Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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        <div xml:id="echoid-div598" type="section" level="1" n="181">
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            <s xml:id="echoid-s4052" xml:space="preserve">
              <pb o="99" file="0157" n="171" rhead="MATHEMATICA. LIB. I. CAP. XXI."/>
            motu primo, in momento hoc, per BL æqualem AB motum continuaſſet,
              <lb/>
            neceſſario juxta directionem L Da via ſua remotum fuit , ſi autem
              <note symbol="*" position="right" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">246.</note>
            gula ABC, BDC ſint æqualia, etiam æqualia erunt BDC, BLC; </s>
            <s xml:id="echoid-s4053" xml:space="preserve">i-
              <lb/>
            deoque linea LD parallela BC; </s>
            <s xml:id="echoid-s4054" xml:space="preserve">id eſt directio vis quæ corpus a linea
              <note symbol="*" position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">39.21.1.</note>
            cta detorquet centrum C verſus dirigitur.</s>
            <s xml:id="echoid-s4055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4056" xml:space="preserve">Si nunc concipiamus curvam quamcunque dividi, lineis ad centrum viri-
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            um ductis, in triangula minima æqualia, horum baſes, temporibus æqua-
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            libus a corpore quod in curva vi centrali retinetur, percurruntur ; </s>
            <s xml:id="echoid-s4057" xml:space="preserve">ſunt
              <note position="right" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">398.</note>
              <note symbol="*" position="right" xlink:label="note-0157-04" xlink:href="note-0157-04a" xml:space="preserve">394.</note>
            corporis velocitates in variis curvæ punctis, ut baſes hæ , quæ ſunt inversè
              <note symbol="*" position="right" xlink:label="note-0157-05" xlink:href="note-0157-05a" xml:space="preserve">94.</note>
            perpendiculares à centro virium in baſes continuatas , id eſt in tangentes
              <note symbol="*" position="right" xlink:label="note-0157-06" xlink:href="note-0157-06a" xml:space="preserve">1@. El. VI.
                <lb/>
              38. El 1.</note>
            vam in punctis de quibus agitur.</s>
            <s xml:id="echoid-s4058" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4059" xml:space="preserve">Maxime generalia ſunt huc uſque in ſcholio hoc demonſtrata, quæ nunc
              <lb/>
              <note position="right" xlink:label="note-0157-07" xlink:href="note-0157-07a" xml:space="preserve">399.</note>
            addam tantum obtinent, ſi vis in hoc cum gravitate congruat, ut agat in cor-
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            poramota ut in quieſcentia, corpora autem ponimus æqualia; </s>
            <s xml:id="echoid-s4060" xml:space="preserve">ſi verò vis & </s>
            <s xml:id="echoid-s4061" xml:space="preserve">in
              <lb/>
            hoc cum gravitate congruat, ut eodem modo agat in ſingulas materiæ parti-
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            culas, non intereſt utrum corpora ſint æqualia nec ne.</s>
            <s xml:id="echoid-s4062" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4063" xml:space="preserve">Lineæ infinitæ exiguæ, viribus æqualibus, a@cedendo adcentrum, percurſæ ſunt,
              <lb/>
              <note position="right" xlink:label="note-0157-08" xlink:href="note-0157-08a" xml:space="preserve">400.</note>
            ut quadrata temporum quibus percurruntur. </s>
            <s xml:id="echoid-s4064" xml:space="preserve">Vis enim pro uniformi in ſpatio
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            infinitè exiguo haberi poteſt, & </s>
            <s xml:id="echoid-s4065" xml:space="preserve">quæ de corporibus cadentibus demonſtrata
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            ſunt , hìc referri poſſunt.</s>
            <s xml:id="echoid-s4066" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">235.</note>
          <p style="it">
            <s xml:id="echoid-s4067" xml:space="preserve">Si vires differant, ſed tempora fuerint æqualia, ſpatia percurſa ſunt ut vi-
              <lb/>
              <note position="right" xlink:label="note-0157-10" xlink:href="note-0157-10a" xml:space="preserve">401.</note>
            res .</s>
            <s xml:id="echoid-s4068" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">107</note>
          <p>
            <s xml:id="echoid-s4069" xml:space="preserve">Ergo ſpatia infinite exigua, viribus centralibus percurſa, ſunt, ut viresipſæ, & </s>
