Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div491" type="section" level="1" n="179">
          <p>
            <s xml:id="echoid-s8278" xml:space="preserve">
              <pb o="191" file="221" n="221" rhead="LIBER QVARTVS."/>
            @ {1/2
              <unsure/>
            }. </s>
            <s xml:id="echoid-s8279" xml:space="preserve">& </s>
            <s xml:id="echoid-s8280" xml:space="preserve">IB, {1/24}. </s>
            <s xml:id="echoid-s8281" xml:space="preserve">& </s>
            <s xml:id="echoid-s8282" xml:space="preserve">KB, {1/48}. </s>
            <s xml:id="echoid-s8283" xml:space="preserve">& </s>
            <s xml:id="echoid-s8284" xml:space="preserve">LB, {1/96}. </s>
            <s xml:id="echoid-s8285" xml:space="preserve">ac proinde recta BL, latus erit Polygoni cir-
              <lb/>
            culo inſcripti, quod 96. </s>
            <s xml:id="echoid-s8286" xml:space="preserve">lateribus æqualibus continetur. </s>
            <s xml:id="echoid-s8287" xml:space="preserve">Quoniam vero BL,
              <lb/>
            poſita eſt 66. </s>
            <s xml:id="echoid-s8288" xml:space="preserve">ſi 66. </s>
            <s xml:id="echoid-s8289" xml:space="preserve">ducantur in 96. </s>
            <s xml:id="echoid-s8290" xml:space="preserve">fiet ambitus Polygoni 6336. </s>
            <s xml:id="echoid-s8291" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-221-01" xlink:href="note-221-01a" xml:space="preserve">8. quinti.</note>
            ambitus Polygoniad diametrum AB, maiorem proportionem habebit, quam
              <lb/>
            6336. </s>
            <s xml:id="echoid-s8292" xml:space="preserve">ad 2017 {1/4}. </s>
            <s xml:id="echoid-s8293" xml:space="preserve">cum diameter A B, oſtenſa ſit minor, quam 2017 {1/4}. </s>
            <s xml:id="echoid-s8294" xml:space="preserve"> Eſt
              <note symbol="b" position="right" xlink:label="note-221-02" xlink:href="note-221-02a" xml:space="preserve">8. quinti.</note>
            proportio 6336. </s>
            <s xml:id="echoid-s8295" xml:space="preserve">ad 2017 {1/4}. </s>
            <s xml:id="echoid-s8296" xml:space="preserve">maior, quam tripla ſuperdecupartiens ſeptuageſi-
              <lb/>
            mas primas, quod proportio 6336. </s>
            <s xml:id="echoid-s8297" xml:space="preserve">ad 2017 {65/223}. </s>
            <s xml:id="echoid-s8298" xml:space="preserve">(qui numerus maior eſt,
              <lb/>
            quam 2107 {1/4}) ſit tripla ſuperdecupartiens ſeptuageſimas primas. </s>
            <s xml:id="echoid-s8299" xml:space="preserve">Ergo ambi-
              <lb/>
            tus Polygoni maiorem habet proportionem ad diametrum, quam 3 {10/71}.
              <lb/>
            </s>
            <s xml:id="echoid-s8300" xml:space="preserve">Cumigitur circumferentia circuliſit maior ambitu Polygoni, habebit
              <note symbol="c" position="right" xlink:label="note-221-03" xlink:href="note-221-03a" xml:space="preserve">8. quinti.</note>
            ferentia ad diametrum multo maiorem proportionem, quam 3 {10/71}. </s>
            <s xml:id="echoid-s8301" xml:space="preserve">Ac proin-
              <lb/>
            de circumferentia diametrum continebit ter, & </s>
            <s xml:id="echoid-s8302" xml:space="preserve">inſuper partem maiorem,
              <lb/>
            quam {10/75}. </s>
            <s xml:id="echoid-s8303" xml:space="preserve">Nam ſi contineret {10/71}. </s>
            <s xml:id="echoid-s8304" xml:space="preserve">haberet circumferentia ad diametrum propor-
              <lb/>
            tionem 3 {10/71}. </s>
            <s xml:id="echoid-s8305" xml:space="preserve">Si autem contineret maiorem partem, quam {10/71}. </s>
            <s xml:id="echoid-s8306" xml:space="preserve">haberet propor-
              <lb/>
            tionemminorem, quam 3 {10/71}. </s>
            <s xml:id="echoid-s8307" xml:space="preserve">cumtamen maiorem habere demonſtratum ſit.
