Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div665" type="section" level="1" n="233">
          <pb o="232" file="262" n="262" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div667" type="section" level="1" n="234">
          <head xml:id="echoid-head252" xml:space="preserve">DE AREA SPHÆROIDIS, EIVSDEM-
            <lb/>
          que portionum.</head>
          <head xml:id="echoid-head253" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          VII.</head>
          <p>
            <s xml:id="echoid-s10818" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10819" xml:space="preserve">
              <emph style="sc">SIt</emph>
            Ellipſis ABCD, cuius maior axis AC, minor B D, priorem ad angulos
              <lb/>
            rectos ſecans. </s>
            <s xml:id="echoid-s10820" xml:space="preserve">Soliditatem ergo Sphæroidis, id eſt, ſolidi ex circumuolu-
              <lb/>
            tione Ellipſis circa axem effecti, ita nanciſcemur. </s>
            <s xml:id="echoid-s10821" xml:space="preserve">Quoniam planum per
              <lb/>
            BD, ductum, & </s>
            <s xml:id="echoid-s10822" xml:space="preserve">rectum ad axem AC, circulum facit, vt à Federico Commandi-
              <lb/>
            no ad propoſ. </s>
            <s xml:id="echoid-s10823" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10824" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10825" xml:space="preserve">Archimedis de Conoidibus, & </s>
            <s xml:id="echoid-s10826" xml:space="preserve">Sphæroidib. </s>
            <s xml:id="echoid-s10827" xml:space="preserve">demonſtratur.
              <lb/>
            </s>
            <s xml:id="echoid-s10828" xml:space="preserve">cuius diameter BD, & </s>
            <s xml:id="echoid-s10829" xml:space="preserve">centrum E; </s>
            <s xml:id="echoid-s10830" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s10831" xml:space="preserve">29. </s>
            <s xml:id="echoid-s10832" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10833" xml:space="preserve">Archimedis de Cono-
              <lb/>
            id. </s>
            <s xml:id="echoid-s10834" xml:space="preserve">& </s>
            <s xml:id="echoid-s10835" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10836" xml:space="preserve">ſemiſsis Sphæroidis A B D, dupla coni ean dem baſem cum illa
              <lb/>
            ſemiſſe, circulum videlicet diametri B D, habentis, & </s>
            <s xml:id="echoid-s10837" xml:space="preserve">altitudinem eandem E A. </s>
            <s xml:id="echoid-s10838" xml:space="preserve">
              <lb/>
            Igitur ſi huius coni ſoliditas per capit. </s>
            <s xml:id="echoid-s10839" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10840" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10841" xml:space="preserve">inueſtigetur, & </s>
            <s xml:id="echoid-s10842" xml:space="preserve">duplicetur,
              <lb/>
              <note position="left" xlink:label="note-262-01" xlink:href="note-262-01a" xml:space="preserve">Soliditas Sphæ
                <lb/>
              roidis.</note>
            exurget ſoliditas ſemiſsis Sphæroidis: </s>
            <s xml:id="echoid-s10843" xml:space="preserve">quæ duplicata ſoliditatem totius Sphę-
              <lb/>
            roidis exhibebit.</s>
            <s xml:id="echoid-s10844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10845" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10846" xml:space="preserve">
              <emph style="sc">Dvcatvr</emph>
            minori axi B D, parallela F G, ſecans maiorem axemin H,
              <lb/>
            ad rectos angulos. </s>
            <s xml:id="echoid-s10847" xml:space="preserve">Si igitur per F G, ducatur planum rectum ad axem, fiet cir-
              <lb/>
            culus in Sphæroide diametrum habens F G, & </s>
            <s xml:id="echoid-s10848" xml:space="preserve">centrum H, vt Federicus Com-
              <lb/>
            mandinus ad propoſ. </s>
            <s xml:id="echoid-s10849" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10850" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10851" xml:space="preserve">Archim. </s>
            <s xml:id="echoid-s10852" xml:space="preserve">de Conoid. </s>
            <s xml:id="echoid-s10853" xml:space="preserve">& </s>
            <s xml:id="echoid-s10854" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10855" xml:space="preserve">demonſtrauit; </s>
            <s xml:id="echoid-s10856" xml:space="preserve">ab-
              <lb/>
              <figure xlink:label="fig-262-01" xlink:href="fig-262-01a" number="167">
                <image file="262-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/262-01"/>
