Clavius, Christoph, Geometria practica

Table of figures

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        <div xml:id="echoid-div551" type="section" level="1" n="199">
          <p>
            <s xml:id="echoid-s9075" xml:space="preserve">
              <pb o="203" file="233" n="233" rhead="LIBER QVARTVS."/>
            Ellipſis ABCD, eſſeæqualem.</s>
            <s xml:id="echoid-s9076" xml:space="preserve"> Quoniam enim eſt, vt BD, ad AC, ita
              <note symbol="a" position="right" xlink:label="note-233-01" xlink:href="note-233-01a" xml:space="preserve">coroll. 20.
                <lb/>
              ſexti.</note>
            ex BD, ad quadratũ ex ex HI. </s>
            <s xml:id="echoid-s9077" xml:space="preserve"> Vt autẽ
              <figure xlink:label="fig-233-01" xlink:href="fig-233-01a" number="147">
                <image file="233-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/233-01"/>
              </figure>
            dratum ex B D, ad quadratum ex HI, ita eſt
              <lb/>
              <note symbol="b" position="right" xlink:label="note-233-02" xlink:href="note-233-02a" xml:space="preserve">2. duodec.</note>
            circulus diametri B D, ad circulum diametri
              <lb/>
            HI. </s>
            <s xml:id="echoid-s9078" xml:space="preserve">Igitur erit quoq;</s>
            <s xml:id="echoid-s9079" xml:space="preserve">, vt BD, ad AC, ita circu
              <lb/>
            lus diametri B D, ad circulum diametri HI.
              <lb/>
            </s>
            <s xml:id="echoid-s9080" xml:space="preserve">Cũ ergo per propoſitionem 5. </s>
            <s xml:id="echoid-s9081" xml:space="preserve">Archimedis
              <lb/>
            de Conoidibus, & </s>
            <s xml:id="echoid-s9082" xml:space="preserve">ſphæroidib. </s>
            <s xml:id="echoid-s9083" xml:space="preserve">ſit quoq;</s>
            <s xml:id="echoid-s9084" xml:space="preserve">, vt
              <lb/>
            maior diameter BD, ad minorem AC, ita cir-
              <lb/>
            culus diametri BD, ad Ellipſim ABCD; </s>
            <s xml:id="echoid-s9085" xml:space="preserve">cha-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-233-03" xlink:href="note-233-03a" xml:space="preserve">11. quinti.</note>
            bebit circulus diametri BD, eandem propor-
              <lb/>
            tionem ad circulum diametri HI, & </s>
            <s xml:id="echoid-s9086" xml:space="preserve">ad Ellipſim ABCD. </s>
            <s xml:id="echoid-s9087" xml:space="preserve"> Ideoque area
              <note symbol="d" position="right" xlink:label="note-233-04" xlink:href="note-233-04a" xml:space="preserve">9. quinti.</note>
            diametri HI, areæ Ellipſis ABCD, æqualis erit. </s>
            <s xml:id="echoid-s9088" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s9089" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div553" type="section" level="1" n="200">
          <head xml:id="echoid-head213" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s9090" xml:space="preserve">AREAM propoſitæ parabolæ inueſtigare.</s>
            <s xml:id="echoid-s9091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9092" xml:space="preserve">
              <emph style="sc">Sit</emph>
            data parabola ABC, cuius baſis AC, & </s>
            <s xml:id="echoid-s9093" xml:space="preserve">axis B D, diuidens baſem bifari-
              <lb/>
            amin D, & </s>
            <s xml:id="echoid-s9094" xml:space="preserve">vertex B. </s>
            <s xml:id="echoid-s9095" xml:space="preserve">Inſcribatur parabolæ triangulum A B C, eandem habens
              <lb/>
            baſem, ac verticem cum parabola. </s>
            <s xml:id="echoid-s9096" xml:space="preserve">Producta autem baſe A C, ſumatur CE, ter-
              <lb/>
            tia pars ipſius A C: </s>
            <s xml:id="echoid-s9097" xml:space="preserve">ita vt AE, ipſius A C, ſit ſeſquitertia. </s>
            <s xml:id="echoid-s9098" xml:space="preserve">Iungatur que recta E B.
              <lb/>
            </s>
            <s xml:id="echoid-s9099" xml:space="preserve">Inquiratur denique per cap. </s>
            <s xml:id="echoid-s9100" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9101" xml:space="preserve">huius libr. </s>
            <s xml:id="echoid-s9102" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-233-02" xlink:href="fig-233-02a" number="148">
                <image file="233-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/233-02"/>
              </figure>
            area triãguli ABE. </s>
            <s xml:id="echoid-s9103" xml:space="preserve">quam dico eſſe æqua-
              <lb/>
            lem areæ parabolæ A B C. </s>
            <s xml:id="echoid-s9104" xml:space="preserve"> Quoniã enim eſt, vt A E, ad A C, ita triangulum ABE, ad
              <lb/>
              <note symbol="e" position="right" xlink:label="note-233-05" xlink:href="note-233-05a" xml:space="preserve">1. ſexti.</note>
            triangulum A B C: </s>
            <s xml:id="echoid-s9105" xml:space="preserve">Eſt autem A E, ipſius
              <lb/>
            A C, ſeſquitertia, ex conſtructione; </s>
            <s xml:id="echoid-s9106" xml:space="preserve">erit
              <lb/>
            quo que triangulum ABE, trianguli ABC,
              <lb/>
            ſeſquitertium. </s>
            <s xml:id="echoid-s9107" xml:space="preserve">Cum ergo, vt Archimedes
              <lb/>
            in lib. </s>
            <s xml:id="echoid-s9108" xml:space="preserve">de Quadratura paraboles demõſtra
              <lb/>
            uit, parabola quo que ABC, trianguli A-
              <lb/>
              <note symbol="f" position="right" xlink:label="note-233-06" xlink:href="note-233-06a" xml:space="preserve">11. quinti.</note>
            BC, ſit ſeſquitertia: </s>
            <s xml:id="echoid-s9109" xml:space="preserve"> habebunt triangulum A B E, & </s>
            <s xml:id="echoid-s9110" xml:space="preserve">parabola ABC, ad
              <note symbol="g" position="right" xlink:label="note-233-07" xlink:href="note-233-07a" xml:space="preserve">11. quinti.</note>
            gulum A B C, eandem proportionem. </s>
            <s xml:id="echoid-s9111" xml:space="preserve"> Ideoque area trianguli A B E, areæ paraboles ABC, æqualis erit. </s>
            <s xml:id="echoid-s9112" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s9113" xml:space="preserve"/>
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        <div xml:id="echoid-div555" type="section" level="1" n="201">
          <head xml:id="echoid-head214" xml:space="preserve">FINIS LIBRI QVARTI.</head>
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