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

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        <div xml:id="echoid-div374" type="section" level="1" n="227">
          <p>
            <s xml:id="echoid-s3633" xml:space="preserve">
              <pb o="154" file="0174" n="174" rhead="GEOMETRIÆ"/>
            ptæ triangulo, & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">Ζ β, erunt in minori ratione, quam omnia qua-
              <lb/>
            drata, Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3635" xml:space="preserve">Ζ β, ergo figurę inſcri-
              <lb/>
            ptæ triangulo, & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">Ζ β, omnia quadrata maiora erunt omnibus qua-
              <lb/>
            dratis trianguli, & </s>
            <s xml:id="echoid-s3637" xml:space="preserve">Ζ β, quod eſt abſurdum, igitur omnia quadrata,
              <lb/>
            AS, non ad minus, quam ſint omnia quadrata trianguli, OES, erunt
              <lb/>
            vt omnia quadrata, Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Ζ β, ſed
              <lb/>
            neque ad maius, vt oſtenſum eſt ergo ad ipſa erunt, vt omnia qua-
              <lb/>
            drata, Τ β, ad omnia quadrata, & </s>
            <s xml:id="echoid-s3639" xml:space="preserve">Ζ β. </s>
            <s xml:id="echoid-s3640" xml:space="preserve">Si autem comparentur om-
              <lb/>
            nia quadrata, AS, Τ β, ad omnia quadrata triangulorum, AEO,
              <lb/>
            TZ &</s>
            <s xml:id="echoid-s3641" xml:space="preserve">, eodem modo fiet demonſtratio, igitur oſtenſum eſt, quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s3642" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div377" type="section" level="1" n="228">
          <head xml:id="echoid-head243" xml:space="preserve">A. COROLLARII SECTIO I.</head>
          <p style="it">
            <s xml:id="echoid-s3643" xml:space="preserve">_H_Inc patet quæcunque de omnibus quadratis parallelogrammorum
              <lb/>
            tales, vel tales conditiones habentium in Propoſ. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3647" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s3648" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3649" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3650" xml:space="preserve">buius Libri oſtenſa ſunt, eadem de omnibus quadratis triangulo-
              <lb/>
            rum, tanquam de eorundem partibus proportionalibus verificari, regu-
              <lb/>
            la vno latere ſumpta, dum triangula circa altitudines, & </s>
            <s xml:id="echoid-s3651" xml:space="preserve">baſes, ſiue à
              <lb/>
            baſibus de ſcriptas figuras, & </s>
            <s xml:id="echoid-s3652" xml:space="preserve">latera æqualiter baſibus inclinata, eaſdem
              <lb/>
            obtinuerint conditiones ibi notatas.</s>
            <s xml:id="echoid-s3653" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div378" type="section" level="1" n="229">
          <head xml:id="echoid-head244" xml:space="preserve">B. SECTIO II.</head>
          <p style="it">
            <s xml:id="echoid-s3654" xml:space="preserve">_I_Gitur triangulorum in eadem altitudine exiſtentium omnia quadra-
              <lb/>
            ta, vel omnes figuræ ſimiles (ſiue ſint ſimiles ad inuicem, quæ ſunt
              <lb/>
              <note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">_9. huius._</note>
            vtriuſque trianguli, ſiue diſſimiles) er unt vt figuræ à baſibus deſcriptæ.</s>
            <s xml:id="echoid-s3655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div380" type="section" level="1" n="230">
          <head xml:id="echoid-head245" xml:space="preserve">C. SECTIO III.</head>
          <p style="it">
            <s xml:id="echoid-s3656" xml:space="preserve">_E_T ſi triangula fuerint in eadem, vel æqualibus baſibus, omnes figu-
              <lb/>
              <note position="left" xlink:label="note-0174-02" xlink:href="note-0174-02a" xml:space="preserve">_10. huius._</note>
            ræ ſimiles, vtriuſque ad inuicem, erunt vt altitudines, vel vt la-
              <lb/>
            tera baſibus æqualiter in clinata.</s>
            <s xml:id="echoid-s3657" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div382" type="section" level="1" n="231">
          <head xml:id="echoid-head246" xml:space="preserve">D. SECTIO IV.</head>
          <p style="it">
            <s xml:id="echoid-s3658" xml:space="preserve">_I_Tem triangulorum omnia quadrata, ſiue omnes figuræ ſimiles, etiamſi
              <lb/>
              <note position="left" xlink:label="note-0174-03" xlink:href="note-0174-03a" xml:space="preserve">_11. huius._</note>
            ſint diſſimiles, quæ ſunt vtriuſq; </s>
            <s xml:id="echoid-s3659" xml:space="preserve">trianguli, habebunt rationem com-
              <lb/>
            poſitam ex ratione figurarum à baſibus deſcriptarum, & </s>
            <s xml:id="echoid-s3660" xml:space="preserve">altitudinum,
              <lb/>
            ſiue laterum baſibus æqualiter inclinatorum.</s>
            <s xml:id="echoid-s3661" xml:space="preserve"/>
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