              </figure>
            ſcindentur que portiones Sphæroidis F A G, minor & </s>
            <s xml:id="echoid-s10857" xml:space="preserve">
              <lb/>
            FCG, maior. </s>
            <s xml:id="echoid-s10858" xml:space="preserve">Vtriuſq; </s>
            <s xml:id="echoid-s10859" xml:space="preserve">ſoliditas ita fiet cognita. </s>
            <s xml:id="echoid-s10860" xml:space="preserve">Quo-
              <lb/>
            niam per propoſ. </s>
            <s xml:id="echoid-s10861" xml:space="preserve">31. </s>
            <s xml:id="echoid-s10862" xml:space="preserve">libri Archimedis de Conoid. </s>
            <s xml:id="echoid-s10863" xml:space="preserve">& </s>
            <s xml:id="echoid-s10864" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-262-02" xlink:href="note-262-02a" xml:space="preserve">Solidit{as} por-
                <lb/>
              tionum Sphæ-
                <lb/>
              roidis.</note>
            Sphęroid. </s>
            <s xml:id="echoid-s10865" xml:space="preserve">Conus, cuius baſis circulus diametri F G, & </s>
            <s xml:id="echoid-s10866" xml:space="preserve">
              <lb/>
            axis H A, ad minorem portionem ſphęroidis F A G,
              <lb/>
            proportionẽ habet, quam maioris portionis axis HC,
              <lb/>
            ad ſummam rectarum EC, HC: </s>
            <s xml:id="echoid-s10867" xml:space="preserve">Si fiat, vt HC, maioris
              <lb/>
            portionis axis ad ſummam rectarum E C, H C, ita co-
              <lb/>
            nus prædictus ad aliud, (qui quidem conus ex cap. </s>
            <s xml:id="echoid-s10868" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s10869" xml:space="preserve">huius libri cognitus erit.) </s>
            <s xml:id="echoid-s10870" xml:space="preserve">prodibit ſoliditas minoris
              <lb/>
            portionis ſphęroidis F A G.</s>
            <s xml:id="echoid-s10871" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10872" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            quia per propoſ. </s>
            <s xml:id="echoid-s10873" xml:space="preserve">33. </s>
            <s xml:id="echoid-s10874" xml:space="preserve">libri Archim. </s>
            <s xml:id="echoid-s10875" xml:space="preserve">de Conoid. </s>
            <s xml:id="echoid-s10876" xml:space="preserve">& </s>
            <s xml:id="echoid-s10877" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10878" xml:space="preserve">conus,
              <lb/>
            cuius baſis circulus diametri F G, & </s>
            <s xml:id="echoid-s10879" xml:space="preserve">axis H C, ad maiorem portionem Sphęro-
              <lb/>
            idis FCG, proportionem habet, quam minoris portionis axis HA, ad ſummam
              <lb/>
            rectarum E A, H A: </s>
            <s xml:id="echoid-s10880" xml:space="preserve">ſi fiat, vt H A, minoris portionis axis ad ſummam rectarum
              <lb/>
            EA, HA, ita prædictus conus (quem per cap. </s>
            <s xml:id="echoid-s10881" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10882" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10883" xml:space="preserve">metieris) ad aliud, pro-
              <lb/>
            creabitur ſoliditas maioris portionis ſphęroidis FCG.</s>
            <s xml:id="echoid-s10884" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div670" type="section" level="1" n="235">
          <head xml:id="echoid-head254" xml:space="preserve">DE AREA CONOIDIS
            <lb/>
          parabolici.</head>
          <head xml:id="echoid-head255" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          VIII.</head>
          <p>
            <s xml:id="echoid-s10885" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10886" xml:space="preserve">
              <emph style="sc">SIt</emph>
            Parabola A B C, cuius axis B D, ad baſem A C, rectus. </s>
            <s xml:id="echoid-s10887" xml:space="preserve">Solidita-
              <lb/>
              <note position="left" xlink:label="note-262-03" xlink:href="note-262-03a" xml:space="preserve">Soliditas Co-
                <lb/>
              noidis Para-
                <lb/>
              bolici.</note>
            tem igitur Conoidis parabolici, quod parabola circa axem circumducta
              <lb/>
            effi cit, ita metiemur. </s>
            <s xml:id="echoid-s10888" xml:space="preserve">Quo niam per ea, quæ ad prop oſ. </s>
            <s xml:id="echoid-s10889" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10890" xml:space="preserve">libri Archim.</s>
            <s xml:id="echoid-s10891" xml:space="preserve"/>
          </p>
        </div>
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