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

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            <s xml:id="echoid-s2981" xml:space="preserve">
              <pb o="72" file="0122" n="132" rhead="PHYSICES ELEMENTA"/>
            runtur motu æquabili, momenta enim temporis adeo exigua coucipipo ſſunt,
              <lb/>
            ut acceleratio aut retardatio inſenſibilis ſit; </s>
            <s xml:id="echoid-s2982" xml:space="preserve">celeritates ergo in punctis F & </s>
            <s xml:id="echoid-s2983" xml:space="preserve">
              <lb/>
            G ſunt, ut F f & </s>
            <s xml:id="echoid-s2984" xml:space="preserve">G g , quæ ſunt inter ſe ut FH ad GI; </s>
            <s xml:id="echoid-s2985" xml:space="preserve">propter
              <note symbol="*" position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">94.</note>
            la ſimilia HBF, A h l, & </s>
            <s xml:id="echoid-s2986" xml:space="preserve">IGB, I mi, ductis lineis H l & </s>
            <s xml:id="echoid-s2987" xml:space="preserve">I m parallelis li-
              <lb/>
            neæ AD; </s>
            <s xml:id="echoid-s2988" xml:space="preserve">& </s>
            <s xml:id="echoid-s2989" xml:space="preserve">propter æquales Hypotenuſas HB, IB, & </s>
            <s xml:id="echoid-s2990" xml:space="preserve">H b, I i.</s>
            <s xml:id="echoid-s2991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2992" xml:space="preserve">Incrementa celeritatum momentis æqualibus minimis in punctis F & </s>
            <s xml:id="echoid-s2993" xml:space="preserve">G, ide ſt
              <lb/>
              <note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">107. 252.</note>
            prefſiones agentes in iſtis punctis , ſunt ut l h & </s>
            <s xml:id="echoid-s2994" xml:space="preserve">m i; </s>
            <s xml:id="echoid-s2995" xml:space="preserve">ſunt enim differentiæ
              <note symbol="*" position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">107.252.</note>
            ritatum in punctis F, f, & </s>
            <s xml:id="echoid-s2996" xml:space="preserve">G, g. </s>
            <s xml:id="echoid-s2997" xml:space="preserve">Sed, propter triangula memorata ſimilia, l h
              <lb/>
            & </s>
            <s xml:id="echoid-s2998" xml:space="preserve">m i ſunt inter ſe, ut FB ad GB; </s>
            <s xml:id="echoid-s2999" xml:space="preserve">idcirco preſſiones, in punctis F & </s>
            <s xml:id="echoid-s3000" xml:space="preserve">G in
              <lb/>
            corpus agentes ſunt inter ſe ut diſtantiæ a puncto medio B.</s>
            <s xml:id="echoid-s3001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3002" xml:space="preserve">Quæ de incrementis celeritatum demonſtrantur in parte AB Hineæ AD,
              <lb/>
            in parte BD de decrementis eodem modo demonſtrantur. </s>
            <s xml:id="echoid-s3003" xml:space="preserve">Agitatur ergo cor-
              <lb/>
            pus juxta legem corporis in cycloïde oſcillati.</s>
            <s xml:id="echoid-s3004" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3005" xml:space="preserve">Detur corpus motu æquabili ſemicir culum percurrens ALD, in tempore
              <lb/>
              <note position="left" xlink:label="note-0122-04" xlink:href="note-0122-04a" xml:space="preserve">306.</note>
            unius vibrationis in cycloide, id eſt in tempore, in quo corpus, in linea
              <lb/>
            recta AD ut explicavimus motum, illam percurrit. </s>
            <s xml:id="echoid-s3006" xml:space="preserve">Ex dictis patet H b,
              <lb/>
            F f, & </s>
            <s xml:id="echoid-s3007" xml:space="preserve">I i, G g, æqualibus temporibus percurri; </s>
            <s xml:id="echoid-s3008" xml:space="preserve">unde ſequitur, cum dire-
              <lb/>
            ctiones ſint parallelæ in L & </s>
            <s xml:id="echoid-s3009" xml:space="preserve">B, celeritates in hiſce punctis eſſe æquales. </s>
            <s xml:id="echoid-s3010" xml:space="preserve">Idcirco
              <lb/>
            corpus celeritate quam corpus pendulum habet in B, in tempore unius vibrationis
              <lb/>
            deſcribit ſemicirculum, cujus diameter eſt arcus cycloidis a corpore percurſus.</s>
            <s xml:id="echoid-s3011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3012" xml:space="preserve">Si corpus integram percurrat cycloidem ABD, diameter hæc erit quadru-
              <lb/>
              <note position="left" xlink:label="note-0122-05" xlink:href="note-0122-05a" xml:space="preserve">307.</note>
            pla diametri FB , & </s>
            <s xml:id="echoid-s3013" xml:space="preserve">velocitas in B erit, quam corpus cadendo ab
              <note position="left" xlink:label="note-0122-06" xlink:href="note-0122-06a" xml:space="preserve">TAB. XI.
