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

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            <s xml:id="echoid-s19166" xml:space="preserve">
              <pb o="(197)" file="0729" n="801" rhead="MATHEMATICA LIB. IV. CAP. XX."/>
            gulæ continent pedes duodecim: </s>
            <s xml:id="echoid-s19167" xml:space="preserve">unde detegitur ope
              <note symbol="*" position="right" xlink:label="note-0729-01" xlink:href="note-0729-01a" xml:space="preserve">1417.</note>
            proportionum, Solis actionem mutare Maris altitudinem
              <lb/>
              <note position="right" xlink:label="note-0729-02" xlink:href="note-0729-02a" xml:space="preserve">1421.</note>
            pedibus duobus, & </s>
            <s xml:id="echoid-s19168" xml:space="preserve">hanc ex Lunæ actione mutari pedibus
              <lb/>
              <note position="right" xlink:label="note-0729-03" xlink:href="note-0729-03a" xml:space="preserve">1422.</note>
            8,95 ; </s>
            <s xml:id="echoid-s19169" xml:space="preserve">& </s>
            <s xml:id="echoid-s19170" xml:space="preserve">ex ambabus actionibus conjunctis agitatio
              <note symbol="*" position="right" xlink:label="note-0729-04" xlink:href="note-0729-04a" xml:space="preserve">1419.</note>
            diocris eſt circiter undecim pedum, quod cum obſervationi-
              <lb/>
              <note position="right" xlink:label="note-0729-05" xlink:href="note-0729-05a" xml:space="preserve">1423.</note>
            bus ſatis congruit; </s>
            <s xml:id="echoid-s19171" xml:space="preserve">nam in Oceano aperto, pro ut Mare magis
              <lb/>
            aut minus patet, elevatur aqua, ad altitudinem ſex, novem,
              <lb/>
            duodecim, vel quindecim pedum; </s>
            <s xml:id="echoid-s19172" xml:space="preserve">in quibus elevationibus etiam
              <lb/>
            differentia datur ex profunditate aquarum. </s>
            <s xml:id="echoid-s19173" xml:space="preserve">Elevationes verò,
              <lb/>
            quæ has multum excedunt, locum habent, ubi magnâ vi
              <lb/>
              <note position="right" xlink:label="note-0729-06" xlink:href="note-0729-06a" xml:space="preserve">1424.</note>
            Mare freta intrat, in quibus impetus non frangitur, niſi
              <lb/>
            majori adſcenſu.</s>
            <s xml:id="echoid-s19174" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div2902" type="section" level="1" n="681">
          <head xml:id="echoid-head886" xml:space="preserve">CAPUT XX.</head>
          <head xml:id="echoid-head887" style="it" xml:space="preserve">De Lunæ Denſitate & Figurâ.</head>
          <p>
            <s xml:id="echoid-s19175" xml:space="preserve">Vires Solis & </s>
            <s xml:id="echoid-s19176" xml:space="preserve">Lunæ ad Mare movendum, ſunt inter ſe in
              <lb/>
              <note position="right" xlink:label="note-0729-07" xlink:href="note-0729-07a" xml:space="preserve">1425.</note>
            ratione compoſitâ, ex ratione quantitatum materiæ in
              <lb/>
            his corporibus , (ſingulæ enim particulæ agunt) & </s>
            <s xml:id="echoid-s19177" xml:space="preserve">ratione in:</s>
            <s xml:id="echoid-s19178" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0729-08" xlink:href="note-0729-08a" xml:space="preserve">1207.</note>
            versâ cuborum diſtantiarum Solis & </s>
            <s xml:id="echoid-s19179" xml:space="preserve">Lunæ à Tellure
              <note symbol="*" position="right" xlink:label="note-0729-09" xlink:href="note-0729-09a" xml:space="preserve">1390. 1402.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s19180" xml:space="preserve">Quantitates materiæ ſunt in ratione compoſitâ, ex ratione
