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

Table of handwritten notes

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            <s xml:id="echoid-s10107" xml:space="preserve">
              <pb o="281" file="0381" n="416" rhead="MATHEMATICA. LIB. II. CAP. XII."/>
            tione; </s>
            <s xml:id="echoid-s10108" xml:space="preserve">id eſt, arcus integrarum vibrationum ſunt ut arcus
              <lb/>
              <note position="right" xlink:label="note-0381-01" xlink:href="note-0381-01a" xml:space="preserve">972.</note>
            deſcenſu deſcripti, quorum dupla ſunt arcus in vacuo de-
              <lb/>
            ſcribendi. </s>
            <s xml:id="echoid-s10109" xml:space="preserve">Ergo Defectus arcuum in fluido deſcriptorum
              <lb/>
              <note position="right" xlink:label="note-0381-02" xlink:href="note-0381-02a" xml:space="preserve">973.</note>
            ab arcubus in vacuo deſcribendorum ſunt differentiæ quan-
              <lb/>
            titatum in eadem ratione, & </s>
            <s xml:id="echoid-s10110" xml:space="preserve">ſunt ut arcus deſcenſu deſcri-
              <lb/>
            pti.</s>
            <s xml:id="echoid-s10111" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10112" xml:space="preserve">Creſcat nunc retardatio in ratione duplicata velocitatis,
              <lb/>
              <note position="right" xlink:label="note-0381-03" xlink:href="note-0381-03a" xml:space="preserve">974.</note>
            & </s>
            <s xml:id="echoid-s10113" xml:space="preserve">vibrationes inæquales peragat corpus pendulum; </s>
            <s xml:id="echoid-s10114" xml:space="preserve">majores
              <lb/>
            erunt magis diuturnæ, propter reſiſtentiam magis creſcen-
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            tem quàm in caſu n. </s>
            <s xml:id="echoid-s10115" xml:space="preserve">971.</s>
            <s xml:id="echoid-s10116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10117" xml:space="preserve">Celeritates tamen, poſitis arcubus non admodum inæqua-
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              <note position="right" xlink:label="note-0381-04" xlink:href="note-0381-04a" xml:space="preserve">975.</note>
            libus, in arcuum deſcriptorum punctis reſpondentibus, ſunt
              <lb/>
            ubique quam proximè in eadem ratione, & </s>
            <s xml:id="echoid-s10118" xml:space="preserve">quidem ratione
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            arcuum deſcenſu deſcriptorum. </s>
            <s xml:id="echoid-s10119" xml:space="preserve">Si retardatio eſſet in ratio-
              <lb/>
            ne celeritatis, hæc proportio obtineret, nunc vero turba-
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            tur propter majorem reſiſtentiam in majori vibratione, qua
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            motus in hac magis minuitur. </s>
            <s xml:id="echoid-s10120" xml:space="preserve">Sed duplici ex cauſa magis
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            acceleratur. </s>
            <s xml:id="echoid-s10121" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10122" xml:space="preserve">Vibratio hæc major diutius durat ,
              <note symbol="*" position="right" xlink:label="note-0381-05" xlink:href="note-0381-05a" xml:space="preserve">974.</note>
            puſque diutius hæret in certo ſpatio quàm in ſpatio reſpon-
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            denti in vibratione minori, & </s>
            <s xml:id="echoid-s10123" xml:space="preserve">per longius tempus accele-
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            ratur. </s>
            <s xml:id="echoid-s10124" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10125" xml:space="preserve">Defectus arcus deſcripti, ab arcu in vacuo deſcri-
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            bendo, major eſt, ſervata proportione, in vibratione ma-
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            jori; </s>
            <s xml:id="echoid-s10126" xml:space="preserve">quia in hac retardatio magis differt a retardatione in mi-
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            nori vibratione, quam in n. </s>
            <s xml:id="echoid-s10127" xml:space="preserve">973. </s>
            <s xml:id="echoid-s10128" xml:space="preserve">Puncta ergo reſponden-
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            tia, ſervata proportione, magis a puncto F in arcu majori
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            quam in minori diſtant, quamdiu in hoc corpus deſcendit;
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            </s>
            <s xml:id="echoid-s10129" xml:space="preserve">major ideo, ſervata proportione, in illo datur acceleratio,
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            quia acceleratio eſt ut corporis diſtantia a puncto F. </s>
            <s xml:id="echoid-s10130" xml:space="preserve">Datur er-
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            go compenſatio, & </s>
            <s xml:id="echoid-s10131" xml:space="preserve">memorata proportio inſtauratur. </s>
            <s xml:id="echoid-s10132" xml:space="preserve">In
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            adſcenſu corporis, duratio retardationis concurrit cum ipſa
              <lb/>
            retardatione ad hanc turbandam proportionem, ſed nunc mi-
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            nus in majori arcu puncta reſpondentia, ſervata proportio-
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            ne, a puncto F diſtant, quàm in minori, & </s>
            <s xml:id="echoid-s10133" xml:space="preserve">ex gravitate
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            minor, ſervata proportione, retardatio datur; </s>
            <s xml:id="echoid-s10134" xml:space="preserve">& </s>
            <s xml:id="echoid-s10135" xml:space="preserve">ita jam,
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            ſervatâ proportione, crevit differentia diſtantiæ </s>
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