                <lb/>
              fig. 4.</note>
            ne FB acquirit , qua celeritate motu æquabili corpus in tempore caſus
              <note symbol="*" position="left" xlink:label="note-0122-07" xlink:href="note-0122-07a" xml:space="preserve">284.</note>
            teſt percurrere lineam duplam ipſius FB Sed ſpatia æqualibus
              <note symbol="*" position="left" xlink:label="note-0122-08" xlink:href="note-0122-08a" xml:space="preserve">271.</note>
            percurſa ſunt ut tempora , id circo tempus caſus per
              <note symbol="*" position="left" xlink:label="note-0122-09" xlink:href="note-0122-09a" xml:space="preserve">257.</note>
            penduli eſt ad tempus unius vibrationis per integram cycloidem, aut arcum
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0122-10" xlink:href="note-0122-10a" xml:space="preserve">95.</note>
            quemcumque , ut dupla FB, ad ſemicircumferentiam circuli, cujus
              <note symbol="*" position="left" xlink:label="note-0122-11" xlink:href="note-0122-11a" xml:space="preserve">280.</note>
            ter eſt quadrupla lineæ FB, aut ad integram circumferentiam, cujus diame-
              <lb/>
            ter eſt etiam dupla FB; </s>
            <s xml:id="echoid-s3014" xml:space="preserve">ergo in genere ut diameter circuli ad hujus circum-
              <lb/>
            ferentiam; </s>
            <s xml:id="echoid-s3015" xml:space="preserve">ut monuimus in n. </s>
            <s xml:id="echoid-s3016" xml:space="preserve">288.</s>
            <s xml:id="echoid-s3017" xml:space="preserve"/>
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        <div xml:id="echoid-div474" type="section" level="1" n="155">
          <head xml:id="echoid-head222" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head223" style="it" xml:space="preserve">De Centro oſcillationis determinando.</head>
          <p>
            <s xml:id="echoid-s3018" xml:space="preserve">Sit CA pendulum compoſitum; </s>
            <s xml:id="echoid-s3019" xml:space="preserve">pondera P & </s>
            <s xml:id="echoid-s3020" xml:space="preserve">Q; </s>
            <s xml:id="echoid-s3021" xml:space="preserve">inter bæc datur centrum oſcil-
              <lb/>
              <note position="left" xlink:label="note-0122-12" xlink:href="note-0122-12a" xml:space="preserve">308.</note>
            lationis O, cujus hæc eſt proprietas, poſitâ virgâ AC rigidâ & </s>
            <s xml:id="echoid-s3022" xml:space="preserve">ſine pon-
              <lb/>
              <note position="left" xlink:label="note-0122-13" xlink:href="note-0122-13a" xml:space="preserve">TAB XII.
                <lb/>
              fig. 3.</note>
            dere, ut pondus Q, multiplicatum per BC, ad pondus P, multiplicatum per
              <lb/>
            AC, ita AO ad OQ. </s>
            <s xml:id="echoid-s3023" xml:space="preserve">Quod ut demonſtremus, conſiderandum eſt pondera Q
              <lb/>
            & </s>
            <s xml:id="echoid-s3024" xml:space="preserve">A moveri directionibus parallelis inter ſe, id eſt æqualiter ad horizontem
              <lb/>
            inclinatis; </s>
            <s xml:id="echoid-s3025" xml:space="preserve">ideo agitari continuo impreſſionibus ex gravitate, quæ, niſi cor-
              <lb/>
            pora virgâ rigidâ juncta forent, illis celeritates communicarent æquales .</s>
            <s xml:id="echoid-s3026" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0122-14" xlink:href="note-0122-14a" xml:space="preserve">118.265.</note>
            Junctorum autem ponderum celeritates neceſſario ſunt inæquales, & </s>
            <s xml:id="echoid-s3027" xml:space="preserve">celeri-
              <lb/>
            tas corporis P, actione ponderis Q, augetur, dum hocalterius actione retardatur;
              <lb/>
            </s>
            <s xml:id="echoid-s3028" xml:space="preserve">quæ actiones contrariæ æquales ſunt . </s>
            <s xml:id="echoid-s3029" xml:space="preserve">Interea punctum intermedium
              <note symbol="*" position="left" xlink:label="note-0122-15" xlink:href="note-0122-15a" xml:space="preserve">247.</note>
            O, centrum nempe oſcillationis, movetur celeritate ex actione gravitatis ori-
              <lb/>
            unda.</s>
            <s xml:id="echoid-s3030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3031" xml:space="preserve">Sit B b, O o, aut A a (has enim æquales ponimus lineas) ſpatium percur-
              <lb/>
            ſum ex actione gravitatis juxta inclinationem quamcunque agentis in tem-
              <lb/>
            pore quocunque minimo. </s>
            <s xml:id="echoid-s3032" xml:space="preserve">Cum punctum O hoc ſpatium percurrit, tantum
              <lb/>
            per BE transſertur Q, & </s>
            <s xml:id="echoid-s3033" xml:space="preserve">potentia quæ in Q agit minuitur quantitate, qua </s>
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