Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div514" type="section" level="1" n="184">
          <pb o="194" file="224" n="224" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div516" type="section" level="1" n="185">
          <head xml:id="echoid-head193" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s8455" xml:space="preserve">Ex data circuli circumferentia, diametrum vera maiorem indagare.</s>
            <s xml:id="echoid-s8456" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8457" xml:space="preserve">Fiat vt 223. </s>
            <s xml:id="echoid-s8458" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8459" xml:space="preserve">ita data circumferentia, verbigratia 88. </s>
            <s xml:id="echoid-s8460" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s8461" xml:space="preserve">Product{us}
              <lb/>
              <note symbol="a" position="left" xlink:label="note-224-01" xlink:href="note-224-01a" xml:space="preserve">2. de Di-
                <lb/>
              menſ. circu-
                <lb/>
              li.</note>
            enim numer{us} 28 {4/223}. </s>
            <s xml:id="echoid-s8462" xml:space="preserve">dabit diametrum vera maiorem. </s>
            <s xml:id="echoid-s8463" xml:space="preserve"> Cum enim circumferentiæ ad diam{et}rum habeat maiorem proportionem, quam triplam ſuperdecupartientem ſe-
              <lb/>
            ptuageſim{as} prim{as}, hoc eſt, maiorem quam 223. </s>
            <s xml:id="echoid-s8464" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s8465" xml:space="preserve">habebit quoque data circumfe-
              <lb/>
            rentia 88. </s>
            <s xml:id="echoid-s8466" xml:space="preserve">ad ſuam diam{et}rum proportionem maiorem, quam ad 28 {4/223}. </s>
            <s xml:id="echoid-s8467" xml:space="preserve"> ac proinde diam{et}er circumferentiæ 88. </s>
            <s xml:id="echoid-s8468" xml:space="preserve">minor erit, quam 28 {4/223}:</s>
            <s xml:id="echoid-s8469" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">10. quinti.</note>
        </div>
        <div xml:id="echoid-div518" type="section" level="1" n="186">
          <head xml:id="echoid-head194" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s8470" xml:space="preserve">Ex data circuli circumferentia diametrum inueſtigare vera minorem.</s>
            <s xml:id="echoid-s8471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8472" xml:space="preserve">Fiat vt 22. </s>
            <s xml:id="echoid-s8473" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8474" xml:space="preserve">ita circumferentia data 88. </s>
            <s xml:id="echoid-s8475" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s8476" xml:space="preserve">Numer{us} enim procreat{us}
              <lb/>
            28. </s>
            <s xml:id="echoid-s8477" xml:space="preserve">offeret diam{et}rum vera maiorem. </s>
            <s xml:id="echoid-s8478" xml:space="preserve"> Cum enim circumferentia ad
              <note symbol="c" position="left" xlink:label="note-224-03" xlink:href="note-224-03a" xml:space="preserve">2. de Dimẽſ.
                <lb/>
              circuli.</note>
            habeat minorem proportionem, quam triplam ſeſquiſeptimam, hoc eſt, quam
              <lb/>
            22. </s>
            <s xml:id="echoid-s8479" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8480" xml:space="preserve">habebit quo que circumferentia data 88. </s>
            <s xml:id="echoid-s8481" xml:space="preserve">ad ſuam diametrum propor-
              <lb/>
            tionem minorem, quam ad 28. </s>
            <s xml:id="echoid-s8482" xml:space="preserve"> atque idcirco diameter circumferentię 88. </s>
            <s xml:id="echoid-s8483" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-224-04" xlink:href="note-224-04a" xml:space="preserve">10. quinti.</note>
            ior erit, quam 28.</s>
            <s xml:id="echoid-s8484" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8485" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8486" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò vt do ceamus, qua ratione area circuli vel ex ſola diametro cog-
              <lb/>
            nita, vel ex ſola circumferentia cognoſcatur, ita vt neceſſe non ſit ex diametro
              <lb/>
            circumferentiam, vel ex circumferentia diametrum inueſtigare, demonſtrandæ
              <lb/>
            prius erunt ſequentes tres propoſitiones, quarum primam deinde lib. </s>
            <s xml:id="echoid-s8487" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8488" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s8489" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8490" xml:space="preserve">ex Pappo Alexandrino aliter quo que demonſtrabimus.</s>
            <s xml:id="echoid-s8491" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div520" type="section" level="1" n="187">
          <head xml:id="echoid-head195" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s8492" xml:space="preserve">Circulorum diametri inter ſe ſunt, vt circumferentiæ.</s>
            <s xml:id="echoid-s8493" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8494" xml:space="preserve">
              <emph style="sc">Sint</emph>
            diametri duorum circulorum AB, DE, & </s>
            <s xml:id="echoid-s8495" xml:space="preserve">rectæ circumferentiis æqua-
              <lb/>
            les BC, EF, quę cum diametris angulos rectos efficiant B, E, compleantur que
              <lb/>
            triangula ABC, DEF. </s>
            <s xml:id="echoid-s8496" xml:space="preserve">Dico ita eſſe diametrum AB, ad diametrum DE, vt eſt cir-
              <lb/>
            cumferentia BC, ad circumferentiam EF. </s>
            <s xml:id="echoid-s8497" xml:space="preserve">Diametris enim AB, DE, inueniatur
              <lb/>
            tertia proportionalis G: </s>
            <s xml:id="echoid-s8498" xml:space="preserve">Et tribus rectis BC, EF, DE, quarta proportionalis
              <lb/>
            H. </s>
            <s xml:id="echoid-s8499" xml:space="preserve">Et quia continuè proportionales ſunt AB, DE, G; </s>
            <s xml:id="echoid-s8500" xml:space="preserve"> erit quadratum ex
              <note symbol="e" position="left" xlink:label="note-224-05" xlink:href="note-224-05a" xml:space="preserve">20. coroll.
                <lb/>
              ſexti.</note>
              <figure xlink:label="fig-224-01" xlink:href="fig-224-01a" number="143">
                <image file="224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/224-01"/>
              </figure>
            ad quadratum ex DE, vt AB, ad G. </s>
            <s xml:id="echoid-s8501" xml:space="preserve"> Sed vt quadratum ex AB, ad
              <note symbol="f" position="left" xlink:label="note-224-06" xlink:href="note-224-06a" xml:space="preserve">2. duodec.</note>
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