Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div643" type="section" level="1" n="224">
          <p>
            <s xml:id="echoid-s10477" xml:space="preserve">
              <pb o="227" file="257" n="257" rhead="LIBER QVINTVS."/>
            @em proportionem, quàm idem quadratum ad numerum productum: </s>
            <s xml:id="echoid-s10478" xml:space="preserve">ideo- que productus numerus maior erit ſuperficie vera.</s>
            <s xml:id="echoid-s10479" xml:space="preserve"/>
          </p>
          <note symbol="a" position="right" xml:space="preserve">10. quinti.</note>
        </div>
        <div xml:id="echoid-div645" type="section" level="1" n="225">
          <head xml:id="echoid-head242" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s10480" xml:space="preserve">EX circumferentia circuli in ſphæra maximi ſuperficiem ſphæræ con-
              <lb/>
            uexam vera minorem eruere.</s>
            <s xml:id="echoid-s10481" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10482" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 22. </s>
            <s xml:id="echoid-s10483" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s10484" xml:space="preserve">ita quadratum ex circumferentia maximi circuli data de-
              <lb/>
              <note position="right" xlink:label="note-257-02" xlink:href="note-257-02a" xml:space="preserve">Superficies
                <lb/>
              ſphæræ minor.
                <lb/>
              quam vera.</note>
            ſcriptum ad aliud. </s>
            <s xml:id="echoid-s10485" xml:space="preserve">Numerus enim genitus minor erit vera ſuperficie ſphæræ.
              <lb/>
            </s>
            <s xml:id="echoid-s10486" xml:space="preserve">Cum enim per pro poſ. </s>
            <s xml:id="echoid-s10487" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10488" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s10489" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10490" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10491" xml:space="preserve">minor ſit proportio quadrati circum-
              <lb/>
            ferentiæ circuli maximi ad ſuperficiem ſphæræ, quam 22. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s10493" xml:space="preserve">Sit autem qua-
              <lb/>
            dratum datæ circumferentiæ ad numerum genitum, vt 22. </s>
            <s xml:id="echoid-s10494" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s10495" xml:space="preserve">habebit quo que
              <lb/>
            quadratum datæ circumferentiæ ad ſuperficiem veram ſphæræ, minorem pro-
              <lb/>
            portionem, quam idem quadratum ad numerum productum. </s>
            <s xml:id="echoid-s10496" xml:space="preserve"> Quam
              <note symbol="b" position="right" xlink:label="note-257-03" xlink:href="note-257-03a" xml:space="preserve">10. quinti.</note>
            numerus productus vera ſuperficie ſphæræ min or erit.</s>
            <s xml:id="echoid-s10497" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div647" type="section" level="1" n="226">
          <head xml:id="echoid-head243" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s10498" xml:space="preserve">EX diametro circuli in ſphęra maximi ſuperficiem ſphærę vera maio-
              <lb/>
            rem elicere.</s>
            <s xml:id="echoid-s10499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10500" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 7. </s>
            <s xml:id="echoid-s10501" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s10502" xml:space="preserve">ita quadratum diametri datæ circuli maximi ad aliud, gi-
              <lb/>
              <note position="right" xlink:label="note-257-04" xlink:href="note-257-04a" xml:space="preserve">Superfici{es}
                <lb/>
              ſphæræ minor,
                <lb/>
              quam vera.</note>
            gnetur que ſuperficies ſphæræ maior, quam vera. </s>
            <s xml:id="echoid-s10503" xml:space="preserve">Nam cum, per propoſ. </s>
            <s xml:id="echoid-s10504" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10505" xml:space="preserve">huius
              <lb/>
            cap. </s>
            <s xml:id="echoid-s10506" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10507" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10508" xml:space="preserve">maior ſit proportio quadrati diametri circuli maximi ad ſuperfi-
              <lb/>
            ciem ſphæræ veram, quam 7. </s>
            <s xml:id="echoid-s10509" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s10510" xml:space="preserve">Sit autem quadratum diametri datæ ad pro-
              <lb/>
            ductum numerum, vt 7. </s>
            <s xml:id="echoid-s10511" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s10512" xml:space="preserve">habebit quo que quadratum datæ diametri ad ſu-
              <lb/>
            perficiem veram ſphærę, maiorem proportionem, quamidem quadratum ad
              <lb/>
            productum numerum. </s>
            <s xml:id="echoid-s10513" xml:space="preserve"> Quo circa procreatus numerus maior er@t, quam
              <note symbol="c" position="right" xlink:label="note-257-05" xlink:href="note-257-05a" xml:space="preserve">10. quint.</note>
            ra ſuperficies ſphærę.</s>
            <s xml:id="echoid-s10514" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div649" type="section" level="1" n="227">
          <head xml:id="echoid-head244" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s10515" xml:space="preserve">EX diametro circuli in ſphæra maximi ſuperficiem ſphærę vera mino-
              <lb/>
            rem colligere.</s>
            <s xml:id="echoid-s10516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10517" xml:space="preserve">
              <emph style="sc">Fiat</emph>
            vt 71. </s>
            <s xml:id="echoid-s10518" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s10519" xml:space="preserve">ita quadratum datæ diametri circuli maximi ad aliud.
              <lb/>
            </s>
            <s xml:id="echoid-s10520" xml:space="preserve">
              <note position="right" xlink:label="note-257-06" xlink:href="note-257-06a" xml:space="preserve">Superfici{es}
                <lb/>
              ſphæræ mi or,
                <lb/>
              quam vera.</note>
            Numerus namque genitus ſuperficiem ſphæræ vera minorem exhibebit. </s>
            <s xml:id="echoid-s10521" xml:space="preserve">Quo
              <lb/>
            niam enim per propoſ. </s>
            <s xml:id="echoid-s10522" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10523" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s10524" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10525" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10526" xml:space="preserve">minor eſt proportio quad ati dia-
              <lb/>
            metri ad ſuperfi ciem ſphærę, quam 71. </s>
            <s xml:id="echoid-s10527" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s10528" xml:space="preserve">Eſt autẽ quadratum datæ diametri
              <lb/>
            ad pro ductum numerum, vt 71. </s>
            <s xml:id="echoid-s10529" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s10530" xml:space="preserve">Erit quoq; </s>
            <s xml:id="echoid-s10531" xml:space="preserve">min or proportio quadrati da-
              <lb/>
            tæ diametriad veram ſuperficiem ſphærę quam eiuſdem quadrati ad numerum
              <lb/>
            productum. </s>
            <s xml:id="echoid-s10532" xml:space="preserve"> Quapropter minor erit productus numerus, quam vera
              <note symbol="d" position="right" xlink:label="note-257-07" xlink:href="note-257-07a" xml:space="preserve">10. quinti.</note>
            ficies ſphærę.</s>
            <s xml:id="echoid-s10533" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10534" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10535" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione ex propoſ. </s>
            <s xml:id="echoid-s10536" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10537" xml:space="preserve">& </s>
            <s xml:id="echoid-s10538" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10539" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s10540" xml:space="preserve">Nũ. </s>
            <s xml:id="echoid-s10541" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10542" xml:space="preserve">eliciuntur quatuor aliæ
              <lb/>
            ſequentes regulę, per quas tam ex circũferentia, quam ex diametro maximi cir-
              <lb/>
            cul inſp ra, e@uitur ſoliditas ſphærę tummai@r, quam vera, t@m minor.</s>
            <s xml:id="echoid-s10543" xml:space="preserve"/>
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