Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div966" type="section" level="1" n="343">
          <p>
            <s xml:id="echoid-s15759" xml:space="preserve">
              <pb o="339" file="367" n="367" rhead="LIBER OCTAVVS."/>
            idem parallelogrammum quadrilatero dato ABCD, æquale eſſe. </s>
            <s xml:id="echoid-s15760" xml:space="preserve"> Quia
              <note symbol="a" position="right" xlink:label="note-367-01" xlink:href="note-367-01a" xml:space="preserve">ſchol. 41.
                <lb/>
              primi.</note>
            parallelogrammum FD, triangulo ABD, & </s>
            <s xml:id="echoid-s15761" xml:space="preserve">parallelogrammum EI, triangulo
              <lb/>
            CBD, æquale eſt; </s>
            <s xml:id="echoid-s15762" xml:space="preserve">erit totum parallelogrammum FI, toti quadrilatero ABCD,
              <lb/>
            æquale.</s>
            <s xml:id="echoid-s15763" xml:space="preserve">
              <unsure/>
            quod eſt propoſitum.</s>
            <s xml:id="echoid-s15764" xml:space="preserve"/>
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        <div xml:id="echoid-div968" type="section" level="1" n="344">
          <head xml:id="echoid-head371" xml:space="preserve">PROBL. 2. PROPOS. 5.</head>
          <p>
            <s xml:id="echoid-s15765" xml:space="preserve">DATO rectangulo ſupra datam rectam æquale rectangulum facilius,
              <lb/>
            quam per propoſ. </s>
            <s xml:id="echoid-s15766" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15767" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15768" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15769" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s15770" xml:space="preserve">conſtituere.</s>
            <s xml:id="echoid-s15771" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15772" xml:space="preserve">
              <emph style="sc">Sit</emph>
            rectangulum A B C D, cui ſupra datam rectam conſtituendum eſt re-
              <lb/>
            ctangulum æquale. </s>
            <s xml:id="echoid-s15773" xml:space="preserve">Producto quolibet latere, ni-
              <lb/>
              <figure xlink:label="fig-367-01" xlink:href="fig-367-01a" number="258">
                <image file="367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/367-01"/>
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            mirum A B, capiatur B E, æqualis datærectæ, ſiue ea
              <lb/>
            ſit maior latere AB, ſiue minor: </s>
            <s xml:id="echoid-s15774" xml:space="preserve">atque ex E, per C,
              <lb/>
            recta ducatur ſecans AD, productam in F, complea-
              <lb/>
            turque rectangulum AH, & </s>
            <s xml:id="echoid-s15775" xml:space="preserve">rectæ BC, DC. </s>
            <s xml:id="echoid-s15776" xml:space="preserve">produ-
              <lb/>
            cantur vſque ad G, I. </s>
            <s xml:id="echoid-s15777" xml:space="preserve"> Eritigitur
              <note symbol="b" position="right" xlink:label="note-367-02" xlink:href="note-367-02a" xml:space="preserve">43. primi.</note>
            CH, complemento CA, ęquale. </s>
            <s xml:id="echoid-s15778" xml:space="preserve">Cumigitur latus CI,
              <lb/>
            ſit lateri BE, id eſt, datærectæ æquale: </s>
            <s xml:id="echoid-s15779" xml:space="preserve">factum erit, quod proponitur.</s>
            <s xml:id="echoid-s15780" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div970" type="section" level="1" n="345">
          <head xml:id="echoid-head372" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s15781" xml:space="preserve">
              <emph style="sc">Datæ</emph>
            rectæ BE, & </s>
            <s xml:id="echoid-s15782" xml:space="preserve">duobus lateribus AB, BC, dati rectanguli,
              <note symbol="c" position="right" xlink:label="note-367-03" xlink:href="note-367-03a" xml:space="preserve">17. ſexti.</note>
            quarta proportionalis C G. </s>
            <s xml:id="echoid-s15783" xml:space="preserve"> Nam rectangulum ſub BE, prima, & </s>
            <s xml:id="echoid-s15784" xml:space="preserve">CG,
              <note symbol="d" position="right" xlink:label="note-367-04" xlink:href="note-367-04a" xml:space="preserve">16. ſexti.</note>
            comprehenſum, rectangulum videlicet C H, æquale erit dato rectangulo AC,
              <lb/>
            ſub ſecunda AB, & </s>
            <s xml:id="echoid-s15785" xml:space="preserve">tertia BC, comprehenſo. </s>
            <s xml:id="echoid-s15786" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s15787" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div972" type="section" level="1" n="346">
          <head xml:id="echoid-head373" xml:space="preserve">PROBL. 3. PROPOS. 6.</head>
          <p>
            <s xml:id="echoid-s15788" xml:space="preserve">DATO rectilineo æquale rectangulum facilius, quam per propoſ. </s>
            <s xml:id="echoid-s15789" xml:space="preserve">45.
