Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div582" type="section" level="1" n="208">
          <p>
            <s xml:id="echoid-s9686" xml:space="preserve">
              <pb o="214" file="244" n="244" rhead="GEOMETR. PRACT."/>
            tam Tetraedri ſuperficiem conficiet: </s>
            <s xml:id="echoid-s9687" xml:space="preserve">In Octaedro deinde duodecies acceptum
              <lb/>
              <note position="left" xlink:label="note-244-01" xlink:href="note-244-01a" xml:space="preserve">Superficies re
                <lb/>
              gularium cor
                <lb/>
              porum & per-
                <lb/>
              pendicular{es}
                <lb/>
              baſium.</note>
            toti ſuperficiei Octaedri adæquabitur: </s>
            <s xml:id="echoid-s9688" xml:space="preserve">Atin Dodecaedro, & </s>
            <s xml:id="echoid-s9689" xml:space="preserve">Icoſaedro tricies
              <lb/>
            ſumptum ſuperficiei totitam Dodecaedri, quam Icoſaedri æquale erit. </s>
            <s xml:id="echoid-s9690" xml:space="preserve">Dicta au-
              <lb/>
            tem perpendicularis EF, in baſe cubi æqualis eſt ſemiſsilateris cubi AB, Quo- niam enim perpendicularis EF, ſecat latus AB, bifariam, eſt que ipſi AF, æqua- lis, quod anguli FAE, FEA, ſemirecti ſint; </s>
            <s xml:id="echoid-s9691" xml:space="preserve">conſtat EF, ſemiſsi lateris cubi eſſe ę-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-244-02" xlink:href="note-244-02a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            qualem. </s>
            <s xml:id="echoid-s9692" xml:space="preserve">Perpendicularis autem DE, in baſe Tetraedri; </s>
            <s xml:id="echoid-s9693" xml:space="preserve">Octaedri, & </s>
            <s xml:id="echoid-s9694" xml:space="preserve">Icoſaedri,
              <lb/>
            ſemiſsis eſt ſemidiametri C D. </s>
            <s xml:id="echoid-s9695" xml:space="preserve"> Cum ergo latus A C, ſit potentia triplum
              <note symbol="b" position="left" xlink:label="note-244-03" xlink:href="note-244-03a" xml:space="preserve">6. primi.</note>
            midiametri CD: </s>
            <s xml:id="echoid-s9696" xml:space="preserve">Si fiat, vt 3. </s>
            <s xml:id="echoid-s9697" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s9698" xml:space="preserve">ita quadratum lateris dati AC, ad aliud, prodi-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-244-04" xlink:href="note-244-04a" xml:space="preserve">2. coroll. 12.
                <lb/>
              tertijdec.</note>
            bit quadratum ſemidiametri C D, cuius radix quadrata ipſam C D, indicabit, e-
              <lb/>
            iuſque ſemiſsis perpendicularem DE, exhibebit. </s>
            <s xml:id="echoid-s9699" xml:space="preserve">Perpendicularis denique FG,
              <lb/>
              <note symbol="d" position="left" xlink:label="note-244-05" xlink:href="note-244-05a" xml:space="preserve">12. tertijdec.</note>
            in baſe Dodecaedrie ſemiſsis eſt ſummæ ex ſemidiametro AF, & </s>
            <s xml:id="echoid-s9700" xml:space="preserve">latere decago-
              <lb/>
              <note symbol="e" position="left" xlink:label="note-244-06" xlink:href="note-244-06a" xml:space="preserve">1. quartidec.</note>
            ni circuli ABD, collectæ, quodlatus decagoni cognoſcetur, vt ad finem Nume.
              <lb/>
            </s>
            <s xml:id="echoid-s9701" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9702" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s9703" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9704" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            verò ſolidum, quod fit ex perpendiculari è centro cuius
              <note symbol="f" position="left" xlink:label="note-244-07" xlink:href="note-244-07a" xml:space="preserve">ſchol. 20. ter-
                <lb/>
              tijdec.</note>
            corporis regularis ad aliquam eius baſem ducta in tertiam partem ſuperficiei i-
              <lb/>
            pſius corporis, ipſi corpori æquale eſt; </s>
            <s xml:id="echoid-s9705" xml:space="preserve">ſi inueſtigetur ſuperficies conuexa dati
              <lb/>
              <note position="left" xlink:label="note-244-08" xlink:href="note-244-08a" xml:space="preserve">Areæ corpo-
                <lb/>
              rumregulari-
                <lb/>
              um aliter in-
                <lb/>
              uentæ.</note>
            corporis regularis, vt proximè docuimus, atque in tertiam eius partem ducatur
              <lb/>
            altitudo vnius pyramidum, in quas corpus ipſum per rectas è centro ipſius du-
              <lb/>
            ctas diuiditur, (quæ altitudo reperietur, vt ſupra tradidimus) hoc eſt, perpendi-
              <lb/>
            cularis è centro corporis in eius baſem demiſſa, procreabitur area, ſiue ſoliditas
              <lb/>
            ipſius corporis. </s>
            <s xml:id="echoid-s9706" xml:space="preserve">Quæ etiam obtinebitur, ſi dicta altitudo ducatur in totam ſu-
              <lb/>
            perficiem conuexam, & </s>
            <s xml:id="echoid-s9707" xml:space="preserve">producti tertia pars capiatur.</s>
            <s xml:id="echoid-s9708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9709" xml:space="preserve">8. </s>
            <s xml:id="echoid-s9710" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            vt vides, tota difficultas in corporibus regularibus dimetien-
              <lb/>
            dis conſiſtit fermè totain altitudine pyramidis baſem habentis eandem cũ cor-
              <lb/>
            pore, verticem autem in centro ſphæræ, exquirenda: </s>
            <s xml:id="echoid-s9711" xml:space="preserve">cuius quideminuentio Ge-
              <lb/>
            ometrica pernumeros moleſtiſsima eſt, propter radices ſurdas, & </s>
            <s xml:id="echoid-s9712" xml:space="preserve">numeros fra-
              <lb/>
              <figure xlink:label="fig-244-01" xlink:href="fig-244-01a" number="156">
                <image file="244-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/244-01"/>
              </figure>
            ctos, quorum numeratores, denominatoreſq; </s>
            <s xml:id="echoid-s9713" xml:space="preserve">nimis magniſunt, adeo vt ope-
              <lb/>
            ræ pretium videatur eſſe eandem mechanicè explorare, vt adinitium Num. </s>
            <s xml:id="echoid-s9714" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9715" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s9716" xml:space="preserve">& </s>
            <s xml:id="echoid-s9717" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9718" xml:space="preserve">diximus, præſertim ſi ex quiſita diligentia in ea per inſtrumentum partium
              <lb/>
            dimetienda adhibeatur. </s>
            <s xml:id="echoid-s9719" xml:space="preserve">Sed quia non ſemper in promptu habemus corpora re-
              <lb/>
            gularia, vt mechanicè eam altitudinem conſequi poſsimus, libetrationem quã-
              <lb/>
            dam nouam, eamque facillimam hic præſcribere, qua ſine moleſtia illa numero-
              <lb/>
            rum, eadem illa altitudo per lineas inueniatur, etiamſi corpus regulare </s>
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