Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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        <body>
          <chap>
            <p type="main">
              <s id="s.000981">
                <pb pagenum="47" xlink:href="023/01/101.jpg"/>
              eam proportionem habeat, quam abcd fruſtum ad por­
                <lb/>
              tionem agd; erit punctum l eius fruſti grauitatis
                <expan abbr="cẽtrum">centrum</expan>
              :
                <lb/>
                <expan abbr="habebitq;">habebitque</expan>
              componendo Kl ad lh proportionem eandem,
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                <arrow.to.target n="marg117"/>
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              quam portio conoidis bgc ad agd portionem. </s>
              <s id="s.000982">
                <expan abbr="Itaq;">Itaque</expan>
              quo
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              niam quadratum bf ad quadratum ae, hoc eſt quadratum
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              bc ad quadratum ad eſt, ut linea fg ad ge: erunt duæ ter­
                <lb/>
              tiæ quadrati bc ad duas tertias quadrati ad, ut hg ad gk:
                <lb/>
              & ſi à duabus tertiis quadrati bc demptæ fuerint duæ ter­
                <lb/>
              tiæ quadrati ad: erit
                <expan abbr="diuidẽdo">diuidendo</expan>
              id, quod relinquitur ad duas
                <lb/>
              tertias quadrati ad, ut hk ad kg. </s>
              <s id="s.000983">Rurſus duæ tertiæ quadra
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              ti ad ad duas tertias quadrati bc ſunt, ut kg ad gh: & duæ
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              tertiæ quadrati bc ad
                <expan abbr="tertiã">tertiam</expan>
                <expan abbr="partẽ">partem</expan>
              ipſius, ut gh ad hf. </s>
              <s id="s.000984">ergo
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              ex æquali id, quod relinquitur ex duabus tertiis quadrati
                <lb/>
              bc, demptis ab ipſis quadrati ad duabus tertiis, ad
                <expan abbr="tertiã">tertiam</expan>
                <lb/>
              partem quadrati bc, ut kh ad hf: & ad portionem
                <expan abbr="eiuſdẽ">eiuſdem</expan>
                <lb/>
              tertiæ partis, ad quam unà cum ipſa portione, duplam pro
                <lb/>
              portionem habeat eius, quæ eſt quadrati bc ad
                <expan abbr="quadratũ">quadratum</expan>
                <lb/>
              ad, ut Kl ad lh. </s>
              <s id="s.000985">habet enim Kl ad lh eandem proportio­
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              nem, quam conoidis portio bgc ad portionem agd: por­
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              tio autem bgc ad portionem agd duplam proportionem
                <lb/>
              habet eius, quæ eſt baſis bc ad baſim ad: hoc eſt quadrati
                <lb/>
                <arrow.to.target n="marg118"/>
                <lb/>
              bc ad quadratum ad; ut proxime demonſtratum eſt. </s>
              <s id="s.000986">quare
                <lb/>
              dempto ad quadrato à duabus tertiis quadrati bc, erit id,
                <lb/>
              quod relinquitur unà cum dicta portione tertiæ partis ad
                <lb/>
              reliquam eiuſdem portionem, ut el ad lf. </s>
              <s id="s.000987">Cum igitur cen­
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              trum grauitatis fruſti abcd ſit l, à quo axis ef in eam,
                <expan abbr="quã">quam</expan>
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              diximus, proportionem diuidatur; conſtat
                <expan abbr="uerũ">uerum</expan>
              eſſe illud,
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              quod demonſtrandum propoſuimus.</s>
            </p>
            <p type="margin">
              <s id="s.000988">
                <margin.target id="marg117"/>
              20. 1. coni
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              corum.</s>
            </p>
            <p type="margin">
              <s id="s.000989">
                <margin.target id="marg118"/>
              30 huius</s>
            </p>
            <p type="head">
              <s id="s.000990">FINIS LIBRI DE CENTROGRAVITATIS SOLIDORVM.</s>
            </p>
            <p type="main">
              <s id="s.000991">Impreſſ. Bononiæ cum licentia Superiorum, </s>
            </p>
          </chap>
        </body>
        <back/>
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    </archimedes>
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