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

Table of contents

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[671.] LIBERI IV. Pars II. Motuum Cœleſtium Cauſæ Phyſicæ. CAPUT XI. De univerſali Gravitate.
Page: 744 ((146))
[672.] CAPUT XII. De Materiâ Cœleſti; ubi Vacuum dari probatur.
Page: 751 ((153))
[673.] CAPUT XIII. De Motu Telluris.
Page: 755 (157)
[674.] CAPUT XIV. De Denſitate Planetarum.
Page: 758 (160)
[675.] CAPUT XV. Totius Syſtematis Planetarii explicatio Phyſica.
Page: 763 (165)
[676.] CAPUT XVI. Motus Lunæ Explicatio Phyſica.
Page: 768 ((170))
[677.] CAPUT XVII. De Planetarum Figuris.
Page: 786 (185)
[678.] CAPUT XVIII. Motus Axeos Telluris Explicatio Phyſica.
Page: 790 (189)
[679.] CAPUT XIX. De Æſtu Maris.
Page: 792 (191)
[680.] Definitio.
Page: 793 (192)
[681.] CAPUT XX. De Lunæ Denſitate & Figurâ.
Page: 801 ((197))
[682.] FINIS LIBRI QUARTI.
Page: 803 ((199))
[683.] INDEX RERUM, Numeri (1), (11), deſignant Tomum pri-mum & ſecundum, p. denotat paginam, & n. numerum in margine.
Page: 805
[684.] FINIS. CATALOGUE Des LIVRES Nouvellement Imprimez à LEIDE, chez PIERRE VANDER Aa.
Page: 815
[685.] FINIS.
Page: 816
[686.] Tom. II. In fine poſt Indicem. USUS TABULÆ.
Page: 818
[687.] TABULA Demonſtrans quorundam numerorum 1æ. & 2dæ. Editionis convenientiam.
Page: 818
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          <p>
            <s xml:id="echoid-s15512" xml:space="preserve">
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            lineis jungantur puncta D, d, & </s>
            <s xml:id="echoid-s15513" xml:space="preserve">B, b, triangula BE b & </s>
            <s xml:id="echoid-s15514" xml:space="preserve">
              <lb/>
            DE d erunt ſimilia, ut notum eſt; </s>
            <s xml:id="echoid-s15515" xml:space="preserve">quod ergo etiam obti-
              <lb/>
            net, ſi ipſi arcus B b, D d fuerint minimi, ita ut pro lineis
              <lb/>
            rectis haberi poſſint.</s>
            <s xml:id="echoid-s15516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15517" xml:space="preserve">Datur idcirco inter ED & </s>
            <s xml:id="echoid-s15518" xml:space="preserve">E b ratio, quæ inter hos ar-
              <lb/>
            cus obtinet, id eſt ED eſt pars tertia ipſius E b, aut EB;
              <lb/>
            </s>
            <s xml:id="echoid-s15519" xml:space="preserve">quia exiguum admodum ponimus arcum B b. </s>
            <s xml:id="echoid-s15520" xml:space="preserve">Dividitur
              <lb/>
            igitur MD in duas partes æquales in E; </s>
            <s xml:id="echoid-s15521" xml:space="preserve">& </s>
            <s xml:id="echoid-s15522" xml:space="preserve">ME eſt pars
              <lb/>
            tertia ipſius EB.</s>
            <s xml:id="echoid-s15523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15524" xml:space="preserve">Si nunc, ut in fig. </s>
            <s xml:id="echoid-s15525" xml:space="preserve">3.</s>
            <s xml:id="echoid-s15526" xml:space="preserve">, formentur triangula B ob, B pb
              <lb/>
            & </s>
            <s xml:id="echoid-s15527" xml:space="preserve">M mn, erit M m pars tertia B b, & </s>
            <s xml:id="echoid-s15528" xml:space="preserve">B p triplum ipſius
              <lb/>
            M n; </s>
            <s xml:id="echoid-s15529" xml:space="preserve">ſi nunc, mutatis mutandis, ad hanc figuram appli-
              <lb/>
            cemus quæ reſpectu fig. </s>
            <s xml:id="echoid-s15530" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15531" xml:space="preserve">demonſtrata ſunt , quia in
              <note symbol="*" position="left" xlink:label="note-0612-01" xlink:href="note-0612-01a" xml:space="preserve">878.</note>
            B p valet 3 M n, cujus quadratum eſt 9 M n
              <emph style="super">9</emph>
            , habe-
              <lb/>
            mus</s>
          </p>
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        <div xml:id="echoid-div2325" type="section" level="1" n="580">
          <head xml:id="echoid-head762" xml:space="preserve">BC
            <emph style="super">q</emph>
          , BL
