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

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          <pb o="103" file="0123" n="123" rhead="LIBER II."/>
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        <div xml:id="echoid-div251" type="section" level="1" n="165">
          <head xml:id="echoid-head178" xml:space="preserve">A. VIII.</head>
          <note position="right" xml:space="preserve">A.</note>
          <p>
            <s xml:id="echoid-s2492" xml:space="preserve">PRopoſita quacunque plana figura, & </s>
            <s xml:id="echoid-s2493" xml:space="preserve">in ea ducta vtcun-
              <lb/>
            que recta linea vſque ad ambitum hinc inde terminata,
              <lb/>
            ſi ipſa recta linea deſcribere quamcumque figuram planam
              <lb/>
            intelligatur, non exiſtentem in plano propoſitę figurę, ac de-
              <lb/>
            inde reliquæ earum, quæ dicuntur omnes lineæ propoſitæ fi-
              <lb/>
            guræ, ſumptę regula iam ducta linea (& </s>
            <s xml:id="echoid-s2494" xml:space="preserve">recti tranſitus ſi de-
              <lb/>
            ſcripta figura ſit erecta plano propoſitę, veleiuſdem obliqui
              <lb/>
            tranſitus, ſi illi ſit inclinata, eius nempè tranſitus, qui fit in
              <lb/>
            tali inclinatione) deſcribere intelligantur figuras planas ſi-
              <lb/>
            miles, ac ſimiliter poſitas, & </s>
            <s xml:id="echoid-s2495" xml:space="preserve">æquidiſtantes primò deſcriptę,
              <lb/>
            ita vt omnes deſcribentes ſint deſcriptarum ſigurarum lineę,
              <lb/>
            vel latera homologa; </s>
            <s xml:id="echoid-s2496" xml:space="preserve">omnes deſcriptæ figuræ ſimul ſumptæ
              <lb/>
            dicentur. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">Omnes figuræ planæ ſimiles talis propoſitæ figurę,
              <lb/>
            ſumptæ regula earum vna, vel regula etiam ipſa linea, vel
              <lb/>
            latere deſcribente; </s>
            <s xml:id="echoid-s2498" xml:space="preserve">vt ſi deſcriptæ figuræ eſſent quadrata, hæ
              <lb/>
            dicerentur. </s>
            <s xml:id="echoid-s2499" xml:space="preserve">Omnia quadrata talis propoſitæ figuræ, vel ſi eſ-
              <lb/>
            ſent triangula ęquilatera dicerentur. </s>
            <s xml:id="echoid-s2500" xml:space="preserve">Omnia triangula ęqui-
              <lb/>
            latera eiuſdem.</s>
            <s xml:id="echoid-s2501" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div252" type="section" level="1" n="166">
          <head xml:id="echoid-head179" xml:space="preserve">B.</head>
          <note position="right" xml:space="preserve">B.</note>
          <p>
            <s xml:id="echoid-s2502" xml:space="preserve">Solidum, cuius omnes deſcriptæ figuræ ſimiles ſunt om-
              <lb/>
            nia plana, dicetur: </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Solidum ſimilare genitum ex propoſita fi-
              <lb/>
            gura iuxta eandem regulam, iuxta quam ſumptæ omnes di-
              <lb/>
            ctæ figuræ ſimiles fuerunt, quæ igitur ex figuris propoſitis,
              <lb/>
            vt ſic generantur, dicentur abſque alio addito: </s>
            <s xml:id="echoid-s2504" xml:space="preserve">Solida ſimi-
              <lb/>
            laria genita ex propoſitis figuris iuxta regulas omnium ſimi-
              <lb/>
            lium figurarum, quæ ipſorum euadunt omnia plana, propo-
              <lb/>
            ſitæ autem figuræ, eorundem genitrices figuræ vocabuntur.</s>
            <s xml:id="echoid-s2505" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div253" type="section" level="1" n="167">
          <head xml:id="echoid-head180" xml:space="preserve">C.</head>
          <note position="right" xml:space="preserve">C.</note>
          <p>
            <s xml:id="echoid-s2506" xml:space="preserve">Cum verò duarum genitricium vtcunq: </s>
            <s xml:id="echoid-s2507" xml:space="preserve">figurarum omnes
              <lb/>
            deſcriptæ figuræ nedum ſimiles erunt: </s>
            <s xml:id="echoid-s2508" xml:space="preserve">quę reperientur in ea-
              <lb/>
            rum vnaquaque, ſed etiam quæ ſunt vnius, inuenientur ſimi-
              <lb/>
            les omnibus figuris ſimilibus alterius propoſitæ figuræ, fue-
              <lb/>
            rint autem in vtroque ſolido figuræ æquè eleuatæ ſuper pla-
              <lb/>
            na genitricium figurarum, tunc ſolida genita ex propoſitis </s>
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