              <lb/>
            </s>
            <s xml:id="echoid-s15790" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15791" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15792" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s15793" xml:space="preserve">conſtituere.</s>
            <s xml:id="echoid-s15794" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15795" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            per duas præcedentes propoſ. </s>
            <s xml:id="echoid-s15796" xml:space="preserve">facilè expedietur. </s>
            <s xml:id="echoid-s15797" xml:space="preserve">Nam ſi figura recti-
              <lb/>
            linea in triangula reſoluatur, conſtituent quælibet duo commune latus haben-
              <lb/>
            tia trapezium, cuius latus commune eſt diameter. </s>
            <s xml:id="echoid-s15798" xml:space="preserve"> Igitur ſi ſingulis trapeziis ſingula rectangula fiant æqualia, atque etiam vltimo triangulo, ſi fortè nume-
              <lb/>
            rus triangulorum eſt impar. </s>
            <s xml:id="echoid-s15799" xml:space="preserve">Deinde, ſi, vt in præcedenti propoſ. </s>
            <s xml:id="echoid-s15800" xml:space="preserve">dictum eſt,
              <lb/>
            vni lateri primi rectanguli, & </s>
            <s xml:id="echoid-s15801" xml:space="preserve">duobus lateribus ſecundi, inueniatur
              <note symbol="e" position="right" xlink:label="note-367-05" xlink:href="note-367-05a" xml:space="preserve">4. hui{us}.</note>
            proportionalis; </s>
            <s xml:id="echoid-s15802" xml:space="preserve"> erit rectangulum ſub aſſumpto latere in primo
              <note symbol="f" position="right" xlink:label="note-367-06" xlink:href="note-367-06a" xml:space="preserve">12. ſexti.</note>
            & </s>
            <s xml:id="echoid-s15803" xml:space="preserve">quarta proportionali, ſecundo rectangulo æquale. </s>
            <s xml:id="echoid-s15804" xml:space="preserve">Quocirca ſi alterum la-
              <lb/>
              <note symbol="g" position="right" xlink:label="note-367-07" xlink:href="note-367-07a" xml:space="preserve">16. ſexti.</note>
            tus prope aſſumptum in primo rectangulo producatur, & </s>
            <s xml:id="echoid-s15805" xml:space="preserve">ex producto abſcin-
              <lb/>
            datur recta æqualis quartæ proportionali, compleatur que totum rectangulum,
              <lb/>
            habebitur rectangulum ex duobus compoſitum æquale duobus primis tra-
              <lb/>
            peziis. </s>
            <s xml:id="echoid-s15806" xml:space="preserve">Et ſi eidem lateri, ac duobus tertij rectanguli reperiatur rurſum quar-
              <lb/>
            ta proportionalis, & </s>
            <s xml:id="echoid-s15807" xml:space="preserve">huic quartæ ſumatur in priori latere producto recta </s>
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