            <emph style="super">q</emph>
          :: 8 R
            <emph style="super">q</emph>
          , J
            <emph style="super">q</emph>
          -R
            <emph style="super">q</emph>
          </head>
          <p>
            <s xml:id="echoid-s15532" xml:space="preserve">Ex qua proportione, ut de fig. </s>
            <s xml:id="echoid-s15533" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15534" xml:space="preserve">dictum, detegitur ar-
              <lb/>
            cus BN, cui æqualis HG; </s>
            <s xml:id="echoid-s15535" xml:space="preserve">& </s>
            <s xml:id="echoid-s15536" xml:space="preserve">quia in hoc caſu</s>
          </p>
        </div>
        <div xml:id="echoid-div2326" type="section" level="1" n="581">
          <head xml:id="echoid-head763" xml:space="preserve">BL, BM:: J, 3R,</head>
          <p>
            <s xml:id="echoid-s15537" xml:space="preserve">Innoteſcit etiam arcus BD, cui propter angulos reflectio-
              <lb/>
            nis, æquales angulis incidentiæ , æquales ſunt DF & </s>
            <s xml:id="echoid-s15538" xml:space="preserve">FH.</s>
            <s xml:id="echoid-s15539" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0612-02" xlink:href="note-0612-02a" xml:space="preserve">805.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s15540" xml:space="preserve">Ex quibus datis, facilè eliciuntur arcus GFDN & </s>
            <s xml:id="echoid-s15541" xml:space="preserve">BH,
              <lb/>
              <note position="left" xlink:label="note-0612-03" xlink:href="note-0612-03a" xml:space="preserve">882.</note>
            quorum ſemi differentia eſt menſura anguli HPB, ab ex-
              <lb/>
            eunte radio cum incidente formato; </s>
            <s xml:id="echoid-s15542" xml:space="preserve">qui angulus in hoc
              <lb/>
            caſu omnium ſimilium eſt minimus, & </s>
            <s xml:id="echoid-s15543" xml:space="preserve">pro diversâ radiorum
              <lb/>
            refrangibilitâte diverſus. </s>
            <s xml:id="echoid-s15544" xml:space="preserve">Unde etiam in hoc caſu poſt du-
              <lb/>
              <note position="left" xlink:label="note-0612-04" xlink:href="note-0612-04a" xml:space="preserve">883.</note>
            plicem reflectionem efficaces variorum colorum, poſitis inci-
              <lb/>
            dentibus parallelis, ſeparantur.</s>
            <s xml:id="echoid-s15545" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div2329" type="section" level="1" n="582">
          <head xml:id="echoid-head764" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          2.</head>
          <p>
            <s xml:id="echoid-s15546" xml:space="preserve">Eodem modo ac præcedens experimentum hoc inſtitui-
              <lb/>
              <note position="left" xlink:label="note-0612-05" xlink:href="note-0612-05a" xml:space="preserve">
                <emph style="sc">TAB. XVIII</emph>
              .
                <lb/>
              fig. 4.</note>
            tur, ſitus phialæ tantum paululum mutatur, ut, poſt duas in
              <lb/>
            phialâ reflexiones, radii ad oculum aut chartam verſus N per-
              <lb/>
            veniant.</s>
            <s xml:id="echoid-s15547" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15548" xml:space="preserve">Huc uſque explicata ad Iridem applicari poſſunt; </s>
            <s xml:id="echoid-s15549" xml:space="preserve">ad quod
              <lb/>
              <note position="left" xlink:label="note-0612-06" xlink:href="note-0612-06a" xml:space="preserve">884.</note>
            phænomenon guttæ aqueæ in aëre ſuſpenſæ requiruntur; </s>
            <s xml:id="echoid-s15550" xml:space="preserve">ut
              <lb/>
            ſpectator, adverſo Sole inter hunc & </s>
            <s xml:id="echoid-s15551" xml:space="preserve">guttas collocetur; </s>
            <s xml:id="echoid-s15552" xml:space="preserve">& </s>
            <s xml:id="echoid-s15553" xml:space="preserve">ut
              <lb/>
            poſt guttas nubes detur obſcura, ut magis ſenſibiles ſint </s>
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