Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000899">
                <pb pagenum="43" xlink:href="023/01/093.jpg"/>
              bm. </s>
              <s id="s.000900">ergo circulus ac circuli kg: & idcirco cylindrus
                <lb/>
              ah cylindri k. </s>
              <s id="s.000901">l duplus erit. </s>
              <s id="s.000902">quare & linea op dupla
                <lb/>
              ipſius pn. </s>
              <s id="s.000903">Deinde inſcripta & circumſcripta portioni
                <lb/>
              alia figura, ita ut inſcripta conſtituatur ex tribus cylin­
                <lb/>
              dris qr, sg, tu: circumſcripta uero ex quatuor ax, yz,
                <lb/>
              K
                <foreign lang="grc">f, θλ·</foreign>
              diuidantur bo, om, mn, nd bifariam in punctis
                <lb/>
                <foreign lang="grc">μνπρ.</foreign>
              Itaque cylindri
                <foreign lang="grc">θλ</foreign>
              centrum grauitatis eſt punctum
                <lb/>
                <foreign lang="grc">μ·</foreign>
              & cylindri k
                <foreign lang="grc">η</foreign>
              centrum
                <foreign lang="grc">ν.</foreign>
              ergo ſi linea
                <foreign lang="grc">μγ</foreign>
              diuidatur in
                <foreign lang="grc">ς,</foreign>
                <lb/>
              ita ut
                <foreign lang="grc">μσ</foreign>
              ad
                <foreign lang="grc">σγ</foreign>
                <expan abbr="proportionẽ">proportionem</expan>
                <expan abbr="eã">eam</expan>
              habeat, quam cylindrus K
                <foreign lang="grc">η</foreign>
                <lb/>
              ad cylindrum
                <foreign lang="grc">θλ,</foreign>
              uidelicet quam quadratum knr ad qua­
                <lb/>
                <arrow.to.target n="marg108"/>
                <lb/>
              dratum
                <foreign lang="grc">θ</foreign>
              o, hoc eſt, quam linea mb ad bo: erit
                <foreign lang="grc">σ</foreign>
              centrum
                <lb/>
              magnitudinis compoſitæ ex cylindris
                <foreign lang="grc">κγ, θλ.</foreign>
              & cum linea
                <lb/>
              mb ſit dupla bo, erit &
                <foreign lang="grc">μσ</foreign>
              ipſius
                <foreign lang="grc">σν</foreign>
              dupla. </s>
              <s id="s.000904">præterea quo­
                <lb/>
              niam cylindri yz centrum grauitatis eſt
                <foreign lang="grc">π,</foreign>
              linea
                <foreign lang="grc">σπ</foreign>
              ita diui
                <lb/>
              ſa in
                <foreign lang="grc">τ,</foreign>
              ut
                <foreign lang="grc">στ</foreign>
              ad
                <foreign lang="grc">τπ</foreign>
              eam habeat proportionem, quam cylin
                <lb/>
              drus yz ad duos cylindros K
                <foreign lang="grc">ν, θλ·</foreign>
              erit
                <foreign lang="grc">τ</foreign>
              centrum magnitu
                <lb/>
              dinis, quæ ex dictis tribus cylindris conſtat. </s>
              <s id="s.000905">cylindrus
                <expan abbr="au-tẽ">au­
                  <lb/>
                tem</expan>
              yz ad cylindrum
                <foreign lang="grc">θλ</foreign>
              eſt, ut linea nb ad bo, hoc eſt ut 3
                <lb/>
              ad 1: & ad cylindrum k
                <foreign lang="grc">η</foreign>
              , ut nb ad bm, uidelicet ut 3 ad 2. </s>
              <lb/>
              <s id="s.000906">quare yz
                <expan abbr="cylĩdrus">cylindrus</expan>
              duobus cylindris k
                <foreign lang="grc">ν, θλ</foreign>
              æqualis erit. </s>
              <s id="s.000907">&
                <lb/>
              propterea linea
                <foreign lang="grc">στ</foreign>
              æqualis ipſi
                <foreign lang="grc">τπ.</foreign>
              denique cylindri ax
                <lb/>
              centrum grauitatis eſt punctum
                <foreign lang="grc">ρ.</foreign>
              & cum
                <foreign lang="grc">τρ</foreign>
              diuiſa fuerit
                <lb/>
              in
                <expan abbr="eã">eam</expan>
              proportionem, quam habet cylindrus ax ad tres cy­
                <lb/>
              lindros yz, k
                <foreign lang="grc">ν, θλ·</foreign>
              erit in eo puncto centrum grauitatis
                <lb/>
              totius figuræ
                <expan abbr="circũſcriptæ">circumſcriptæ</expan>
              . </s>
              <s id="s.000908">Sed cylindrus ax ad ipſum yz
                <lb/>
              eſt ut linea db ad bn: hoc eſt ut 4 ad 3: & duo cylindri k
                <foreign lang="grc">η
                  <lb/>
                θλ</foreign>
              cylindro y ſunt æquales. </s>
              <s id="s.000909">cylindrus igitur ax ad tres
                <lb/>
              iam dictos cylindros eſt ut 2 ad 3. Sed
                <expan abbr="quoniã">quoniam</expan>
                <foreign lang="grc">μ σ</foreign>
              eſt dua­
                <lb/>
              rum partium, &
                <foreign lang="grc">ς γ</foreign>
              unius, qualium
                <foreign lang="grc">μ π</foreign>
              eſt ſex; erit
                <foreign lang="grc">ς π</foreign>
              par­
                <lb/>
              tium quatuor:
                <expan abbr="proptereaq;">proptereaque</expan>
                <foreign lang="grc">τπ</foreign>
              duarum, &
                <foreign lang="grc">νπ,</foreign>
              hoc eſt
                <foreign lang="grc">πρ</foreign>
                <lb/>
              trium. </s>
              <s id="s.000910">quare ſequitur ut punctum
                <foreign lang="grc">π</foreign>
              totius figuræ circum
                <lb/>
              ſcriptæ ſit centrum. </s>
              <s id="s.000911">Itaque fiat
                <foreign lang="grc">νυ</foreign>
              ad
                <foreign lang="grc">υπ,</foreign>
              ut
                <foreign lang="grc">μσ</foreign>
              ad
                <foreign lang="grc">σγ.</foreign>
              &
                <foreign lang="grc">υρ</foreign>
                <lb/>
              bifariam diuidatur in
                <foreign lang="grc">φ.</foreign>
              Similiter ut in circumſcripta figu
                <lb/>
              ra oſtendetur centrum magnitudinis compoſitæ ex </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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