="preserve">ſub his ſpatijs, ſcilicet quadrato, VS, 1. </s>
            <s xml:id="echoid-s8336" xml:space="preserve">quadrati, SR,
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            & </s>
            <s xml:id="echoid-s8337" xml:space="preserve">rectangulo ſub ſexquitertia, RS, & </s>
            <s xml:id="echoid-s8338" xml:space="preserve">ſub, SV.</s>
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            <s xml:id="echoid-s8340" xml:space="preserve">Huius demonſtratio non eſt alia à demonſtratione Propoſ. </s>
            <s xml:id="echoid-s8341" xml:space="preserve">41.
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            <s xml:id="echoid-s8342" xml:space="preserve">ideò ibi in ſecunda eiuſdem parte recolatur.</s>
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          <head xml:id="echoid-head503" xml:space="preserve">THEOREMA XLIII. PROP. XLV.</head>
          <p>
            <s xml:id="echoid-s8344" xml:space="preserve">INeodem Propoſ. </s>
            <s xml:id="echoid-s8345" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">Schemate oſtendemus omnia qua-
              <lb/>
            drata figuræ, CBHF, demptis omnibus qua dratis trili-
              <lb/>
            nei, BCE, ad omnia quadrata ſemiparabolæ, BHG, eſſe
              <lb/>
            vt reliquum parallelepipedi ſub, BG, & </s>
            <s xml:id="echoid-s8347" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8348" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8349" xml:space="preserve">qua-
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            drato, FG, {1/2}. </s>
            <s xml:id="echoid-s8350" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8351" xml:space="preserve">rectangulo ſub, FG, & </s>
            <s xml:id="echoid-s8352" xml:space="preserve">ſex-
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            quitertia, GH, ab eodem dempta ſexta parte parallelepi-
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            pediſub, CE, & </s>
            <s xml:id="echoid-s8353" xml:space="preserve">quadrato, FG, ad dimidium parallelepi-
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            pediſub, BG, & </s>
            <s xml:id="echoid-s8354" xml:space="preserve">quadrato, GH.</s>
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            <s xml:id="echoid-s8356" xml:space="preserve">Etenim omnia quadrata figuræ, CBHF, demptis omnibus
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            quadratis trilinei, BCE, ad omnia quadrata, AF, conuertendo,
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            ſunt vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8357" xml:space="preserve">his ſpatijs, ſcilicet quadrato.
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            </s>
            <s xml:id="echoid-s8358" xml:space="preserve">FG, {1/2}. </s>
            <s xml:id="echoid-s8359" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8360" xml:space="preserve">rectangulo ſub, FG, & </s>
            <s xml:id="echoid-s8361" xml:space="preserve">ſexquitertia, G
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            H, ab eodem dempto {1/6}. </s>
            <s xml:id="echoid-s8362" xml:space="preserve">parallelepipedi ſub, CE, & </s>
            <s xml:id="echoid-s8363" xml:space="preserve">quadrato, </s>
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