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

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            <s xml:id="echoid-s4151" xml:space="preserve">
              <pb o="170" file="0190" n="190" rhead="GEOMETRIÆ"/>
            cta demon tratione propoſitum oſtendemus; </s>
            <s xml:id="echoid-s4152" xml:space="preserve">vnde patebit pariter quadra-
              <lb/>
            ta maxim trum abſciſſarum propoſitæ rectæ lineæ, vt ipſius, EM, adiun-
              <lb/>
            cta quædam, vt, EF, ad quadrata omnium abſciſſarum eiuſdem adiuncta
              <lb/>
            eadem, eſſe vt quadratum vnius maximarum abſciſſarum adiuncta iam
              <lb/>
            dicta .</s>
            <s xml:id="echoid-s4153" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4154" xml:space="preserve">vt quadratum compoſitæ ex propoſita, & </s>
            <s xml:id="echoid-s4155" xml:space="preserve">adiuncta, adrectangu-
              <lb/>
            lum ſub hac compoſita, & </s>
            <s xml:id="echoid-s4156" xml:space="preserve">ſub adiuncta, vnacum, {1/3}, quadrati differen-
              <lb/>
            tiæhuius compoſitæ, & </s>
            <s xml:id="echoid-s4157" xml:space="preserve">adiunctæ .</s>
            <s xml:id="echoid-s4158" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4159" xml:space="preserve">vt quadratum, MF, ad rectangu-
              <lb/>
            lum ſub, MF, FE, vnacum, {1/3}, quadrati, EM, quæ eſt differentia ea-
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            rundem, & </s>
            <s xml:id="echoid-s4160" xml:space="preserve">eſt etiam propoſita linea.</s>
            <s xml:id="echoid-s4161" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div421" type="section" level="1" n="256">
          <head xml:id="echoid-head271" xml:space="preserve">THEOREMA XXIX. PROPOS. XXIX.</head>
          <p>
            <s xml:id="echoid-s4162" xml:space="preserve">CViuſcunque parallelogrammi omnia quadrata regula
              <lb/>
            vno laterum ad omnia quadrata eiuſdem regula altero
              <lb/>
            laterum cum prædicto angulum continentium, erunt vt pri-
              <lb/>
            ma regula ad ſecundam.</s>
            <s xml:id="echoid-s4163" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4164" xml:space="preserve">Sit quodcunq; </s>
            <s xml:id="echoid-s4165" xml:space="preserve">parallelogrammum, AD. </s>
            <s xml:id="echoid-s4166" xml:space="preserve">Dico omnia quadrata
              <lb/>
            eiuſdem, regula, DB, eſſe vt, CD, ad, DB: </s>
            <s xml:id="echoid-s4167" xml:space="preserve">Omnia enim quadra-
              <lb/>
            ta, AD, regula, CD, ad omnia quadrata, AD, regula, DB, ha-
              <lb/>
            bent rationem compoſitam ex ea, quam habet quadratum, CD, ad
              <lb/>
              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">11. huius.</note>
              <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a" number="110">
                <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0190-01"/>
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            quadratum, DB, & </s>
            <s xml:id="echoid-s4168" xml:space="preserve">ex ea,
              <lb/>
            quam habet, BD, ad, DC,
              <lb/>
            (quia, BD, &</s>
            <s xml:id="echoid-s4169" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4170" xml:space="preserve">qualiter inclina-
              <lb/>
            tur baſi, CD, ac, CD, ipſi
              <lb/>
            baſi, DB, nam ſunt circa eun-
              <lb/>
            dem angulum) .</s>
            <s xml:id="echoid-s4171" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4172" xml:space="preserve">ex ea, quam
              <lb/>
              <note position="left" xlink:label="note-0190-02" xlink:href="note-0190-02a" xml:space="preserve">5. huius.</note>
            habet quadratum, BD, ad re-
              <lb/>
            ctangulum ſub, BD, DC, duæ autem rationes, nempè quadrati, C
              <lb/>
            D, ad quadratum, BD, & </s>
            <s xml:id="echoid-s4173" xml:space="preserve">quadrati, BD, ad rectangulum ſub, B
              <lb/>
            D, DC, componunt rationem quadrati, CD, ad rectangulum ſub,
              <lb/>
              <note position="left" xlink:label="note-0190-03" xlink:href="note-0190-03a" xml:space="preserve">Diffin. 12.
                <lb/>
              lib. 1.</note>
            BD, DC, quę eſt eadem ei, quam habet, CD, ad, DB, ergo om-
              <lb/>
              <note position="left" xlink:label="note-0190-04" xlink:href="note-0190-04a" xml:space="preserve">5. huius.</note>
            nia quadrata, AD, regula, CD, ad omnia quadrata eiuſdem, AD,
              <lb/>
            regula, DB, erunt vt, CD, prima regula ad, DB, ſecundam, quod
              <lb/>
            oſtendere opus erat.</s>
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        <div xml:id="echoid-div423" type="section" level="1" n="257">
          <head xml:id="echoid-head272" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s4175" xml:space="preserve">_H_Inc patet, ſi iungamus, CB, omnia quadrata trianguli, CBD,
              <lb/>
            regula, CD, ad omnia quadratratrianguli eiuſdem, regula, DB,
              <lb/>
            eſſe vt, CD, primam regulam ad, D B, ſecundam, nam omnia </s>
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