Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div570" type="section" level="1" n="206">
          <p>
            <s xml:id="echoid-s9373" xml:space="preserve">
              <pb o="209" file="239" n="239" rhead="LIBER QVINTVS."/>
            quoque, vt GI, ad IH, ita tam KP, ad PN, quam MR, ad RN. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">Contractisergo
              <lb/>
            hiſce magnitudinibus ad numeros, erit numerus factus ex GI, primò in
              <note symbol="a" position="right" xlink:label="note-239-01" xlink:href="note-239-01a" xml:space="preserve">19. ſept.</note>
            quartum, æqualis ei, quifit ex IH, ſecundò in KP, tertium. </s>
            <s xml:id="echoid-s9375" xml:space="preserve">Item numerus fa-
              <lb/>
            ctus ex GI, primò in RN, quartum æqualis ei, qui fit ex IH, ſecundò in MR, ter-
              <lb/>
            tium: </s>
            <s xml:id="echoid-s9376" xml:space="preserve"> Ac propterea duo, qui fiunt ex GI, in PN, & </s>
            <s xml:id="echoid-s9377" xml:space="preserve">ex GI, in RN,
              <note symbol="b" position="right" xlink:label="note-239-02" xlink:href="note-239-02a" xml:space="preserve">2. pronunc.</note>
            erunt duobus, qui fiunt ex IH, in KP, & </s>
            <s xml:id="echoid-s9378" xml:space="preserve">IH, in MR. </s>
            <s xml:id="echoid-s9379" xml:space="preserve">Adiecto ergo communi, qui
              <lb/>
            fit ex GI, in KM, erunt tres, qui fiunt ex GI, in KM, & </s>
            <s xml:id="echoid-s9380" xml:space="preserve">in PN, & </s>
            <s xml:id="echoid-s9381" xml:space="preserve">in RN, æquales
              <lb/>
            tribus, qui fiunt ex GI, in KM, & </s>
            <s xml:id="echoid-s9382" xml:space="preserve">ex IH, in KP, & </s>
            <s xml:id="echoid-s9383" xml:space="preserve">in MR. </s>
            <s xml:id="echoid-s9384" xml:space="preserve">Sed hi poſteriores tres
              <lb/>
            tripli ſunt fruſti pyramidis ABCDEF, vt ad fin. </s>
            <s xml:id="echoid-s9385" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s9386" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9387" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s9388" xml:space="preserve">Ergo
              <lb/>
            & </s>
            <s xml:id="echoid-s9389" xml:space="preserve">priores tres, qui nimirum fiunt ex GI, altitudine fruſti in KM, & </s>
            <s xml:id="echoid-s9390" xml:space="preserve">in PN, & </s>
            <s xml:id="echoid-s9391" xml:space="preserve">in
              <lb/>
            RN, hoc eſt, in ſummam ex KM, baſi ABC, æquali, & </s>
            <s xml:id="echoid-s9392" xml:space="preserve">ex PN, baſi DEF, æqua-
              <lb/>
            li, & </s>
            <s xml:id="echoid-s9393" xml:space="preserve">ex RN, media proportionali inter baſes collectam, tripli erunt eiuſdem fru-
              <lb/>
            ſti: </s>
            <s xml:id="echoid-s9394" xml:space="preserve">ideoque tertia eorum pars æqualis erit areæ fruſti. </s>
            <s xml:id="echoid-s9395" xml:space="preserve">quod erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s9396" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9397" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9398" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ratione fruſtũ Coni ABDC, producetur ex altitudine GI, in ſum-
              <lb/>
            mam ex baſe AB, & </s>
            <s xml:id="echoid-s9399" xml:space="preserve">baſe CD, & </s>
            <s xml:id="echoid-s9400" xml:space="preserve">ſuperficie media proportionali inter baſes colle-
              <lb/>
            ctam: </s>
            <s xml:id="echoid-s9401" xml:space="preserve">vt conſtat, ſi concipiantur quadrata KM, NP, baſibus æqualia, & </s>
            <s xml:id="echoid-s9402" xml:space="preserve">proinde ſu-
              <lb/>
            perficies RN, media proportionalis inter baſes, &</s>
            <s xml:id="echoid-s9403" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9404" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div576" type="section" level="1" n="207">
          <head xml:id="echoid-head223" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s9405" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9406" xml:space="preserve">
              <emph style="sc">Si</emph>
            ea, quæ hactenus dicta ſunt, rebus materialibus accommodentur, licebit
              <lb/>
