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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            <s xml:id="echoid-s8363" xml:space="preserve">
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            G, ad parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8364" xml:space="preserve">quadrato, HF; </s>
            <s xml:id="echoid-s8365" xml:space="preserve">item omnia
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            quadrata, AF, ad omnia quadrata, AG, ſunt vt quadratum, FH,
              <lb/>
            ad quadratum, HG, .</s>
            <s xml:id="echoid-s8366" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8367" xml:space="preserve">ſumpta, BG, communi altitudine, vt pa-
              <lb/>
            rallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8368" xml:space="preserve">quadrato, FH, ad parallelepipedum
              <lb/>
            ſub, BG, & </s>
            <s xml:id="echoid-s8369" xml:space="preserve">quadrato, HG: </s>
            <s xml:id="echoid-s8370" xml:space="preserve">_Tandem omnia quadrata,_ AG, dupla
              <lb/>
            ſunt omnium quadratorum ſemiparabolæ, BHG, ergo, ex æquali,
              <lb/>
            omnia quadrata figuræ, CBHF, demptis omnibus quadratis trili-
              <lb/>
            nei, BCE, ad omnia quadrata ſemiparabolæ, BHG, erunt vt pa-
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            rallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8371" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8372" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8373" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8374" xml:space="preserve">quadra-
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            ti, GH, & </s>
            <s xml:id="echoid-s8375" xml:space="preserve">rectangulo ſub, FG, & </s>
            <s xml:id="echoid-s8376" xml:space="preserve">ſexquitertia, GH, ab eodem
              <lb/>
            dempto {1/6}. </s>
            <s xml:id="echoid-s8377" xml:space="preserve">parallelepipedi ſub, CE, & </s>
            <s xml:id="echoid-s8378" xml:space="preserve">quadrato, FG, ad dimidium
              <lb/>
            parallelepipedi ſub, BG, & </s>
            <s xml:id="echoid-s8379" xml:space="preserve">quadrato, GH, quod erat demonſtran-
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            dum.</s>
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          <head xml:id="echoid-head504" xml:space="preserve">THEOREMA XLIV. PROP. XLVI.</head>
          <p>
            <s xml:id="echoid-s8381" xml:space="preserve">IN parabola ducta axi, vel diametro æquidiſtanter rect@
              <lb/>
            linea, ſi deinde fiat parallelogrammum ſub eadem du-
              <lb/>
            cta, & </s>
            <s xml:id="echoid-s8382" xml:space="preserve">ſub baſi, angulum habens æqualem angulo i
              <gap/>
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            tionis eiuſdem ductæ ad baſim, regula ſumpta baſi. </s>
            <s xml:id="echoid-s8383" xml:space="preserve">Re
              <gap/>
              <lb/>
            gula ſub parallelogram
              <gap/>
            , in quæ dictum parallelogram-
              <lb/>
            mum diuiditur à ducta linea, ſunt dupla rectangulorum
              <lb/>
            ſub portionibus fruſti parabolæ, dicto parallelogrammo in-
              <lb/>
            cluſæ, per eandem ductam conſtituris.</s>
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          </p>
          <p>
            <s xml:id="echoid-s8385" xml:space="preserve">Sit parabola, AZG, in baſi, ZG, circa axim, vel diametrum,
              <lb/>
              <figure xlink:label="fig-0359-01" xlink:href="fig-0359-01a" number="243">
                <image file="0359-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0359-01"/>
              </figure>
            AQ, cui parallela ducatur vt-
              <lb/>
            cumque recta, DP, fiat autem
              <lb/>
            parallelogrammum ſub, ZQ,
              <lb/>
            DP, angulum habens æqualẽ
              <lb/>
            angulo inclinationis, DP, ad
              <lb/>
            ZG, .</s>
            <s xml:id="echoid-s8386" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8387" xml:space="preserve">angulo, qui ſit, DPG,
              <lb/>
            vtcunque exduobus, DPG,
              <lb/>
            DPZ, ſit autem hoc paralle.
              <lb/>
            </s>
            <s xml:id="echoid-s8388" xml:space="preserve">logrammum, HG, regula ve. </s>
            <s xml:id="echoid-s8389" xml:space="preserve">
              <lb/>
            ro, HG. </s>
            <s xml:id="echoid-s8390" xml:space="preserve">Dico ergo, rectãgula
              <lb/>
            ſub, HP, PE, dupla eſſe rectãgulorũ ſub portionibus, BDPZ, DGP. </s>
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            Sumpto ergo vtcunq; </s>
            <s xml:id="echoid-s8392" xml:space="preserve">in, DP, puncto, T, per, T, ducatur, RF, ipſi,
              <lb/>
            ZG, æquidiſtans ſecanſq; </s>
            <s xml:id="echoid-s8393" xml:space="preserve">curuam parabolæ in, SI, &</s>
            <s xml:id="echoid-s8394" xml:space="preserve">, AQ, in, O. </s>
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              <lb/>
            Rectangulum ergo, ZPQ, ad rectangulum, STI, habet </s>
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