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

Table of handwritten notes

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            <s xml:id="echoid-s5813" xml:space="preserve">
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            go, vt quadratum, EY, ad quadratum, YS, ita rectangulum, TZ
              <lb/>
              <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">Ex 3. Co-
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              nic. p. 17.</note>
            S, ad rectangulum, BZA, eodem modo (ſumptoin, AB, vtcun-
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            quepuncto, M, & </s>
            <s xml:id="echoid-s5814" xml:space="preserve">per, M, ducta, CMG, parallela ipſi, BF,) ſe-
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            quetur rectangulum, GMC, ad rectangulum, BMA, eſſe vt qua-
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            dratum, EY, ad quadratum, YS, ergo rectangulum, TZS, ad re-
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            ctangulum, BZA, erit vt rectangulum, GMC, ad rectangulum,
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            BMA, & </s>
            <s xml:id="echoid-s5815" xml:space="preserve">ſic dereliquis oſtendemus .</s>
            <s xml:id="echoid-s5816" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5817" xml:space="preserve">rectangula ſub portione, AS
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            B, & </s>
            <s xml:id="echoid-s5818" xml:space="preserve">quadrilineo, AHTFB, adrectangula ſub omnibus abſciſſis,
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            AB, & </s>
            <s xml:id="echoid-s5819" xml:space="preserve">reſiduis abſciſſarum eiuſdem .</s>
            <s xml:id="echoid-s5820" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5821" xml:space="preserve">adrectangula ſub triangulis,
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            ABD, AVD, (ſunt .</s>
            <s xml:id="echoid-s5822" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5823" xml:space="preserve">rectangula ſub omnibus abſciſſis, AB, & </s>
            <s xml:id="echoid-s5824" xml:space="preserve">
              <lb/>
            reſiduis abſciſſarum eiuſdem, æqualia rectangulis ſub duobus triangu-
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              <note position="right" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">Coroll. 2.</note>
            lis, ABD, AVD,) erunt vt rectangulum, TZS, adrectangulum,
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              <note position="right" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">Prop. 19.
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              lib. 2.</note>
            AZB, ideſt vt quadratum, EY, ad quadratum, YS, vel vt quadra-
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            tum, SX, ad quadratum, XE, vel vt quadratum, ST, ad quadra-
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            tum, ER; </s>
            <s xml:id="echoid-s5825" xml:space="preserve">ergo rectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5826" xml:space="preserve">quadrilineo, A
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            HTFB, ad rectangula ſub triangulis, ABD, AVD, erunt vt qua-
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            dratum, ST, ad quadratum, ER; </s>
            <s xml:id="echoid-s5827" xml:space="preserve">quod oſtendere oportebat.</s>
            <s xml:id="echoid-s5828" xml:space="preserve"/>
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        <div xml:id="echoid-div577" type="section" level="1" n="341">
          <head xml:id="echoid-head358" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s5829" xml:space="preserve">HINC patet, quoniam probauimus, omnia quadrata, AD, ſex-
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            cupla eſſe rectangulorum ſub triangulis, ABD, AVD, quod
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            in circulo eadem quadrat a ſint ſexcupla rectangulorum ſub portione,
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            ASB, & </s>
            <s xml:id="echoid-s5830" xml:space="preserve">quadrilineo, AHTFB. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">In ellipſi verò, quia pariter om-
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            nia quadrata, AD, rectangulorum ſub triangulis, ABD, AVD,
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            ſunt ſexcupla .</s>
            <s xml:id="echoid-s5832" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">ſunt ad illa, vt cubus, AB, ad ſui ipſius ſextam par-
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            tem, inſuper rectangula ſub triangulis, ABD, AVD, adrectangula
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              <note position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">Cor. 24.
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              lib. 2.</note>
            ſub portione, ASB, & </s>
            <s xml:id="echoid-s5834" xml:space="preserve">quadrilineo, AHTFB, ſunt vt quadra-
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            tum, ER, conuertendo ad quadratum, ST, .</s>
            <s xml:id="echoid-s5835" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5836" xml:space="preserve">vt ſexta pars cubi, AB,
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            ad eiuſdein talem partem, ad quam ipſa ſextapars ſit, vt quadratum, E
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            R, ad quadratum, ST, binc ex æquali omnia quadrata, AD, in elli-
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            pſi, ad rectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5837" xml:space="preserve">quadrilineo, AHTFB,
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            erunt vt cubus, AB, ad ſui ipſius eam partem, ad quam eiuſdem cubi,
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            AB, ſextapars ſit veluti quadratum, ER, ad quadratum, ST. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">Ve-
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            rum ſi in ellipſi diametri non ſint axes, vice cubi, AB, concludemus
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            omnia quadrata, AD, adrectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5839" xml:space="preserve">quadri-
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            lineo, AHTFB, eſſe vt parallelepipedum ſub altitudine, AB, baſi
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            rhombo quod ab ipſa, AB, deſeribitur, ad ſui ipſius eam partem, ad
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            quam eiuſdem parallelepipedi pars ſexta ſit veluti quadratum, ER, ad
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            quadratum, ST,</s>
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