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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.002412">
                <pb pagenum="459" xlink:href="010/01/467.jpg"/>
                <arrow.to.target n="marg619"/>
                <lb/>
              quæ moles ab infimo eiuſdem fiſtulæ orificio egredi­
                <lb/>
              untur, & propterea vna, & eadem velocitate deter­
                <lb/>
              minata ab eius ſumma altitudine aqua fluit, (ſi tamen
                <lb/>
              ſemper fiſtula repleta ſupponatur); ergo æqualibus
                <lb/>
              temporibus tanta aquæ moles ſupernè infunditur,
                <lb/>
              quanta inferiùs ab eadem fiſtula egreditur, quare in
                <lb/>
              progreſſu motus intra fiſtulam
                <expan abbr="eadẽ">eadem</expan>
              velocitate à qua
                <lb/>
              excurrit, qua infernè egreditur, cùmque hæc veloci­
                <lb/>
              tas ab altitudine caſus, ſeu longitudine penduli, vel
                <lb/>
              fiſtulæ determinetur, igitur velocitas aquæ intra ca­
                <lb/>
              nalem fiſtulæ ſemper eumdem gradum habet, æqua­
                <lb/>
              lem ſcilicèt ei, qui fiſtulæ longitudini competit. </s>
              <s id="s.002413">po­
                <lb/>
              ſtea, vt ſubſequentes propoſitiones demonſtrari com­
                <lb/>
              modiùs poſſint; Primò ſupponendum eſt vt euidens,
                <lb/>
                <arrow.to.target n="marg620"/>
                <lb/>
              quòd ab eodem fiſtulæ orificio,
                <expan abbr="perpẽdicularitèr">perpendicularitèr</expan>
              ta­
                <lb/>
              men erecto ad directionem aquæ fluentis, duæ moles
                <lb/>
              æquales aquæ æqualibus temporibus egreſſæ neceſ­
                <lb/>
              ſariò æqualibus velocitatibus egredi debent; & è
                <expan abbr="cõ-uerſo">con­
                  <lb/>
                uerſo</expan>
              ſi velocitates æquales fuerint, paritèr moles a­
                <lb/>
              quæ æqualibus temporibus effluxæ erunt quoque in­
                <lb/>
              ter ſe æquales. </s>
              <s id="s.002414">Vnde colligitur, quòd velocitatę
                <lb/>
              dupla eodem tempore paritèr dupla moles aquæ ab
                <lb/>
              æquali foramine egreditur, idemque dicendum eſt
                <lb/>
              de qualibet æquè multiplici proportione: paritèrque
                <lb/>
              ſi velocitas partes fuerit alterius velocitatis, paritèr
                <lb/>
              moles aquæ ab æqualibus foraminibus eodem tem­
                <lb/>
              pore egredientes eamdem proportionem commen­
                <lb/>
              ſurabilem habebunt, quam habent
                <expan abbr="earũ">earum</expan>
              velocitates.
                <lb/>
                <arrow.to.target n="marg621"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.002415">
                <margin.target id="marg619"/>
              Cap. 11. gra­
                <lb/>
              uia in fluido
                <lb/>
              velocitati­
                <lb/>
              bus inæqua­
                <lb/>
              libus ferri
                <lb/>
              debere.</s>
            </p>
            <p type="margin">
              <s id="s.002416">
                <margin.target id="marg620"/>
              Supp. 1.</s>
            </p>
            <p type="margin">
              <s id="s.002417">
                <margin.target id="marg621"/>
              Supp. 2.</s>
            </p>
            <p type="main">
              <s id="s.002418">Non ſecùs ſi ab eodem foramine eadem velocita-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>