Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000939">
                <pb pagenum="45" xlink:href="023/01/097.jpg"/>
              ad punctum
                <foreign lang="grc">ω.</foreign>
              Sed quoniam
                <foreign lang="grc">π</foreign>
              circumſcripta itidem alia
                <lb/>
              figura æquali interuallo ad portionis centrum accedit, ubi
                <lb/>
              primum
                <foreign lang="grc">φ</foreign>
              applicuerit ſe ad
                <foreign lang="grc">ω,</foreign>
              &
                <foreign lang="grc">π</foreign>
              ad
                <expan abbr="punctũ">punctum</expan>
                <foreign lang="grc">ψ,</foreign>
              hoc eſt ad
                <lb/>
              portionis centrum ſe applicabit. </s>
              <s id="s.000940">quod fieri nullo modo
                <lb/>
              poſſe perſpicuum eſt. </s>
              <s id="s.000941">non aliter idem abſurdum ſequetur,
                <lb/>
              fi ponamus centrum portionis recedere à medio ad par­
                <lb/>
              tes
                <foreign lang="grc">ω;</foreign>
              eſſet enim aliquando centrum figuræ inſcriptæ idem
                <lb/>
              quod portionis
                <expan abbr="centrũ">centrum</expan>
              . </s>
              <s id="s.000942">ergo punctum e centrum erit gra
                <lb/>
              uitatis portionis abc. quod demonſtrare oportebat.</s>
            </p>
            <p type="margin">
              <s id="s.000943">
                <margin.target id="marg103"/>
              7. huius</s>
            </p>
            <p type="margin">
              <s id="s.000944">
                <margin.target id="marg104"/>
              8. primi
                <lb/>
              libri Ar­
                <lb/>
              chimedis</s>
            </p>
            <p type="margin">
              <s id="s.000945">
                <margin.target id="marg105"/>
              11. duo­
                <lb/>
              decimi.</s>
            </p>
            <p type="margin">
              <s id="s.000946">
                <margin.target id="marg106"/>
              15. quinti</s>
            </p>
            <p type="margin">
              <s id="s.000947">
                <margin.target id="marg107"/>
              2. duode­
                <lb/>
              cimi</s>
            </p>
            <p type="margin">
              <s id="s.000948">
                <margin.target id="marg108"/>
              20. primi
                <lb/>
                <expan abbr="conicorũ">conicorum</expan>
              </s>
            </p>
            <p type="margin">
              <s id="s.000949">
                <margin.target id="marg109"/>
              19.
                <lb/>
              quinti</s>
            </p>
            <p type="main">
              <s id="s.000950">Quod autem ſupra
                <expan abbr="demõſtratum">demonſtratum</expan>
              eſt in portione conoi­
                <lb/>
              dis recta per figuras, quæ ex cylindris æqualem altitudi­
                <lb/>
              dinem habentibus conſtant, idem ſimiliter demonſtrabi­
                <lb/>
              mus per figuras ex cylindri portionibus conſtantes in ea
                <lb/>
              portione, quæ plano non ad axem recto abſcinditur. </s>
              <s id="s.000951">ut
                <lb/>
              enim tradidimus in commentariis in undecimam propoſi
                <lb/>
              tionem libri Archimedis de conoidibus & ſphæroidibus. </s>
              <lb/>
              <s id="s.000952">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
                <lb/>
              ſe proportionem habent, quam ipſarum baſes: baſes
                <expan abbr="autẽ">autem</expan>
                <lb/>
                <arrow.to.target n="marg110"/>
                <lb/>
              quæ ſunt ellipſes ſimiles eandem proportionem habere,
                <lb/>
              quam quadrata diametrorum eiuſdem rationis, ex corol­
                <lb/>
              lario ſeptimæ propoſitionis libri de conoidibus, & ſphæ­
                <lb/>
              roidibus, manifeſte apparet.</s>
            </p>
            <p type="margin">
              <s id="s.000953">
                <margin.target id="marg110"/>
              corol. 15
                <lb/>
              de conoi­
                <lb/>
              dibus &
                <lb/>
              ſphæroi­
                <lb/>
              dibus.</s>
            </p>
            <p type="head">
              <s id="s.000954">THEOREMA XXIIII. PROPOSITIO XXX.</s>
            </p>
            <p type="main">
              <s id="s.000955">Si à portione conoidis rectanguli alia portio
                <lb/>
              abſcindatur, plano baſi æquidiſtante; habebit
                <lb/>
              portio tota ad eam, quæ abſciſſa eſt, duplam pro
                <lb/>
              portion em eius, quæ eſt baſis maioris portionis
                <lb/>
              ad baſi m minoris, uel quæ axis maioris ad axem
                <lb/>
              minoris.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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