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

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          <pb o="155" file="0175" n="175" rhead="LIBER II."/>
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        <div xml:id="echoid-div384" type="section" level="1" n="232">
          <head xml:id="echoid-head247" xml:space="preserve">E. SECTIO V.</head>
          <p style="it">
            <s xml:id="echoid-s3662" xml:space="preserve">_E_T triangulorum, quorum baſium figuræ altitudinibus, vel lateri-
              <lb/>
            bus æqualiter bafibus inclinatis reciprocantur, omnes figuræ, ſi-
              <lb/>
              <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">_12. huius._</note>
            miles baſium figuris, ſunt æquales: </s>
            <s xml:id="echoid-s3663" xml:space="preserve">Et ſi omnes figuræ, ſimiles baſium fi-
              <lb/>
            guris, ſint æquales, figuras baſium altitudinibus, vel latoribus æquali-
              <lb/>
            ter baſibus inclinatis reciprocè reſpondentes habebunt.</s>
            <s xml:id="echoid-s3664" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div386" type="section" level="1" n="233">
          <head xml:id="echoid-head248" xml:space="preserve">F. SECTIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s3665" xml:space="preserve">_E_T tandem ſimilium triangulorum omnia quadrata erunt in tripla
              <lb/>
              <note position="right" xlink:label="note-0175-02" xlink:href="note-0175-02a" xml:space="preserve">_Iuxt. dif-_
                <lb/>
              _fin. 1. Sex-_
                <lb/>
              _ti Elem._</note>
            ratione laterum bomotogorum, ſiue vt eorum cubi; </s>
            <s xml:id="echoid-s3666" xml:space="preserve">regulas verò
              <lb/>
            in ſupradictis ſuppono ſemper duo illorum triangulorum latera, quæ ba-
              <lb/>
            ſes voco; </s>
            <s xml:id="echoid-s3667" xml:space="preserve">hic verò intellige illorum triangulorum latera bomologa. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">His
              <lb/>
            autem ſequentem Tropoſitionem ſubiungam, tum buius gratia, tum eo-
              <lb/>
              <note position="right" xlink:label="note-0175-03" xlink:href="note-0175-03a" xml:space="preserve">_12. huius._</note>
            rum, quæ ſequentur.</s>
            <s xml:id="echoid-s3669" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div388" type="section" level="1" n="234">
          <head xml:id="echoid-head249" xml:space="preserve">THEOR EMA XXIII. PROPOS. XXIII.</head>
          <p>
            <s xml:id="echoid-s3670" xml:space="preserve">SI, expoſita quacunque figura plana, in ea ducatur vtcun-
              <lb/>
            que recta linea, quæ ſit ſumpta pro regula, eadem verò
              <lb/>
            in puncto, vel punctis diuiſa, prout lib. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3672" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3673" xml:space="preserve">ſupponitur
              <lb/>
            ſecari, per puncta diuiſionum lineas duxerimus rectas, ſiue
              <lb/>
            curuas, figuram diuidentes, & </s>
            <s xml:id="echoid-s3674" xml:space="preserve">ſemeltantum ſecantes quam-
              <lb/>
            uis aliam regulæ parallelam, ſiregula in vno puncto tantum
              <lb/>
            diuiſa ſit, vel toties, quot ſunt puncta diuiſionum regulę (ex-
              <lb/>
            ceptis tamen extremis, in quibus linearum ſectæ partes in
              <lb/>
            puncta aliquando degenerare poſſunt.) </s>
            <s xml:id="echoid-s3675" xml:space="preserve">Quæcunq; </s>
            <s xml:id="echoid-s3676" xml:space="preserve">in dict, 2.
              <lb/>
            </s>
            <s xml:id="echoid-s3677" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3678" xml:space="preserve">demonſtrantur hac diuiſione ſuppoſita circa vel quadra-
              <lb/>
            ta, vel rectangula eidem rectæ lineæ applicata, eadem de
              <lb/>
            omnibus quadratis dictæ figuræ, vel eiuſdem partium, vel
              <lb/>
              <note position="right" xlink:label="note-0175-04" xlink:href="note-0175-04a" xml:space="preserve">D. Diff. 8.
                <lb/>
              huius.</note>
            de rectangulis ſub ipſis pariter verificabuntur.</s>
            <s xml:id="echoid-s3679" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3680" xml:space="preserve">Sit expoſita vtcunq; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">figura plana, ABCD, in qua ducta, BD,
              <lb/>
            recta linea vtcunq; </s>
            <s xml:id="echoid-s3682" xml:space="preserve">ſit illa ſumpta pro regula, & </s>
            <s xml:id="echoid-s3683" xml:space="preserve">ea diuiſa in vno, vel
              <lb/>
            pluribus punctis, prout poſtulant Propoſ. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3685" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3686" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3687" xml:space="preserve">per puncta di-
              <lb/>
            uifionum ducantur lineæ fiue rectę, ſiue curuę, AEC, AFI, toties
              <lb/>
            quamuis aliam ipſi, BD, parallelam in figura, BADC, </s>
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