              <lb/>
              <note position="right" xlink:label="note-0729-10" xlink:href="note-0729-10a" xml:space="preserve">1354.</note>
            voluminum, id eſt cuborum diametrorum, & </s>
            <s xml:id="echoid-s19181" xml:space="preserve">ratione denſita-
              <lb/>
            tum ; </s>
            <s xml:id="echoid-s19182" xml:space="preserve">quare vires memoratæ ſunt directè ut denſitates &</s>
            <s xml:id="echoid-s19183" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0729-11" xlink:href="note-0729-11a" xml:space="preserve">288. 79.</note>
            cubi diametrorum, & </s>
            <s xml:id="echoid-s19184" xml:space="preserve">inversè ut cubi diſtantiarum.</s>
            <s xml:id="echoid-s19185" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19186" xml:space="preserve">Diametri apparentes corporum, id eſt, anguli ſub quibus
              <lb/>
            videntur’, creſcunt ut ipſæ diametri, & </s>
            <s xml:id="echoid-s19187" xml:space="preserve">minuuntur ut diſtantiæ;
              <lb/>
            </s>
            <s xml:id="echoid-s19188" xml:space="preserve">id eſt, ſunt directè ut diametri, & </s>
            <s xml:id="echoid-s19189" xml:space="preserve">inversè ut diſtantiæ; </s>
            <s xml:id="echoid-s19190" xml:space="preserve">id-
              <lb/>
            circo ratio compoſita ex ratione cuborum diametrorum appa-
              <lb/>
            rentium Solis & </s>
            <s xml:id="echoid-s19191" xml:space="preserve">Lunæ, & </s>
            <s xml:id="echoid-s19192" xml:space="preserve">ex ratione denſitatum, erit ratio vi-
              <lb/>
              <note position="right" xlink:label="note-0729-12" xlink:href="note-0729-12a" xml:space="preserve">1426.</note>
            rium, quibus hæc corpora Mare movent. </s>
            <s xml:id="echoid-s19193" xml:space="preserve">Ideoque horum cor-
              <lb/>
            porum denſitates ſunt directè ut vires, quibus Mare movent,
              <lb/>
            & </s>
            <s xml:id="echoid-s19194" xml:space="preserve">inversè ut cubi diametrorum apparentium: </s>
            <s xml:id="echoid-s19195" xml:space="preserve">& </s>
            <s xml:id="echoid-s19196" xml:space="preserve">dividendo
              <lb/>
            vires per cubos harum diametrorum, datur ratio denſitatum.</s>
            <s xml:id="echoid-s19197" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19198" xml:space="preserve">Vis Solis eſt ad vim Lunæ, ut 1. </s>
            <s xml:id="echoid-s19199" xml:space="preserve">ad 4,4815, ; </s>
            <s xml:id="echoid-s19200" xml:space="preserve">media
              <note symbol="*" position="right" xlink:label="note-0729-13" xlink:href="note-0729-13a" xml:space="preserve">1419.</note>
            ter apparens Solis eſt 32′. </s>
            <s xml:id="echoid-s19201" xml:space="preserve">12″, & </s>
            <s xml:id="echoid-s19202" xml:space="preserve">media Lunæ diameter ap-
              <lb/>
            parens eſt 31′. </s>
            <s xml:id="echoid-s19203" xml:space="preserve">16 {1/2}″. </s>
            <s xml:id="echoid-s19204" xml:space="preserve">id eſt, ſunt inter ſe, ut 3864 ad 3753. </s>
            <s xml:id="echoid-s19205" xml:space="preserve">Eſt
              <lb/>
            igitur denſitas Solis ad Lunæ denſitatem, ut 10000 ad 48911.</s>
            <s xml:id="echoid-s19206" xml:space="preserve">:
              <lb/>
              <note position="right" xlink:label="note-0729-14" xlink:href="note-0729-14a" xml:space="preserve">1427.</note>
            quæ Lunæ denſitas cum Jovis, Saturni, & </s>
            <s xml:id="echoid-s19207" xml:space="preserve">Telluris </s>
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