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

Table of figures

< >
< >
page |< < (103) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div621" type="section" level="1" n="183">
          <p>
            <s xml:id="echoid-s4292" xml:space="preserve">
              <pb o="103" file="0161" n="175" rhead="MATHEMATICA, LIB I. CAP. XXI."/>
            FA, AC:</s>
            <s xml:id="echoid-s4293" xml:space="preserve">: iL, aut MN, IL = {MN x AC/FA}</s>
          </p>
          <p>
            <s xml:id="echoid-s4294" xml:space="preserve">Subſtituendo pro IL valorem in hac æquatione GL
              <emph style="super">q</emph>
            = {
              <emph style="super">2</emph>
            IL x AF
              <emph style="super">q</emph>
            /AC} habe-
              <lb/>
            mus GL
              <emph style="super">q</emph>
            =
              <emph style="super">2</emph>
            MN x AF, cui quantitati etiam æquale eſt OM
              <emph style="super">q</emph>
            , ſunt ergo
              <lb/>
              <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">413.</note>
            æquales GL & </s>
            <s xml:id="echoid-s4295" xml:space="preserve">OM, unde patet in Ellipſi corpus in extremitate axeos mino-
              <lb/>
            ris eadem velocitate moveri qua aliud fertur in circulo cujus diameter æqualis eſt axi
              <lb/>
            Ellipſeos majori, ſi eadem vi centrali quæ ad ſocum Ellipſeos dirigitur, ambo in
              <lb/>
            curvis retineantur.</s>
            <s xml:id="echoid-s4296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4297" xml:space="preserve">Quia curva in A parallela eſt ipſi Axi BD, ſunt æqualia triangula CAL,
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">37. El. 1.</note>
            FAL ; </s>
            <s xml:id="echoid-s4298" xml:space="preserve">triangula rectangula CAL, FAM, quorum baſes ſunt æqua- les ſunt inter ſe ut altitudines AC, AF aut CD; </s>
            <s xml:id="echoid-s4299" xml:space="preserve">In hac eadem ratione
              <lb/>
            ſunt inter ſe areæ Ellipſeos, & </s>
            <s xml:id="echoid-s4300" xml:space="preserve">circuli. </s>
            <s xml:id="echoid-s4301" xml:space="preserve">Idcirco alternando area trianguli
              <lb/>
            CAL, aut FAL, ad aream Ellipſeos, ut area trianguli FAM ad aream
              <lb/>
            circuli: </s>
            <s xml:id="echoid-s4302" xml:space="preserve">ergo tempus in quo corpus movetur per AL ad tempus periodicum
              <lb/>
            in Ellipſi, ut tempus in quo percurritur AM ad tempus periodicum in cir-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0161-03" xlink:href="note-0161-03a" xml:space="preserve">354. 396.</note>
            culo ; </s>
            <s xml:id="echoid-s4303" xml:space="preserve">antecedentia ſunt æqualia ideò & </s>
            <s xml:id="echoid-s4304" xml:space="preserve">conſequentia Q. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4306" xml:space="preserve">E.</s>
            <s xml:id="echoid-s4307" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div639" type="section" level="1" n="184">
          <head xml:id="echoid-head259" xml:space="preserve">SCHOLIUM 4.</head>
          <head xml:id="echoid-head260" style="it" xml:space="preserve">De Motu in orbitâ agitatâ</head>
          <p>
            <s xml:id="echoid-s4308" xml:space="preserve">Detur curva quæcunque a corpore vi centrali deſcripta, AF; </s>
            <s xml:id="echoid-s4309" xml:space="preserve">centrum vi-
              <lb/>
              <note position="right" xlink:label="note-0161-04" xlink:href="note-0161-04a" xml:space="preserve">414</note>
            rium C. </s>
            <s xml:id="echoid-s4310" xml:space="preserve">Dividatur curva hæc ductis radiis ex centro C, CA, CB,
              <lb/>
              <note position="right" xlink:label="note-0161-05" xlink:href="note-0161-05a" xml:space="preserve">TAB. XV.
