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

Table of contents

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[121.] Experimentum 2.
[122.] CAPUT XV. De Potentiis obliquis.
[123.] Machina Qua demonſtrantur quæ ſpectant punctum quod filis ad partes diverſas trabitur.
[124.] Experimentum 1.
[125.] Experimentum 2.
[126.] Experimentum 3.
[127.] Experimentum 4.
[128.] Experimentum 5.
[129.] Experimentum 6.
[130.] Definitio 1.
[131.] Definitio 2.
[132.] Definitio 3
[133.] Machina, Qua plani inclinati affectiones exhibentur.
[134.] Experimentum 7.
[135.] Experimentum 8.
[136.] Experimentum 9.
[137.] LIBRI I. PARS III. De Motibus, Potentiarum actionibus, variatis. CAPUT XVI. De Naturæ legibus Newtonianis.
[138.] Lex I.
[139.] Lex II.
[140.] Lex III.
[141.] Experimentum.
[142.] CAPUT XVII. De Acceleratione & Retardatione Gravium. Definitio 1.
[143.] Definitio 2.
[144.] CAPUT XVIII. De deſcenſu Gravium ſuper plano inclinato.
[145.] Experimentum 1.
[146.] Experimentum 2.
[147.] Machina, Qua corporum Cadentium velocitates conferuntur.
[148.] Experimentum 3.
[149.] CAPUT XIX. De Oſcillatione pendulorum. Definitio.
[150.] Experimentum i.
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            <s xml:id="echoid-s2819" xml:space="preserve">
              <pb o="67" file="0117" n="127" rhead="MATHEMATICA. LIB. I. CAP. XIX."/>
            dendo poteſt percurrere diametrum AB ; </s>
            <s xml:id="echoid-s2820" xml:space="preserve">id eſt,
              <note symbol="*" position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">268.</note>
            nem duplam longitudinis penduli: </s>
            <s xml:id="echoid-s2821" xml:space="preserve">in tempore æquali, ad-
              <lb/>
            ſcendet per chordam BF ; </s>
            <s xml:id="echoid-s2822" xml:space="preserve">in tempore ergo integræ vibr
              <note symbol="*" position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">273.</note>
            nis, corpus cadendo poſſet percurrere quatuor diametros ; </s>
            <s xml:id="echoid-s2823" xml:space="preserve">id
              <note symbol="*" position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">255</note>
            longitudinem octuplam longitudinis penduli. </s>
            <s xml:id="echoid-s2824" xml:space="preserve">Cumque deſcen-
              <lb/>
            ſus & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">adſcenſus per omnes chordas fiat in tempore æquali, o-
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            mnes vibrationes per chordas, ſive magnas, ſive exiguas, ſunt æ-
              <lb/>
            què diuturnæ. </s>
            <s xml:id="echoid-s2826" xml:space="preserve">In vibrationibus exiguis harum durationes, dum
              <lb/>
            in circulo movetur corpus, cum durationibus vibrationum in
              <lb/>
            chordis conſtantem rationem habent, nempe quæ datur inter
              <lb/>
            circuli peripheriæ quadrantem & </s>
            <s xml:id="echoid-s2827" xml:space="preserve">diametrum; </s>
            <s xml:id="echoid-s2828" xml:space="preserve">idcirco ejuſdem
              <lb/>
              <note position="right" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">280.</note>
            penduli vibrationes exiguæ, licet inæquales, ad ſenſum ſunt
              <lb/>
            æque diuturnæ.</s>
            <s xml:id="echoid-s2829" xml:space="preserve"/>
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        <div xml:id="echoid-div446" type="section" level="1" n="150">
          <head xml:id="echoid-head216" xml:space="preserve">
            <emph style="sc">Experimentum i</emph>
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          <p>
            <s xml:id="echoid-s2830" xml:space="preserve">Pendula duo CP & </s>
            <s xml:id="echoid-s2831" xml:space="preserve">cp æqualia, ſi a punctis P & </s>
            <s xml:id="echoid-s2832" xml:space="preserve">p eo-
              <lb/>
              <note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">281.</note>
            dem temporis momento dimittantur, eodem tempore per-
              <lb/>
              <note position="right" xlink:label="note-0117-06" xlink:href="note-0117-06a" xml:space="preserve">TAB. XI.
                <lb/>
              fig. 3.</note>
            venient in B & </s>
            <s xml:id="echoid-s2833" xml:space="preserve">b, & </s>
            <s xml:id="echoid-s2834" xml:space="preserve">deinde in F & </s>
            <s xml:id="echoid-s2835" xml:space="preserve">f; </s>
            <s xml:id="echoid-s2836" xml:space="preserve">& </s>
            <s xml:id="echoid-s2837" xml:space="preserve">ſic motum con-
              <lb/>
            tinuabunt per arcus PBF & </s>
            <s xml:id="echoid-s2838" xml:space="preserve">pbf, ſemper eodem tem-
              <lb/>
            pore.</s>
            <s xml:id="echoid-s2839" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2840" xml:space="preserve">Hæc autem æqualitas plenius explicanda eſt, & </s>
            <s xml:id="echoid-s2841" xml:space="preserve">quare vi-
              <lb/>
            brationes in circulo ad vibrationem per chordas quam dixi
              <lb/>
            rationem habeant.</s>
            <s xml:id="echoid-s2842" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2843" xml:space="preserve">Rotetur circulus FEBſuper lineâ AD donec punctum B
              <lb/>
              <note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">282.</note>
            in A ad lineam hanc perveniat; </s>
            <s xml:id="echoid-s2844" xml:space="preserve">hoc motu punctum B deſcri-
              <lb/>
              <note position="right" xlink:label="note-0117-08" xlink:href="note-0117-08a" xml:space="preserve">TAB. XI.
                <lb/>
              fig. 4.</note>
            bit curvæ portionem BPA: </s>
            <s xml:id="echoid-s2845" xml:space="preserve">eodem modo ſimilis curvæ
              <lb/>
            portio B| D deſcribitur, totaque curva ABD vocatur Cy-
              <lb/>
            cloïs, circulus FEB generator dicitur.</s>
            <s xml:id="echoid-s2846" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2847" xml:space="preserve">Dividatur in duas partes æquales in B, portioneſque BA
              <lb/>
              <note position="right" xlink:label="note-0117-09" xlink:href="note-0117-09a" xml:space="preserve">283.</note>
            & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">BD diſponantur, ut puncta A & </s>
            <s xml:id="echoid-s2849" xml:space="preserve">D jungantur in C; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">pun-
              <lb/>
            ctum vero B cum punctis A & </s>
            <s xml:id="echoid-s2851" xml:space="preserve">D lineæ AD coincidat.
              <lb/>
            </s>
            <s xml:id="echoid-s2852" xml:space="preserve">Juxta harum portionum curvaturam laminæ metallicæ in-
              <lb/>
            flectantur, ita ut filum penduli in C ſuſpenſi, motu ſuo vi-
              <lb/>
            bratorio, ab utraque parte ſeſe laminis iſtis applicet, & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">ean-
              <lb/>
            dem curvaturam cum iſtis adipiſcatur. </s>
            <s xml:id="echoid-s2854" xml:space="preserve">Nunc poſita longi-
              <lb/>
            tudine penduli CB, corpus P in vibrationibus ſuis deſcri-
              <lb/>
            bet cycloïdem ABD, ut in ſequenti ſcholio 3° </s>
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