Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <pb o="98" file="134" n="135" rhead="Comment. in I. Cap. Sphæræ"/>
        </div>
        <div xml:id="echoid-div257" type="section" level="1" n="88">
          <head xml:id="echoid-head92" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s4764" xml:space="preserve">Ex omnibusiis, quæ demonſtrata ſunt, perſpicuum eſt circu-
              <lb/>
              <note position="left" xlink:label="note-134-01" xlink:href="note-134-01a" xml:space="preserve">@Circul’ om
                <lb/>
              nibus figu-
                <lb/>
              @is rectili-
                <lb/>
              neis ſibi iſo
                <lb/>
              perimetris
                <lb/>
              maior eſt.</note>
            lum abſolute omnium figurarum rectilinearum ſibi iſoperimetra-
              <lb/>
            rum maximum eſſe.</s>
            <s xml:id="echoid-s4765" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4766" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            enim ex propoſitione 5. </s>
            <s xml:id="echoid-s4767" xml:space="preserve">habetur, regularium figurarum iſoperime-
              <lb/>
            trarum eam, quæ plura latera continet, eſſe maiorem: </s>
            <s xml:id="echoid-s4768" xml:space="preserve">Rurſus ex propoſitione 12. </s>
            <s xml:id="echoid-s4769" xml:space="preserve">conſtat,
              <lb/>
            inter omnes figuras iſoperimetras æqualia numero latera habentes, eam maximam eſ-
              <lb/>
            ſe, quę regularis eſt: </s>
            <s xml:id="echoid-s4770" xml:space="preserve">Ex hac denique 13. </s>
            <s xml:id="echoid-s4771" xml:space="preserve">propoſitioue perſpicuum eſt, circulum omnium
              <lb/>
            figurarum iſoperimet rarum regularium eſſe maximum: </s>
            <s xml:id="echoid-s4772" xml:space="preserve">Manifeſte concluditur, circu-
              <lb/>
            lum abſolute ac ſimpliciter omnium figurarum rectilinearum ſibi iſoperimetrarum ma-
              <lb/>
            ximum eſſe quod eſt propoſitum.</s>
            <s xml:id="echoid-s4773" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div259" type="section" level="1" n="89">
          <head xml:id="echoid-head93" style="it" xml:space="preserve">THEOR. 12. PROPOS. 14.</head>
          <p style="it">
            <s xml:id="echoid-s4774" xml:space="preserve">
              <emph style="sc">Area</emph>
            cuiuslibet pyramidis æqualis eſt ſolido rectangulo conten-
              <lb/>
              <note position="left" xlink:label="note-134-02" xlink:href="note-134-02a" xml:space="preserve">Pyramis
                <lb/>
              quælibet
                <lb/>
              cui paralle-
                <lb/>
              lepipedo ſit
                <lb/>
              @qualis.</note>
            to ſub perpendiculari à uertice ad baſim protracta, & </s>
            <s xml:id="echoid-s4775" xml:space="preserve">tertia parte
              <lb/>
            baſis.</s>
            <s xml:id="echoid-s4776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4777" xml:space="preserve">
              <emph style="sc">Sit</emph>
            pyramis, cuius baſis quotcu nque laterum A B C D E, & </s>
            <s xml:id="echoid-s4778" xml:space="preserve">uertex F.
              <lb/>
            </s>
            <s xml:id="echoid-s4779" xml:space="preserve">
              <figure xlink:label="fig-134-01" xlink:href="fig-134-01a" number="36">
                <image file="134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/134-01"/>
              </figure>
            Solidum autem rectangulu
              <unsure/>
            m G N, cu-
              <lb/>
            ius baſis G H I K, æqualis ſit tertię par-
              <lb/>
            ti baſis A B C D E, altitudo uero, ſiue
              <lb/>
            perpendicularis G L, æqualis altitudini
              <lb/>
            pyramidis, ſiue perpendiculari à uerti-
              <lb/>
            ce pyramidis ad eius baſim productæ.
              <lb/>
            </s>
            <s xml:id="echoid-s4780" xml:space="preserve">Dico ſolidum rectangulum G N, ęqua-
              <lb/>
            le eſſe pyramidi A B C D E F. </s>
            <s xml:id="echoid-s4781" xml:space="preserve">Ducan-
              <lb/>
            tur enim ab oibus angulis baſis G H I K,
              <lb/>
            ad aliquod punctum baſis oppoſitę, ni-
              <lb/>
            mirum ad L, lineę rectæ, ita ut conſti-
              <lb/>
            tuatur pyramis G H I K L, eandem ha-
              <lb/>
            bens baſim cum ſolido G N, eand emq́ue
              <lb/>
            altitudinem & </s>
            <s xml:id="echoid-s4782" xml:space="preserve">cum eodem ſolido G N,
              <lb/>
            & </s>
            <s xml:id="echoid-s4783" xml:space="preserve">cum pyramide A B C D E F. </s>
            <s xml:id="echoid-s4784" xml:space="preserve">Quo-
              <lb/>
            niam igitur pyramis A B C D E F, tri-
              <lb/>
            pla eſt pyramidis G H I K L, ut in ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s4785" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4786" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4787" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4788" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4789" xml:space="preserve">demonſtraui-
              <lb/>
            mus: </s>
            <s xml:id="echoid-s4790" xml:space="preserve">Et ſolidum G N, triplum quoque
              <lb/>
            eſt, ex coroll. </s>
            <s xml:id="echoid-s4791" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4792" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4793" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4795" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4796" xml:space="preserve">
              <lb/>
            eiuſdem pyramidis G H I K L; </s>
            <s xml:id="echoid-s4797" xml:space="preserve">erit ſo-
              <lb/>
            lidum G N, pyramidi A B C D E F, ęqua
              <lb/>
            le. </s>
            <s xml:id="echoid-s4798" xml:space="preserve">Quapropter area cuiuslibet pyrami-
              <lb/>
            dis ęqualis eſt ſolido rectãgulo, &</s>
            <s xml:id="echoid-s4799" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4800" xml:space="preserve">quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s4801" xml:space="preserve"/>
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