Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000741">
                <pb pagenum="36" xlink:href="023/01/079.jpg"/>
              grauitatis magnitudinis, quæ ex utriſque pyramidibus
                <expan abbr="cõ">con</expan>
                <lb/>
              ſtat; hoc eſt ipſius fruſti. </s>
              <s id="s.000742">Sed fruſti centrum eſt etiam in a­
                <lb/>
              xe gh. </s>
              <s id="s.000743">ergo in puncto
                <foreign lang="grc">φ,</foreign>
              in quo lineæ zu, gh conueniunt. </s>
              <lb/>
              <s id="s.000744">
                <arrow.to.target n="marg90"/>
                <lb/>
              Itaque u
                <foreign lang="grc">φ</foreign>
              ad
                <foreign lang="grc">φ</foreign>
              z eam proportionem habet, quam pyramis
                <lb/>
              bcfed ad pyramidem abcd. </s>
              <s id="s.000745">& componendo uz ad z
                <foreign lang="grc">φ</foreign>
                <lb/>
              eam habet, quam fruſtum ad pyramidem abcd. </s>
              <s id="s.000746">Vt uero
                <lb/>
              uz ad z
                <foreign lang="grc">φ</foreign>
              , ita op ad p
                <foreign lang="grc">φ</foreign>
              ob ſimilitudinem triangulorum,
                <lb/>
              uo
                <foreign lang="grc">φ</foreign>
              , zp
                <foreign lang="grc">φ.</foreign>
              quare op ad p
                <foreign lang="grc">φ</foreign>
              eſt ut fruſtum ad pyramidem
                <lb/>
              abcd. </s>
              <s id="s.000747">ſed ita erat op ad pq.</s>
              <s id="s.000748"> æquales igitur ſunt p
                <foreign lang="grc">φ</foreign>
              , pq: &
                <lb/>
                <arrow.to.target n="marg91"/>
                <lb/>
              q
                <foreign lang="grc">φ</foreign>
              unum atque idem punctum. </s>
              <s id="s.000749">ex quibus ſequitur lineam. </s>
              <lb/>
              <s id="s.000750">zu ſecare op in q: & propterea
                <expan abbr="pũctum">punctum</expan>
              q ipſius fruſti gra­
                <lb/>
              uitatis centrum eſſe.</s>
            </p>
            <p type="margin">
              <s id="s.000751">
                <margin.target id="marg87"/>
              3. diffi. </s>
              <s id="s.000752">hu
                <lb/>
              ius.</s>
            </p>
            <p type="margin">
              <s id="s.000753">
                <margin.target id="marg88"/>
              Vltima
                <expan abbr="e-iuſdẽ">e­
                  <lb/>
                iuſdem</expan>
              libri
                <lb/>
              Archime­
                <lb/>
              dis.</s>
            </p>
            <p type="margin">
              <s id="s.000754">
                <margin.target id="marg89"/>
              2. ſexti.</s>
            </p>
            <p type="margin">
              <s id="s.000755">
                <margin.target id="marg90"/>
              8. primi
                <lb/>
              libri Ar­
                <lb/>
              chimedis
                <lb/>
              de
                <expan abbr="cẽtro">centro</expan>
                <lb/>
              grauta­
                <lb/>
              tis plano
                <lb/>
              rum</s>
            </p>
            <p type="margin">
              <s id="s.000756">
                <margin.target id="marg91"/>
              7. quinti.</s>
            </p>
            <p type="main">
              <s id="s.000757">Sit fruſtum ag à pyramide, quæ quadrangularem baſim
                <lb/>
              habeat abſciſſum, cuius maior baſis abcd, minor efgh,
                <lb/>
              & axis kl. diuidatur autem
                <expan abbr="primũ">primum</expan>
              kl, ita ut quam propor­
                <lb/>
              tionem habet duplum lateris ab unà cum latere ef ad du
                <lb/>
              plum lateris ef unà cum ab; habeat km ad ml. </s>
              <s id="s.000758">deinde à
                <lb/>
                <expan abbr="pũcto">puncto</expan>
              m ad k ſumatur quarta pars ipſius mk quæ ſit mn. </s>
              <lb/>
              <s id="s.000759">& rurſus ab l ſumatur quarta pars totius axis lk, quæ ſit
                <lb/>
              lo. </s>
              <s id="s.000760">poſtremo fiat on ad np, ut fruſtum ag ad
                <expan abbr="pyramidẽ">pyramidem</expan>
              ,
                <lb/>
              cuius baſis ſit eadem, quæ fruſti, & altitudo æqualis. </s>
              <s id="s.000761">Dico
                <lb/>
              punctum p fruſti ag grauitatis centrum eſſe. </s>
              <s id="s.000762">ducantur
                <lb/>
              enim ac, eg: & intelligantur duo fruſta triangulares ba­
                <lb/>
              ſes habentia, quorum alterum lf ex baſibus abc, efg
                <expan abbr="cõ-ſtet">con­
                  <lb/>
                ſtet</expan>
              ; alterum lh ex baſibus acd, egh. </s>
              <s id="s.000763">
                <expan abbr="Sitq;">Sitque</expan>
              fruſti lf axis
                <lb/>
              qr; in quo grauitatis centrum s: fruſti uero lh axis tu, &
                <lb/>
              x grauitatis centrum: deinde iungantur ur, tq, xs. </s>
              <s id="s.000764">tranſi­
                <lb/>
              bit ur per l: quoniam l eſt centrum grauitatis quadran­
                <lb/>
              guli abcd: & puncta ru grauitatis centra triangulorum
                <lb/>
              abc, acd; in quæ quadrangulum ipſum diuiditur. </s>
              <s id="s.000765">eadem
                <lb/>
              quoque ratione tq per punctum k tranſibit. </s>
              <s id="s.000766">At uero pro
                <lb/>
              portiones, ex quibus fruſtorum grauitatis centra inquiri­
                <lb/>
              mus, eædem ſunt in toto fruſto ag, & in fruſtis lf, lh. </s>
              <s id="s.000767">Sunt
                <lb/>
              enim per octauam huius quadrilatera abcd, efgh ſimilia: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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