Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div611" type="section" level="1" n="215">
          <p>
            <s xml:id="echoid-s9943" xml:space="preserve">
              <pb o="221" file="251" n="251" rhead="LIBER QVINTVS."/>
            Contineatur autem quarta pars rectanguli G I, tam ſub {1/4}. </s>
            <s xml:id="echoid-s9944" xml:space="preserve">diametri F I, & </s>
            <s xml:id="echoid-s9945" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-251-01" xlink:href="note-251-01a" xml:space="preserve">1. ſexti.</note>
            cumferentia F G, quam ſub {1/4}. </s>
            <s xml:id="echoid-s9946" xml:space="preserve">circumferentiæ F G, & </s>
            <s xml:id="echoid-s9947" xml:space="preserve">diametro F I; </s>
            <s xml:id="echoid-s9948" xml:space="preserve">liquido con-
              <lb/>
            ſtat, quod proponitur.</s>
            <s xml:id="echoid-s9949" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div613" type="section" level="1" n="216">
          <head xml:id="echoid-head233" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s9950" xml:space="preserve">QVADRATVM circumferentiæ circuli maximi in ſphæra ad ſuper-
              <lb/>
            ficiem ſphæræ conuexam, maiorem proportionem habet, quam 223.
              <lb/>
            </s>
            <s xml:id="echoid-s9951" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s9952" xml:space="preserve">minorem verò, quam 22. </s>
            <s xml:id="echoid-s9953" xml:space="preserve">ad 7.</s>
            <s xml:id="echoid-s9954" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9955" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim per præcedentem ſit, vt quadratum circumferentiæ maximi cir-
              <lb/>
            culi ad ſuperficiem conuexam ſphærę, ita circumferentia eiuſdem circuli ad
              <lb/>
            diametrum: </s>
            <s xml:id="echoid-s9956" xml:space="preserve"> ſit autem maior proportio circumferentię ad diametrum,
              <note symbol="b" position="right" xlink:label="note-251-02" xlink:href="note-251-02a" xml:space="preserve">2. de Dimẽſ@
                <lb/>
              circuli lib. 4.</note>
            3 {10/71}. </s>
            <s xml:id="echoid-s9957" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s9958" xml:space="preserve">hoc eſt, quam 223. </s>
            <s xml:id="echoid-s9959" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s9960" xml:space="preserve">minor verò, quam 3 {1/7}. </s>
            <s xml:id="echoid-s9961" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s9962" xml:space="preserve">hoc eſt, quam
              <lb/>
            22. </s>
            <s xml:id="echoid-s9963" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s9964" xml:space="preserve">liquetid, quod propoſitum eſt.</s>
            <s xml:id="echoid-s9965" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div615" type="section" level="1" n="217">
          <head xml:id="echoid-head234" xml:space="preserve">PROPOSITIO V.</head>
          <p>
            <s xml:id="echoid-s9966" xml:space="preserve">QVADRATVM diametri circuli in ſphæra maximi ad ſuperficiem
              <lb/>
            ſphæræ conuexam, maiorem proportionem habet, quam 7. </s>
            <s xml:id="echoid-s9967" xml:space="preserve">ad 22.
              <lb/>
            </s>
            <s xml:id="echoid-s9968" xml:space="preserve">minorem verò, quam 71. </s>
            <s xml:id="echoid-s9969" xml:space="preserve">ad 223.</s>
            <s xml:id="echoid-s9970" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9971" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim per propoſ. </s>
            <s xml:id="echoid-s9972" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9973" xml:space="preserve">ſit, vt quadratum diametri ad ſuperficiem ſphærę,
              <lb/>
            ita diameter ad circumferentiam: </s>
            <s xml:id="echoid-s9974" xml:space="preserve"> Sit autem maior proportio diametri ad
              <note symbol="c" position="right" xlink:label="note-251-03" xlink:href="note-251-03a" xml:space="preserve">26. quinti.</note>
            cumferentiam, quam 7. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s9976" xml:space="preserve">( quod minor ſit proportio circumferentię
              <note symbol="d" position="right" xlink:label="note-251-04" xlink:href="note-251-04a" xml:space="preserve">2. de Dimẽſ.
                <lb/>
              circuli lib. 4.</note>
            diametrum, quam 22. </s>
            <s xml:id="echoid-s9977" xml:space="preserve">ad 7.) </s>
            <s xml:id="echoid-s9978" xml:space="preserve">minor verò, quam 71. </s>
            <s xml:id="echoid-s9979" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s9980" xml:space="preserve">( quod maior ſit proportio circumferentię ad diametrum, quam 223. </s>
            <s xml:id="echoid-s9981" xml:space="preserve">ad 71.) </s>
            <s xml:id="echoid-s9982" xml:space="preserve">patet verum eſſe,
              <lb/>
            quod proponitur.</s>
            <s xml:id="echoid-s9983" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div617" type="section" level="1" n="218">
          <head xml:id="echoid-head235" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s9984" xml:space="preserve">PROPORTIO cubi ex circumferentia maximi in ſphæra circuli de-
              <lb/>
            ſcripti, ad ſphæram maior eſt, quam 298374. </s>
            <s xml:id="echoid-s9985" xml:space="preserve">ad 5041. </s>
            <s xml:id="echoid-s9986" xml:space="preserve">minor autem,
              <lb/>
            quam 2904. </s>
            <s xml:id="echoid-s9987" xml:space="preserve">ad 49.</s>
            <s xml:id="echoid-s9988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9989" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim ſit per propoſ. </s>
            <s xml:id="echoid-s9990" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9991" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9992" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9993" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9994" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">vt circumferentia maximi circuli in
              <lb/>
            quauis ſphæra, ad circumferentiam maximi circuli in quauis alia ſphęra, ita dia-
              <lb/>
            meter ad diametrum: </s>
            <s xml:id="echoid-s9996" xml:space="preserve"> habeat autem cubus circumferentię prioris ſphærę ad cubum circumferentię ſphærę poſterioris, proportionem triplicatam circum-
              <lb/>
              <note symbol="e" position="right" xlink:label="note-251-05" xlink:href="note-251-05a" xml:space="preserve">33. vndec.</note>
            ferentię ad circumferentiam; </s>
            <s xml:id="echoid-s9997" xml:space="preserve"> Item ſphæra prior ad poſteriorem ſphęram, proportionem triplicatam diametri ad diametrum: </s>
            <s xml:id="echoid-s9998" xml:space="preserve">erit vt cubus ex circumfe-
              <lb/>
              <note position="right" xlink:label="note-251-06" xlink:href="note-251-06a" xml:space="preserve">18. duodec.</note>
            rentia prioris ſphærę deſcriptus ad cubum ex poſterioris ſphærę circumferen-
              <lb/>
            tia deſcriptum, ita ſphæra prior ad poſteriorem ſphęram; </s>
            <s xml:id="echoid-s9999" xml:space="preserve">Et permutando, vt cu-
              <lb/>
            bus circumferentię ſphærę prioris ad priorem ſphęram, ita cubus circumferen-
              <lb/>
            tiæ poſterioris ſphęrę ad ſphęram poſteriorem.</s>
            <s xml:id="echoid-s10000" xml:space="preserve"/>
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