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

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          <p>
            <s xml:id="echoid-s3435" xml:space="preserve">
              <pb o="145" file="0165" n="165" rhead="LIBER II."/>
            ipſi, CX, æquidiſtans ad ſibi homologam in figura, ΠΩ, ipſi, ΩΛ,
              <lb/>
            æquidiſtantem, vel quælibet in quacunque figurarum ipſi, BC, in
              <lb/>
            ſolido, AP, æquidiſtantium, ad ſibi homologam in ſolido, V & </s>
            <s xml:id="echoid-s3436" xml:space="preserve">
              <lb/>
            lgitur ſimilia ſolida ſunt in tripla ratione linearum, vel laterum ho-
              <lb/>
            mologorum, quæ ſunt in eorundem homologis figuris, quod nobis
              <lb/>
            oſtendendum erat.</s>
            <s xml:id="echoid-s3437" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div354" type="section" level="1" n="216">
          <head xml:id="echoid-head231" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s3438" xml:space="preserve">_E_T quia iam dicta ſimilia ſolida oſtenſa ſunt eſſe in tripla ratione li-
              <lb/>
            nearum bomologarum, quæ ſunt in homologis figuris, æquidiſtan-
              <lb/>
            tibus oppoſitis planis tangentibus vtcunque ſumptis, ideò clarum eſt ea-
              <lb/>
            dem ſimilia ſolida eſſe in tripla ratione quarumuis homologarum in ipſis
              <lb/>
            ſolidis deſoriptibilium, & </s>
            <s xml:id="echoid-s3439" xml:space="preserve">duas quaſuis homologas ſumptas iuxta quæ-
              <lb/>
            dam oppoſita tangentia plana, eſſe vt duas quaſuis homologas ſumptas
              <lb/>
            iuxta alia oppoſita tangentia plana.</s>
            <s xml:id="echoid-s3440" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div355" type="section" level="1" n="217">
          <head xml:id="echoid-head232" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s3441" xml:space="preserve">_V_Niuersè inſuper habetur, ſi fuerint quatuor rectæ lineæ deinceps
              <lb/>
            proportionales, vt prima ad quartam, ita eſſe ſolidum deſcriptum
              <lb/>
            à prima ad ſolidum illi ſimile deſ criptum à ſecunda, & </s>
            <s xml:id="echoid-s3442" xml:space="preserve">huius conuer-
              <lb/>
            ſim; </s>
            <s xml:id="echoid-s3443" xml:space="preserve">dummodò deſcribentes ſint lineæ, vel latera homologa ſimilium fi-
              <lb/>
            gurarum, quæ in ipſis homologæ vocantur.</s>
            <s xml:id="echoid-s3444" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div356" type="section" level="1" n="218">
          <head xml:id="echoid-head233" xml:space="preserve">THE OREMA XVIII. PROPOS. XVIII.</head>
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            <s xml:id="echoid-s3445" xml:space="preserve">SI quaturor rectę lineę proportionales fuerint, ſolidum de-
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            ſeriptum à prima ad ſolidum ſibi ſimile deſcriptum à ſe-
              <lb/>
            cunda, erit, vt ſolidum deſcriptum à tertia ad ſibi ſimile de-
              <lb/>
            ſcriptum à quarta. </s>
            <s xml:id="echoid-s3446" xml:space="preserve">Et ſi fuerint quatuor ſolida proportiona-
              <lb/>
            lia, quorum quæ ſunt eiuſdem proportionis termini ſint ſimi-
              <lb/>
            lia, eadem deſcribentia erunt proportionalia; </s>
            <s xml:id="echoid-s3447" xml:space="preserve">dummodò ta-
              <lb/>
            men ſemper deſcribentia ſint vel lineæ, vel latera homologa
              <lb/>
            figurarum, quæ in ipſis homologæ vocantur.</s>
            <s xml:id="echoid-s3448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3449" xml:space="preserve">Sint ergo quatuor rectę lineę proportionales, AB, CD, FG, H
              <lb/>
            M, & </s>
            <s xml:id="echoid-s3450" xml:space="preserve">ſint ab ipſis, AB, CD, deſcripta ſimilia ſolida, AXB, CV
              <lb/>
            D, & </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ab, FG, HM, ſimilia ſolida, OFPG, NHQM, ita vt
              <lb/>
            duæ, AB, CD, ſint homologę figurarum, AEBY, DKC ℟, &</s>
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