              <note position="right" xlink:label="note-239-03" xlink:href="note-239-03a" xml:space="preserve">Solidit{as} mu-
                <lb/>
              ri.</note>
            nobis per cap. </s>
            <s xml:id="echoid-s9407" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9408" xml:space="preserve">metiri murum quemcunque vniformis craſſitiei, tanquam pa-
              <lb/>
            rallelepipedum quoddam, cuius longitudo eadem ſit, quæ longitudo muri: </s>
            <s xml:id="echoid-s9409" xml:space="preserve">lati-
              <lb/>
            tudo verò eadem quæ muri latitudo: </s>
            <s xml:id="echoid-s9410" xml:space="preserve">altitudo denique, ſiue profunditas eadem,
              <lb/>
            quæ altitudo muri.</s>
            <s xml:id="echoid-s9411" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9412" xml:space="preserve">
              <emph style="sc">Eademqve</emph>
            ratione metiemur fruſtum alicuius marmoris, vel alterius ſaxi,
              <lb/>
            tanquam priſma quodpiam, ſi vniformem habeat craſſitiem, lateraque ad baſes
              <lb/>
            ſint recta.</s>
            <s xml:id="echoid-s9413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9414" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter ſaccum tritici, tanquam Cylindrum quendam, dimetiemur, plus
              <lb/>
              <note position="right" xlink:label="note-239-04" xlink:href="note-239-04a" xml:space="preserve">Solidit{as} ali-
                <lb/>
              cui{us} fruſti
                <lb/>
              marmoris.</note>
            minus. </s>
            <s xml:id="echoid-s9415" xml:space="preserve">Nam cum ſaccus non ſit accuratus Cylindrus, vera eius menſura haberi
              <lb/>
            non poteſt.</s>
            <s xml:id="echoid-s9416" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9417" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9418" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            per caput 2. </s>
            <s xml:id="echoid-s9419" xml:space="preserve">aceruum tritici, tanquam conum aliquem, eodem
              <lb/>
            modo, plus minus, metiri licebit. </s>
            <s xml:id="echoid-s9420" xml:space="preserve">Itaque ſi cognoſcemus, quot grana, vel libræ
              <lb/>
            tritici in cubo, verbi gratia, vnius palmi contineantur, multiplicenturque grana,
              <lb/>
              <note position="right" xlink:label="note-239-05" xlink:href="note-239-05a" xml:space="preserve">Capacit{as} ſac-
                <lb/>
              citritici.</note>
            vel libræ vnius cubiti in numerum cuborum, qui in toto ſacco, vel aceruo reperti
              <lb/>
            ſunt, producetur numerus granorum, vellibrarum in eodem ſacco, vel aceruo exi-
              <lb/>
              <note position="right" xlink:label="note-239-06" xlink:href="note-239-06a" xml:space="preserve">Capacit{as} a-
                <lb/>
              ceruitritici.</note>
            ſtentium.</s>
            <s xml:id="echoid-s9421" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9422" xml:space="preserve">
              <emph style="sc">Sic</emph>
            etiam, ſi detur vas aliquod excauatum in modum parallelepipedi, aut Cy-
              <lb/>
            lindri, ſciemus eius capacitatem, ſi eius parallelepipedum interius aut Cylindrum,
              <lb/>
            non ſecus, ac ſi ſolida figura eſſet, metiemur: </s>
            <s xml:id="echoid-s9423" xml:space="preserve">ita vt ſi cognitum fuerit, quot men-
              <lb/>
            ſuræ aquæ alteriusue liquoris in cubo, verbi gratia, vnius palmi contineantur,
              <lb/>
            ignorari non poſsit, quot menſurę in cubis in toto vaſe contentis comprehen-
              <lb/>
              <note position="right" xlink:label="note-239-07" xlink:href="note-239-07a" xml:space="preserve">Capacit{as} va-
                <lb/>
              ſis excauati.</note>
            dantur, ſi nimirum menſuræ vnius cubi ducantur in numerum cuborum, quos
              <lb/>
            in vaſe comprehendi inuenimus.</s>
            <s xml:id="echoid-s9424" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9425" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9426" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            ſi deſideretur ſoliditas alicuius vaſis, quod tam interius,
              <lb/>
            quam exterius formam habeat parallelepipedi, ſeu priſmatis, Cylindriue, </s>
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