              <lb/>
            </s>
            <s xml:id="echoid-s8308" xml:space="preserve">Et quoniam {1/8}. </s>
            <s xml:id="echoid-s8309" xml:space="preserve">minor eſt, quam {10/71}. </s>
            <s xml:id="echoid-s8310" xml:space="preserve">liquet ex hac ſecunda parte propoſitionis,
              <lb/>
            circumferentiam continere diametrum ter, & </s>
            <s xml:id="echoid-s8311" xml:space="preserve">plus, quam {1/8}. </s>
            <s xml:id="echoid-s8312" xml:space="preserve">diametri. </s>
            <s xml:id="echoid-s8313" xml:space="preserve">
              <lb/>
            Cum ergo ex prima parte conſtet, circumferentiam continere diametrum ter,
              <lb/>
            & </s>
            <s xml:id="echoid-s8314" xml:space="preserve">minus, quam {1/7}. </s>
            <s xml:id="echoid-s8315" xml:space="preserve">diametri: </s>
            <s xml:id="echoid-s8316" xml:space="preserve">perſpicuum eſt, veram proportionem circumfe-
              <lb/>
            rentiæ ad diametrum conſiſtere inter triplam ſeſquiſeptimam, & </s>
            <s xml:id="echoid-s8317" xml:space="preserve">triplam ſeſqui-
              <lb/>
            octauam.</s>
            <s xml:id="echoid-s8318" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div504" type="section" level="1" n="180">
          <head xml:id="echoid-head187" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s8319" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            ſi diameter per 3 {1/7}. </s>
            <s xml:id="echoid-s8320" xml:space="preserve">multiplicetur, gignetur numerus maior, quam
              <lb/>
            circumferentia: </s>
            <s xml:id="echoid-s8321" xml:space="preserve">ſi verò multiplicetur per 3 {10/71}. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">pro creabitur minor numerus,
              <lb/>
            quam circumferentia. </s>
            <s xml:id="echoid-s8323" xml:space="preserve">Econtrario, ſi circumferentia diuidatur per 3 {1/7}. </s>
            <s xml:id="echoid-s8324" xml:space="preserve">produ-
              <lb/>
            cetur numerus minor, quam diameter: </s>
            <s xml:id="echoid-s8325" xml:space="preserve">ſi vero diuidatur per 3 {10/71}. </s>
            <s xml:id="echoid-s8326" xml:space="preserve">prodibit nume-
              <lb/>
            rus maior, quam diameter.</s>
            <s xml:id="echoid-s8327" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div505" type="section" level="1" n="181">
          <head xml:id="echoid-head188" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s8328" xml:space="preserve">CIRCVLVS quilibet ad quadratum diametri proportionem habet,
              <lb/>
            quam ad 11. </s>
            <s xml:id="echoid-s8329" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s8330" xml:space="preserve">proximé.</s>
            <s xml:id="echoid-s8331" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8332" xml:space="preserve">
              <emph style="sc">Sit</emph>
            circulus A B C D, & </s>
            <s xml:id="echoid-s8333" xml:space="preserve">quadratum diametri B D, circulo circumſcri-
              <lb/>
              <figure xlink:label="fig-221-01" xlink:href="fig-221-01a" number="141">
                <image file="221-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/221-01"/>
              </figure>
            ptum E G H I. </s>
            <s xml:id="echoid-s8334" xml:space="preserve">Dico circulum ad quadra-
              <lb/>
            tum eſſe, vt 11. </s>
            <s xml:id="echoid-s8335" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s8336" xml:space="preserve">proximè. </s>
            <s xml:id="echoid-s8337" xml:space="preserve">Pro-
              <lb/>
            ducto enim latere E G, ſumatur E K, ip-
              <lb/>
            ſius E G, tripla, & </s>
            <s xml:id="echoid-s8338" xml:space="preserve">K F, ſeptima pars dia-
              <lb/>
            metri B D, vel lateris E G; </s>
            <s xml:id="echoid-s8339" xml:space="preserve"/>
          </p>
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