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

Table of contents

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[271.] CAPUT II. De Actione Fluidorum in Fundos, Latera, & Opercula, vaſorum quibus continentur.
Page: 312 (204)
[272.] Machina
Page: 313 (205)
[273.] Experimentum 1.
Page: 314 (206)
[274.] Experimentum 2.
Page: 318 (207)
[275.] Experimentum 3.
Page: 318 (207)
[276.] Machina Qua demonſtratur Preſſio Fluidorum lateralis.
Page: 319 (208)
[277.] Experimentum 4.
Page: 319 (208)
[278.] Experimentum 5.
Page: 320 (209)
[279.] Follis hydrostaticus.
Page: 320 (209)
[280.] Experimentum 6.
Page: 320 (209)
[281.] CAPUT III. De Solidis fluidis immerſis.
Page: 322 (211)
[282.] Definitio 1.
Page: 322 (211)
[283.] Definitio. 2.
Page: 322 (211)
[284.] Definitio. 3.
Page: 322 (211)
[285.] Definitio. 4.
Page: 322 (211)
[286.] Experimentum 1.
Page: 323 (212)
[287.] Experimentum 2.
Page: 323 (212)
[288.] Experimentum 3.
Page: 325 (214)
[289.] Definitio 5.
Page: 325 (214)
[290.] Experimentum 4.
Page: 329 (215)
[291.] Experimentum. 5.
Page: 329 (215)
[292.] Experimentum 6.
Page: 330 (216)
[293.] Experimentum 7.
Page: 330 (216)
[294.] Experimentum 8.
Page: 331 (217)
[295.] Experimentum 9.
Page: 331 (217)
[296.] Experimentum. 10.
Page: 332 (218)
[297.] Experimentum 11.
Page: 332 (218)
[298.] CAPUT IV. De comparandis Fluidorum Denſitatibus.
Page: 336 (219)
[299.] Experimentum 1.
Page: 336 (219)
[300.] Machina Qua Fluidorum denſitates conferuntur.
Page: 337 (220)
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        <div xml:id="echoid-div985" type="section" level="1" n="243">
          <head xml:id="echoid-head343" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          3.</head>
          <p>
            <s xml:id="echoid-s7069" xml:space="preserve">Sectio horizontalis Machinæ, in n. </s>
            <s xml:id="echoid-s7070" xml:space="preserve">615 deſcriptæ, hîc re-
              <lb/>
              <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">640.</note>
            præſentatur, applicatis huic Machinæ tribus globis ebur-
              <lb/>
              <note position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">
                <emph style="sc">TA XXIV.</emph>
                <lb/>
              fig. 4.5.</note>
            neis in deſcriptione memoratis. </s>
            <s xml:id="echoid-s7071" xml:space="preserve">Si corpora Q, Q, eodem
              <lb/>
            momento dimittantur ab æqualibus altitudinibus, & </s>
            <s xml:id="echoid-s7072" xml:space="preserve">forme-
              <lb/>
            tur parallelogrammum abcf cujus latera ab, ac, ſunt dire-
              <lb/>
            ctiones corporum Q, Q, continuatæ, & </s>
            <s xml:id="echoid-s7073" xml:space="preserve">æqualia ſubtenſis
              <lb/>
            arcuum per quos corpora Q, Q, deſcendunt; </s>
            <s xml:id="echoid-s7074" xml:space="preserve">corpus P,
              <lb/>
            ſi angulus QPQ ſit acutus minori adſcendit velocitate, quàm
              <lb/>
            qua adſcendendo poſſet percurrere arcum cujus ſubtenſa me-
              <lb/>
            morati parallelogrammi foret diagonalis.</s>
            <s xml:id="echoid-s7075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7076" xml:space="preserve">Poſito autem angulo obtuſo ad majorem adſcendit alti-
              <lb/>
            tudinem quam quæ diagonali parallelogrammi determina-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s7077" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7078" xml:space="preserve">Quæ cum explicatis in n. </s>
            <s xml:id="echoid-s7079" xml:space="preserve">634. </s>
            <s xml:id="echoid-s7080" xml:space="preserve">636. </s>
            <s xml:id="echoid-s7081" xml:space="preserve">conveniunt.</s>
            <s xml:id="echoid-s7082" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div987" type="section" level="1" n="244">
          <head xml:id="echoid-head344" xml:space="preserve">SCHOLIUM 1.</head>
          <head xml:id="echoid-head345" xml:space="preserve">Demonſtrationes n. 623. 625. 626. 627.</head>
          <p>
            <s xml:id="echoid-s7083" xml:space="preserve">Dentur tria corpora A, B, C, directè in ſe mutuo impingentia, poſitâ pri-
              <lb/>
              <note position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">641.</note>
            mi velocitate a, ſecundi b, tertii c, ſumma virium eſt A a a - B b b -
              <lb/>
            C c c ; </s>
            <s xml:id="echoid-s7084" xml:space="preserve">ſi A & </s>
            <s xml:id="echoid-s7085" xml:space="preserve">B ad eandem partem & </s>
            <s xml:id="echoid-s7086" xml:space="preserve">C in contrariam tendant, ciximus
              <note symbol="*" position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">470.</note>
            n. </s>
            <s xml:id="echoid-s7087" xml:space="preserve">623. </s>
            <s xml:id="echoid-s7088" xml:space="preserve">ſummam hanc fore, datis velocitatibus reſpectivis omnium mini-
              <lb/>
            mam, ſi A a - B b = C c; </s>
            <s xml:id="echoid-s7089" xml:space="preserve">Quod ex quiete corporum poſt ictum, in n. </s>
            <s xml:id="echoid-s7090" xml:space="preserve">624.
