Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div649" type="section" level="1" n="227">
          <pb o="228" file="258" n="258" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div651" type="section" level="1" n="228">
          <head xml:id="echoid-head245" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s10544" xml:space="preserve">EX circumferentia circuli maximi in ſphæra ſoliditatem ſphæræ produ-
              <lb/>
            cere vera maiorem.</s>
            <s xml:id="echoid-s10545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10546" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 298374. </s>
            <s xml:id="echoid-s10547" xml:space="preserve">ad 5041. </s>
            <s xml:id="echoid-s10548" xml:space="preserve">ita cubus ex data circumferentia maximi circuli
              <lb/>
              <note position="left" xlink:label="note-258-01" xlink:href="note-258-01a" xml:space="preserve">Solidit{as} ſphæ-
                <lb/>
              ræmaior, quã
                <lb/>
              vera.</note>
            deſcriptus ad aliud. </s>
            <s xml:id="echoid-s10549" xml:space="preserve">Numerus enim genitus dabit ſphærę ſoliditatem vera ma-
              <lb/>
            iorem. </s>
            <s xml:id="echoid-s10550" xml:space="preserve">Nam cum, per propoſ. </s>
            <s xml:id="echoid-s10551" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10552" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s10553" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10554" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10555" xml:space="preserve">maior ſit proportio cubi
              <lb/>
            datæ circumferentiæ ad ſphæram, quam 298374. </s>
            <s xml:id="echoid-s10556" xml:space="preserve">ad 5041. </s>
            <s xml:id="echoid-s10557" xml:space="preserve">Sit autem cubus datę
              <lb/>
            circumferentię ad numerum procreatum, vt 298374. </s>
            <s xml:id="echoid-s10558" xml:space="preserve">ad 5041. </s>
            <s xml:id="echoid-s10559" xml:space="preserve">habebit quo que
              <lb/>
            cubus datę circumferentię ad ſphærę ſoliditatem veram, maiorem proportio-
              <lb/>
            nem, quam idem cubus ad productum numerum: </s>
            <s xml:id="echoid-s10560" xml:space="preserve"> Ideoque productus
              <note symbol="a" position="left" xlink:label="note-258-02" xlink:href="note-258-02a" xml:space="preserve">10. quinti.</note>
            rus maior erit, quam vera ſoliditas ſphærę.</s>
            <s xml:id="echoid-s10561" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div653" type="section" level="1" n="229">
          <head xml:id="echoid-head246" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s10562" xml:space="preserve">EX circumferentia circuli maximi in ſphæra ſoliditatem ſphærę vera
              <lb/>
            minorem procreare.</s>
            <s xml:id="echoid-s10563" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10564" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            , vt 2904. </s>
            <s xml:id="echoid-s10565" xml:space="preserve">ad 49. </s>
            <s xml:id="echoid-s10566" xml:space="preserve">ita cubus datę circumferentiæ ad aliud. </s>
            <s xml:id="echoid-s10567" xml:space="preserve">Nam pro-
              <lb/>
              <note position="left" xlink:label="note-258-03" xlink:href="note-258-03a" xml:space="preserve">Solidit{as} ſphæ-
                <lb/>
              ræminor, quã
                <lb/>
              vera.</note>
            ductus numerus offeret ſphærę ſoliditatem vera minorem. </s>
            <s xml:id="echoid-s10568" xml:space="preserve">Cum enim per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s10569" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10570" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s10571" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10572" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10573" xml:space="preserve">minor ſit pro portio cubi circumferentiæ datę ad ſphę-
              <lb/>
            ram, quam 2904. </s>
            <s xml:id="echoid-s10574" xml:space="preserve">ad 49. </s>
            <s xml:id="echoid-s10575" xml:space="preserve">ſit autem cubus datę circumferentię ad numerum pro-
              <lb/>
            creatum, vt 2904. </s>
            <s xml:id="echoid-s10576" xml:space="preserve">ad 49. </s>
            <s xml:id="echoid-s10577" xml:space="preserve">habebit quoque cubus datę circumferentiæ ad veram
              <lb/>
            ſoliditatem ſphæræ, minorem proportionem, quàm idem cubus ad numerum
              <lb/>
            productum. </s>
            <s xml:id="echoid-s10578" xml:space="preserve"> Ideo que numerus productus minor erit vera ſoliditate ſphæræ.</s>
            <s xml:id="echoid-s10579" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">10. quinti.</note>
        </div>
        <div xml:id="echoid-div655" type="section" level="1" n="230">
          <head xml:id="echoid-head247" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s10580" xml:space="preserve">EX diametro maximi circuli in ſphęra ſoliditatem ſphærę colligere ve-
              <lb/>
            ra maiorem.</s>
            <s xml:id="echoid-s10581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10582" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 21. </s>
            <s xml:id="echoid-s10583" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s10584" xml:space="preserve">ita cubus diametri datæ ad aliud. </s>
            <s xml:id="echoid-s10585" xml:space="preserve">Procreatus namque nu-
              <lb/>
              <note position="left" xlink:label="note-258-05" xlink:href="note-258-05a" xml:space="preserve">Solidit{as} ſphæ-
                <lb/>
              ræ maior, quã
                <lb/>
              vera.</note>
            merus ſoliditatem ſphæræ dabit vera maiorem. </s>
            <s xml:id="echoid-s10586" xml:space="preserve">Cum enim per propoſ. </s>
            <s xml:id="echoid-s10587" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10588" xml:space="preserve">huius
              <lb/>
            cap. </s>
            <s xml:id="echoid-s10589" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10590" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10591" xml:space="preserve">maior ſit proportio cubi diametriſphæræ ad ſphæram, quàm 21. </s>
            <s xml:id="echoid-s10592" xml:space="preserve">ad
              <lb/>
            11. </s>
            <s xml:id="echoid-s10593" xml:space="preserve">Sit autem cubus datæ diametri ad numerum productum, vt 21. </s>
            <s xml:id="echoid-s10594" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s10595" xml:space="preserve">habe-
              <lb/>
            bit quo que maiorem proportionem cubus datæ diametri ad veram ſoliditatem
              <lb/>
            ſphæræ, quamidem cubus ad numerum genitum. </s>
            <s xml:id="echoid-s10596" xml:space="preserve"> Quapropter numerus
              <note symbol="c" position="left" xlink:label="note-258-06" xlink:href="note-258-06a" xml:space="preserve">10. quinti.</note>
            creatus maior erit vera ſoliditate ſphæræ.</s>
            <s xml:id="echoid-s10597" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div657" type="section" level="1" n="231">
          <head xml:id="echoid-head248" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s10598" xml:space="preserve">EX diametro maximi circuli in ſphæra ſoliditatem ſphæræ concludere
              <lb/>
            vera minorem.</s>
            <s xml:id="echoid-s10599" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Solidit{as} ſphæ-
            <lb/>
          ræminor, quã
            <lb/>
          vera.</note>
          <p>
            <s xml:id="echoid-s10600" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 426. </s>
            <s xml:id="echoid-s10601" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s10602" xml:space="preserve">ita cubus datę diametri ad aliud. </s>
            <s xml:id="echoid-s10603" xml:space="preserve">Numerus enim pro-
              <lb/>
            ueniens minor erit, quàm vera ſoliditas ſphærę. </s>
            <s xml:id="echoid-s10604" xml:space="preserve">Nam cum per propoſ. </s>
            <s xml:id="echoid-s10605" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10606" xml:space="preserve"/>
          </p>
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