Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000110">
                <pb pagenum="21" xlink:href="010/01/029.jpg"/>
                <arrow.to.target n="marg21"/>
                <lb/>
              punctum I eſſe centrum grauitatis communis ponde­
                <lb/>
              rum A, & B (cum funes nullius ponderis
                <expan abbr="ſupponãtur">ſupponantur</expan>
              )
                <lb/>
              deinde reuoluta trochlea
                <expan abbr="aſcẽdat">aſcendat</expan>
              pondus B ad L, &
                <lb/>
              oppoſitum pondus A deſcendat vſque ad K
                <expan abbr="coniũga-turque">coniunga­
                  <lb/>
                turque</expan>
              recta KL ſecans rectam AB
                <lb/>
                <figure id="id.010.01.029.1.jpg" xlink:href="010/01/029/1.jpg"/>
                <lb/>
              in G. dico duo pondera A, & B iņ
                <lb/>
              communi eorum centro grauitatis
                <lb/>
              I circa libræ centrum ſtabile G mo­
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              tu directo, & perpendiculari ad
                <lb/>
              horizontem
                <expan abbr="deſcẽdere">deſcendere</expan>
              . </s>
              <s id="s.000111">quia in tro­
                <lb/>
              chleæ reuolutione
                <expan abbr="tãtumdẽ">tantumdem</expan>
                <expan abbr="deſcẽ-dit">deſcen­
                  <lb/>
                dit</expan>
              terminus funis A quanta eſt ex­
                <lb/>
              plicatio funis è rota CDE, & pon­
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              dus B aſcendit quantum funis BQS
                <lb/>
              circumuoluitur circa rotam QSR
                <lb/>
              cùmque duæ rotæ concentricè con­
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              nexæ ſimul tempore
                <expan abbr="reuoluãtur">reuoluantur</expan>
              cir­
                <lb/>
              ca fixum axim F, ergo deſcenſus AK
                <lb/>
              ad
                <expan abbr="aſcẽſum">aſcenſum</expan>
              BL eamdem proportio­
                <lb/>
              nem habet, quam peripheria CDE ad peripheriam R
                <lb/>
              SQ, ſeu
                <expan abbr="eamdẽ">eamdem</expan>
              proportionem, quam habet radius
                <lb/>
              FE ad radium
                <expan abbr="Fq;">Fque</expan>
              quare in triangulis AGK, & BGL
                <lb/>
              ſimilibus, ob æquidiſtantiam laterum AK, & BL, erit
                <lb/>
              AG ad GB vt KG ad GL, ſeu vt AK ad BL;
                <expan abbr="proindeq;">proindeque</expan>
                <lb/>
              in eodem puncto fixo G duæ libræ AB, & KL ſe mutuò
                <lb/>
              ſecabunt in eadem proportione, quam habent motus
                <lb/>
              eorumdem terminorum, vnde, ex mechanicis, erit
                <lb/>
              punctum G centrum, & fulcimentum firmum̨
                <lb/>
              vtriuſque libræ AB, & KL poſtremò ducatur per I </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>