            <s xml:id="echoid-s4070" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0157-12" xlink:href="note-0157-12a" xml:space="preserve">402.</note>
            ut quadrata temporum; </s>
            <s xml:id="echoid-s4071" xml:space="preserve">in ratione nempe compoſita ex hiſce ambabus ratio-
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            nibus.</s>
            <s xml:id="echoid-s4072" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4073" xml:space="preserve">Ex hiſce deducimus, corpus, quod vi centrali in curva retinetur, in ſingu-
              <lb/>
              <note position="right" xlink:label="note-0157-13" xlink:href="note-0157-13a" xml:space="preserve">403.</note>
            lis momentis infinitè exiguis moveri juxta leges explicatas de corporibus
              <note symbol="*" position="right" xlink:label="note-0157-14" xlink:href="note-0157-14a" xml:space="preserve">327. 331.</note>
            jectis. </s>
            <s xml:id="echoid-s4074" xml:space="preserve">Nam, licet corpus tendat ad centrum, ſi ſpatium percurſum ſit in-
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            finitè exiguum reſpectu diſtantiæ a centro, lineæ ad centrum ductæ pro pa-
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            rallelis haberi poſſunt.</s>
            <s xml:id="echoid-s4075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4076" xml:space="preserve">Sit Curva AFGE in qua corpus movetur; </s>
            <s xml:id="echoid-s4077" xml:space="preserve">C centrum virium; </s>
            <s xml:id="echoid-s4078" xml:space="preserve">AD
              <lb/>
              <note position="right" xlink:label="note-0157-15" xlink:href="note-0157-15a" xml:space="preserve">TAB. XV.
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              fig. 3.</note>
            tangens ad curvam in puncto A; </s>
            <s xml:id="echoid-s4079" xml:space="preserve">ponamus AD infinitè exiguam, lineas-
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            que BF & </s>
            <s xml:id="echoid-s4080" xml:space="preserve">DG ad AC dari parallelas, erunt hæ ut quadrata linearum
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            AB, AD , quæ ſunt ut tempora quibus AF, AG percurruntur.</s>
            <s xml:id="echoid-s4081" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">331. 327.</note>
        </div>
        <div xml:id="echoid-div611" type="section" level="1" n="182">
          <head xml:id="echoid-head255" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head256" style="it" xml:space="preserve">De Motu in Circulo.</head>
          <p>
            <s xml:id="echoid-s4082" xml:space="preserve">Vis quæcunque qua corpus in circulo retinetur, ſi ad circuli centrum dirigatur,
              <lb/>
              <note position="right" xlink:label="note-0157-17" xlink:href="note-0157-17a" xml:space="preserve">404.</note>
            agit ſemper perpendiculariter ad motus directionem; </s>
            <s xml:id="echoid-s4083" xml:space="preserve">tangens enim ad ra-
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            dium perpendicularis eſt . </s>
            <s xml:id="echoid-s4084" xml:space="preserve">Idcirco actio hujus vis nunquam cum
              <note symbol="*" position="right" xlink:label="note-0157-18" xlink:href="note-0157-18a" xml:space="preserve">18. El. 114.</note>
            corporis conſpiràt, aut contrarie agit, quare agit eodem modo ac in corpus qui-
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            eſcens ageret; </s>
            <s xml:id="echoid-s4085" xml:space="preserve">hac de cauſa non intereſt utrum vis in omni caſu eodem modo
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            poſſit agere in corpus motum ac in quieſcens ut gravitas, an non.</s>
            <s xml:id="echoid-s4086" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4087" xml:space="preserve">Moveatur corpus in circulo cujus Diameter eſt GL; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">C centrum circuli
              <lb/>
              <note position="right" xlink:label="note-0157-19" xlink:href="note-0157-19a" xml:space="preserve">405.</note>
            & </s>
            <s xml:id="echoid-s4089" xml:space="preserve">virium. </s>
            <s xml:id="echoid-s4090" xml:space="preserve">Detur corpus æquale per AD projectum, velocitate qua cor-
              <lb/>
              <note position="right" xlink:label="note-0157-20" xlink:href="note-0157-20a" xml:space="preserve">TAB XV.
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              fig. 4.</note>
            pus in circulo movetur.</s>
            <s xml:id="echoid-s4091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4092" xml:space="preserve">Corpora hæc æqualibus temporibus percurrunt lineas æquales, </s>
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