Commandino, Federico, Liber de centro gravitatis solidorum, 1565
page |< < of 101 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000618">
                <pb pagenum="30" xlink:href="023/01/067.jpg"/>
                <arrow.to.target n="marg71"/>
                <lb/>
              pra demonſtratum eſt, ita eſſe cylindrum, uel cylindri por­
                <lb/>
              tionem ad priſma, cuius baſis rectilinea figura, & æqua­
                <lb/>
              lis altitudo. </s>
              <s id="s.000619">ergo per conuerſionem rationis, ut circulus,
                <lb/>
              uel ellipſis ad portiones, ita conus, uel coni portio ad por­
                <lb/>
              tiones ſolidas. </s>
              <s id="s.000620">quare conus uel coni portio ad portiones
                <lb/>
              ſolidas maiorem habet proportionem, quam ge ad ef: &
                <lb/>
              diuidendo, pyramis ad portiones ſolidas maiorem pro­
                <lb/>
              portionem habet, quam gf ad fe. </s>
              <s id="s.000621">fiat igitur qf ad fe
                <lb/>
              ut pyramis ad dictas portiones. </s>
              <s id="s.000622">Itaque quoniam a cono
                <lb/>
              uel coni portione, cuius grauitatis centrum eſt f, aufer­
                <lb/>
              tur pyramis, cuius centrum e; reliquæ magnitudinis,
                <lb/>
              quæ ex ſolidis portionibus conſtat, centrum grauitatis
                <lb/>
              erit in linea ef protracta, & in puncto q.</s>
              <s id="s.000623"> quod fieri
                <lb/>
              non poteſt: eſt enim centrum grauitatis intra. </s>
              <s id="s.000624">Conſtat
                <lb/>
              igitur coni, uel coni portionis grauitatis centrum eſſe pun
                <lb/>
              ctum e. </s>
              <s id="s.000625">quæ omnia demonſtrare oportebat.</s>
            </p>
            <p type="margin">
              <s id="s.000626">
                <margin.target id="marg71"/>
              8 huius</s>
            </p>
            <p type="head">
              <s id="s.000627">THEOREMA XIX. PROPOSITIO XXIII.</s>
            </p>
            <p type="main">
              <s id="s.000628">QVODLIBET fruſtum à pyramide, quæ
                <lb/>
              triangularem baſim habeat, abſciſſum, diuiditur
                <lb/>
              in tres pyramides proportionales, in ea proportio
                <lb/>
              ne, quæ eſt lateris maioris baſis ad latus minoris
                <lb/>
              ipſi reſpondens.</s>
            </p>
            <p type="main">
              <s id="s.000629">Hoc demonſtrauit Leonardus Piſanus in libro, qui de­
                <lb/>
              praxi geometriæ inſcribitur. </s>
              <s id="s.000630">Sed quoniam is adhuc im­
                <lb/>
              preſſus non eſt, nos ipſius demonſtrationem breuiter
                <lb/>
              perſtringemus, rem ipſam ſecuti, non uerba. </s>
              <s id="s.000631">Sit fru­
                <lb/>
              ſtum pyramidis abcdef, cuius maior baſis triangulum
                <lb/>
              abc, minor def: & iunctis ae, cc, cd, per, line­
                <lb/>
              as ae, ec ducatur planum ſecans fruſtum: itemque per
                <lb/>
              lineas ec, cd; & per cd, da alia plana ducantur, quæ
                <lb/>
              diuident fruſtum in trcs pyramides abce, adce, defc. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum