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

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          <p>
            <s xml:id="echoid-s5148" xml:space="preserve">
              <pb o="210" file="0230" n="230" rhead="GEOMETRIÆ"/>
            dictæ portionis ſuper omnia quadrata dicti trianguli, ad omnia qua-
              <lb/>
            drata dicti trianguli, ſunt vt d@midia totius axis, vel diametri ad axim,
              <lb/>
              <figure xlink:label="fig-0230-01" xlink:href="fig-0230-01a" number="142">
                <image file="0230-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0230-01"/>
              </figure>
            vel diametrum reliquæ portionis, opor-
              <lb/>
            tet ergo, quod dicta ratio diuiſa ſit ma-
              <lb/>
            ior ea, quam habet, FM, ad, MA, quæ
              <lb/>
            componendo euadit ſexquialtera: </s>
            <s xml:id="echoid-s5149" xml:space="preserve">ſit er-
              <lb/>
            go data ratio, quam habet, BH, ad, N
              <lb/>
            R, maior ſexquialtera, & </s>
            <s xml:id="echoid-s5150" xml:space="preserve">abſcindatur,
              <lb/>
            HS, æqualis ipſi, NR, & </s>
            <s xml:id="echoid-s5151" xml:space="preserve">fiat, vt, BS,
              <lb/>
            ad, SH, ita, FM, ad, MO, & </s>
            <s xml:id="echoid-s5152" xml:space="preserve">ducatur
              <lb/>
            per, O, ipſa, DE, ad axim, vel diame-
              <lb/>
            trum, AM, ordinatim applicata, & </s>
            <s xml:id="echoid-s5153" xml:space="preserve">iun-
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            gantur, DA, AE; </s>
            <s xml:id="echoid-s5154" xml:space="preserve">quoniam ergo, vt,
              <lb/>
            BS, ad, SH, ita eſt, FM, ad, MO,
              <lb/>
            componendo, BH, ad, HS, vel, NR,
              <lb/>
            crit, vt, FM, MO, ad, MO, ſunt autem omnia quadrata portio-
              <lb/>
            nis, DAE, (regula, DE,) ad omnia quadrata trianguli, DAE,
              <lb/>
              <note position="left" xlink:label="note-0230-01" xlink:href="note-0230-01a" xml:space="preserve">@. Huius.</note>
            vt, FM, MO, ad, MO, & </s>
            <s xml:id="echoid-s5155" xml:space="preserve">ideò ſunt ad ea in ratione data, in ea .</s>
            <s xml:id="echoid-s5156" xml:space="preserve">ſ.
              <lb/>
            </s>
            <s xml:id="echoid-s5157" xml:space="preserve">quam habet, BH, ad, NR, quod efficere opus erat.</s>
            <s xml:id="echoid-s5158" xml:space="preserve"/>
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        <div xml:id="echoid-div520" type="section" level="1" n="311">
          <head xml:id="echoid-head328" xml:space="preserve">THEOREMA VIII. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s5159" xml:space="preserve">OMnia quadrata circuli, vel ellipſis, regula altero axium,
              <lb/>
            vel diametrorum, ad omnia quadrata eiuſdem, re-
              <lb/>
            gula reliquo axium, vel diametrorum, erunt, vt dictus pri-
              <lb/>
            mus axis, vel diameter, ad dictum ſecundum axim, vel dia-
              <lb/>
            metrum.</s>
            <s xml:id="echoid-s5160" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5161" xml:space="preserve">Sit circulus, vel ellipſis, MPCF, cuius axes, vel diametri coniu-
              <lb/>
              <figure xlink:label="fig-0230-02" xlink:href="fig-0230-02a" number="143">
                <image file="0230-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0230-02"/>
              </figure>
            gatæ, MC, PF. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">Dico ergo omnia qua-
              <lb/>
            drata circuli, vel ellipſis, MP, CF, regu-
              <lb/>
            la, MC, ad omnia quadrata eiuſdem, re-
              <lb/>
            gula, PF, eſſe, vt, MC, ad, PF; </s>
            <s xml:id="echoid-s5163" xml:space="preserve">ducan-
              <lb/>
            tur per puncta, M, P, C, F, tangentes cir-
              <lb/>
            culum, vel ellipſim, MPCF, quę ſint, A
              <lb/>
            N, ND, DH, HA, conſtituentes paral-
              <lb/>
            lelogrammum, AD, circulo, vel ellipſi,
              <lb/>
            MPCF, circumſcriptum, cuius latera
              <lb/>
            parallela ſint ipſis, PF, MC, axibus, vel
              <lb/>
            diametris coniugatis: </s>
            <s xml:id="echoid-s5164" xml:space="preserve">Omnia ergo qua-
              <lb/>
            drata circuli, vel ellipſis, MPCF, regula, MC, ſunt </s>
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