              <lb/>
            </s>
            <s xml:id="echoid-s7091" xml:space="preserve">demonſtrato, quidem ſequitur, ſed directè etiam probatur, ſi velocitatem
              <lb/>
            quamcunque concipiamus auctam aut diminutam quantitate quacunque ut x,
              <lb/>
            & </s>
            <s xml:id="echoid-s7092" xml:space="preserve">computatio ineatur de ſumma virium.</s>
            <s xml:id="echoid-s7093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7094" xml:space="preserve">Sit Ex. </s>
            <s xml:id="echoid-s7095" xml:space="preserve">Gr. </s>
            <s xml:id="echoid-s7096" xml:space="preserve">Corporis A velocitas a - x; </s>
            <s xml:id="echoid-s7097" xml:space="preserve">ut ſerventur velocitates reſpecti-
              <lb/>
            væ movetur B velocitate b - x; </s>
            <s xml:id="echoid-s7098" xml:space="preserve">& </s>
            <s xml:id="echoid-s7099" xml:space="preserve">corporis C velocitas erit c - x. </s>
            <s xml:id="echoid-s7100" xml:space="preserve">ſumma
              <lb/>
            virium eſt A aa + 2A a x + A xx + B bb + 2B bx + B xx + C cc - 2C cx
              <lb/>
            + C x x, quæ excedit primam quantitate A x x + B x x + C x x ſublatis 2A a x +
              <lb/>
            2 B b x - C c x quæ ſeſe mutuo deſtruunt; </s>
            <s xml:id="echoid-s7101" xml:space="preserve">cum autem exceſſus detur quo-
              <lb/>
            modocunque velocitates mutatas ſervatis velocitatibus reſpectivis, conci-
              <lb/>
            piamus, ſequitur ſummam in caſu memorato fuiſſe minimam.</s>
            <s xml:id="echoid-s7102" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7103" xml:space="preserve">liſdem poſitis, velocitas reſpectiva corporum A & </s>
            <s xml:id="echoid-s7104" xml:space="preserve">B eſt a-b ; </s>
            <s xml:id="echoid-s7105" xml:space="preserve">
              <note position="left" xlink:label="note-0256-05" xlink:href="note-0256-05a" xml:space="preserve">642.</note>
              <note symbol="*" position="left" xlink:label="note-0256-06" xlink:href="note-0256-06a" xml:space="preserve">474.</note>
            A & </s>
            <s xml:id="echoid-s7106" xml:space="preserve">C eſt a + c ; </s>
            <s xml:id="echoid-s7107" xml:space="preserve">& </s>
            <s xml:id="echoid-s7108" xml:space="preserve">tandem velocitas reſpectiva corporum B & </s>
            <s xml:id="echoid-s7109" xml:space="preserve">C
              <note symbol="*" position="left" xlink:label="note-0256-07" xlink:href="note-0256-07a" xml:space="preserve">475.</note>
            b + c . </s>
            <s xml:id="echoid-s7110" xml:space="preserve">Vis amiſſa datis hiſce velocitatibus reſpectivis valet ſummam
              <note symbol="*" position="left" xlink:label="note-0256-08" xlink:href="note-0256-08a" xml:space="preserve">475.</note>
            rium in hoc caſu, in quo ſumma hæc eſt minima , & </s>
            <s xml:id="echoid-s7111" xml:space="preserve">in quo A a + B b = C c.</s>
            <s xml:id="echoid-s7112" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0256-09" xlink:href="note-0256-09a" xml:space="preserve">621.</note>
            Vim hanc amiſſam diximus æqualem </s>
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