                <lb/>
              fig. 9.</note>
            CD & </s>
            <s xml:id="echoid-s4311" xml:space="preserve">c, angulos æquales infinitè exiguos inter ſe continentibus.</s>
            <s xml:id="echoid-s4312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4313" xml:space="preserve">Concipiamus ſingulos angulos ſervarâ radiorum longitudine æqualiterau-
              <lb/>
            geri aut minui, novamque curvam dari a f per radiorum extrema tranſeuntem.</s>
            <s xml:id="echoid-s4314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4315" xml:space="preserve">Triangula ACB, acb propter baſes æquales CA, ca, ſunt inter ſe utaltitu-
              <lb/>
            dines , quæ ſunt ut anguli ACB, acb; </s>
            <s xml:id="echoid-s4316" xml:space="preserve">ſinguli autem anguli in unâ
              <note symbol="*" position="right" xlink:label="note-0161-06" xlink:href="note-0161-06a" xml:space="preserve">1. El. VI</note>
            vâ ſunt ad reſpondentes in aliâ in eâdem ratione; </s>
            <s xml:id="echoid-s4317" xml:space="preserve">in ſingulis enim curvis
              <lb/>
            ſunt omnes æquales inter ſe; </s>
            <s xml:id="echoid-s4318" xml:space="preserve">ideo triangula quæcunque reſpondentia ut
              <lb/>
            ACB acb; </s>
            <s xml:id="echoid-s4319" xml:space="preserve">BCD, bcd, ſunt in eadem ratione, & </s>
            <s xml:id="echoid-s4320" xml:space="preserve">ſummæ quæcunque
              <lb/>
            triangulorum reſpondentium etiam in eadem ratione; </s>
            <s xml:id="echoid-s4321" xml:space="preserve">idcirco triangula hæc
              <lb/>
            mixta ſunt proportionalia ACE, ace:</s>
            <s xml:id="echoid-s4322" xml:space="preserve">: ECF, ecf; </s>
            <s xml:id="echoid-s4323" xml:space="preserve">& </s>
            <s xml:id="echoid-s4324" xml:space="preserve">alternando
              <lb/>
            ACE, ECF:</s>
            <s xml:id="echoid-s4325" xml:space="preserve">: ace, ecf.</s>
            <s xml:id="echoid-s4326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4327" xml:space="preserve">Ponamus nunc corpus in curva af moveri, dum corpus quod vi centrali
              <lb/>
            ad C tendenti curvam AF percurrit; </s>
            <s xml:id="echoid-s4328" xml:space="preserve">concipiamus ulterius, dum corpus unum
              <lb/>
            percurrit AB, alterum per ab transferri, dum primum ad D pertingit, alterum da-
              <lb/>
            ri in d, & </s>
            <s xml:id="echoid-s4329" xml:space="preserve">ſic ulterius; </s>
            <s xml:id="echoid-s4330" xml:space="preserve">eodem tempore ergo percurruntur AF, ae, & </s>
            <s xml:id="echoid-s4331" xml:space="preserve">tem-
              <lb/>
            pore etiam eodem percurruntur EF & </s>
            <s xml:id="echoid-s4332" xml:space="preserve">ef. </s>
            <s xml:id="echoid-s4333" xml:space="preserve">idcirco tempora quibus AE, EF
              <lb/>
            percurruntur ſunt ut illa quibus per ae, ef corpus movetur. </s>
            <s xml:id="echoid-s4334" xml:space="preserve">Tempora autem
              <lb/>
            illa ſunt ut areæ ACE; </s>
            <s xml:id="echoid-s4335" xml:space="preserve">ECF ; </s>
            <s xml:id="echoid-s4336" xml:space="preserve">quæ ſunt ut areæ ace, ecf; </s>
            <s xml:id="echoid-s4337" xml:space="preserve">in qua
              <note symbol="*" position="right" xlink:label="note-0161-07" xlink:href="note-0161-07a" xml:space="preserve">354. 396.</note>
            ratione ſunt tempora quibus per ae, & </s>
            <s xml:id="echoid-s4338" xml:space="preserve">ef, corpus transfertur; </s>
            <s xml:id="echoid-s4339" xml:space="preserve">quæ eadem de-
              <lb/>
            monſtratio cumlocum habeat, ſumtis arcubus quibuſcunque; </s>
            <s xml:id="echoid-s4340" xml:space="preserve">ſequitur corpus
              <lb/>
            in curva af translatum deſcribere areas lineis ad centrum c ductis tempori-
              <lb/>
            bus proportionales, & </s>
            <s xml:id="echoid-s4341" xml:space="preserve">retineri in curvâ vi centrali ad c tendenti .</s>
            <s xml:id="echoid-s4342" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">355. 397.</note>
          <p>
            <s xml:id="echoid-s4343" xml:space="preserve">Concipiamus nunc curvam AC circa centrum C moveri ita, ut motus
              <lb/>
              <note position="right" xlink:label="note-0161-09" xlink:href="note-0161-09a" xml:space="preserve">TAB. XV.
                <lb/>
              fig. 10.</note>
            angularis curvæ ſequatur proportionem motus angularis corporis in hac
              <lb/>
            curva agitati: </s>
            <s xml:id="echoid-s4344" xml:space="preserve">dum corpus in curva ab A ad F movetur ipſius motus an-
              <lb/>
            gularis eſt ACF, ponamus curvam interea transferri motu angulari, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum