Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000284">
                <pb pagenum="12" xlink:href="023/01/031.jpg"/>
              Itaque ſolidi parallelepipedi y
                <foreign lang="grc">γ</foreign>
              centrum grauitatis eſt in
                <lb/>
              linea
                <foreign lang="grc">δε·</foreign>
              ſolidi u
                <foreign lang="grc">β</foreign>
              centrum eſt in linea
                <foreign lang="grc">εη·</foreign>
              & ſolidi sz in li
                <lb/>
              nea
                <foreign lang="grc">η</foreign>
              m, quæ quidem lineæ axes ſunt, cum planorum oppo
                <lb/>
              ſitorum centra coniungant. </s>
              <s id="s.000285">ergo magnitudinis ex his ſoli
                <lb/>
              dis compoſitæ centrum grauitatis eſt in linea
                <foreign lang="grc">δ</foreign>
              m, quod ſit
                <lb/>
                <foreign lang="grc">θ</foreign>
              ; & iuncta
                <foreign lang="grc">θ</foreign>
              o producatur: à puncto autem h ducatur h
                <foreign lang="grc">α</foreign>
                <lb/>
              ipſi mk æquidiſtans, quæ cum
                <foreign lang="grc">θ</foreign>
              o in
                <foreign lang="grc">μ</foreign>
              conueniat. </s>
              <s id="s.000286">triangu
                <lb/>
              lum igitur ghk ad omnia triangula gzr,
                <foreign lang="grc">β</foreign>
              t, t
                <foreign lang="grc">γ</foreign>
              x, x
                <foreign lang="grc">δ</foreign>
              k,
                <lb/>
              k
                <foreign lang="grc">δ</foreign>
              y, yu, us, s
                <foreign lang="grc">α</foreign>
              h eandem habet proportionem, quam hm
                <lb/>
              ad mq ; hoc eſt, quam
                <foreign lang="grc">μθ</foreign>
              ad
                <foreign lang="grc">θλ·</foreign>
              nam ſi hm,
                <foreign lang="grc">μθ</foreign>
              produci in
                <lb/>
              telligantur, quouſque coeant; erit ob linearum qy, mk æ­
                <lb/>
              quidiſtantiam, ut hq ad qm, ita
                <foreign lang="grc">μλ</foreign>
              ad ad
                <foreign lang="grc">λθ·</foreign>
              & componen
                <lb/>
              do, ut hm ad mq, ita
                <foreign lang="grc">μθ</foreign>
              ad
                <foreign lang="grc">θλ.</foreign>
              </s>
              <s id="s.000287"> linea uero
                <foreign lang="grc">θ</foreign>
              o maior eſt,
                <lb/>
                <arrow.to.target n="marg40"/>
                <lb/>
              quàm
                <foreign lang="grc">θλ·</foreign>
              habebit igitur
                <foreign lang="grc">μθ</foreign>
              ad
                <foreign lang="grc">θλ</foreign>
              maiorem proportio­
                <lb/>
              nem, quàm ad
                <foreign lang="grc">θ</foreign>
              o. </s>
              <s id="s.000288">quare triangulum etiam ghk ad omnia
                <lb/>
              iam dicta triangula maiorem
                <expan abbr="proportionẽ">proportionem</expan>
              habebit, quàm
                <lb/>
                <foreign lang="grc">μθ</foreign>
              ad
                <foreign lang="grc">θ</foreign>
              o. </s>
              <s id="s.000289">ſed ut
                <expan abbr="triangulũ">triangulum</expan>
              ghk ad omnia triangula, ita
                <expan abbr="to-tũ">to­
                  <lb/>
                tum</expan>
              priſma afad omnia priſmata gzr, r
                <foreign lang="grc">β</foreign>
              t, t
                <foreign lang="grc">γ</foreign>
              x, x
                <foreign lang="grc">δκ, κδ</foreign>
              y,
                <lb/>
              yu, us, s
                <foreign lang="grc">α</foreign>
              h: quoniam enim ſolida parallelepipeda æque al
                <lb/>
              ta, eandem inter ſe proportionem habent, quam baſes; ut
                <lb/>
              ex trigeſimaſecunda undecimi elementorum conſtat. </s>
              <s id="s.000290">ſunt
                <lb/>
                <arrow.to.target n="marg41"/>
                <lb/>
              autem ſolida parallelepipeda priſmatum triangulares ba­
                <lb/>
                <arrow.to.target n="marg42"/>
                <lb/>
              ſes habentium dupla: ſequitur, ut etiam huiuſmodi priſ­
                <lb/>
              mata inter ſe ſint, ſicut eorum baſes. </s>
              <s id="s.000291">ergo totum priſma ad
                <lb/>
              omnia priſmata maiorem proportionem habet, quam
                <foreign lang="grc">μθ</foreign>
                <lb/>
                <arrow.to.target n="marg43"/>
                <lb/>
              ad
                <foreign lang="grc">θ</foreign>
              o: & diuidendo ſolida parallelepipeda y
                <foreign lang="grc">γ,</foreign>
              u
                <foreign lang="grc">β,</foreign>
              sz ad o­
                <lb/>
              mnia priſmata proportionem habent maiorem, quàm
                <foreign lang="grc">μ</foreign>
              o
                <lb/>
              ad o
                <foreign lang="grc">θ</foreign>
              . </s>
              <s id="s.000292">fiat
                <foreign lang="grc">ν</foreign>
              o ad o
                <foreign lang="grc">θ,</foreign>
              ut ſolida parallelepipeda y
                <foreign lang="grc">γ,</foreign>
              u
                <foreign lang="grc">β,</foreign>
              sz ad
                <lb/>
              omnia priſmata. </s>
              <s id="s.000293">Itaque cum à priſmate af, cuius
                <expan abbr="cẽtrum">centrum</expan>
                <lb/>
              grauitatis eſt o, auferatur magnitudo ex ſolidis parallelepi
                <lb/>
              pedis y
                <foreign lang="grc">γ,</foreign>
              u
                <foreign lang="grc">β,</foreign>
              sz conſtans: atque ipſius grauitatis centrum
                <lb/>
              ſit
                <foreign lang="grc">θ·</foreign>
              reliquæ magnitudinis, quæ ex omnibus priſmatibus
                <lb/>
              conſtat, grauitatis centrum erit in linea
                <foreign lang="grc">θ</foreign>
              o producta: &
                <lb/>
              in puncto
                <foreign lang="grc">f</foreign>
              , ex octava propoſitione eiusdem libri </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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