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

Table of contents

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[81.] Experimentum 5.
[82.] Experimentum 6.
[83.] Definitio 7.
[84.] Experimentum 7.
[85.] Experimentum 8.
[86.] Experimentum 9.
[87.] Experimentum 10.
[88.] Experimentum 11.
[89.] Experimentum 13.
[90.] SCHOLIUM De centro Gravitatis.
[91.] De Centri gravitatis inveſtigatione.
[92.] SCHOLIUM 2. Arithmetica Mechanica.
[93.] CAPUT X. De Vecte, Machinarum ſimplicium prima. Definitio 1.
[94.] Experimentum 1. 2. & 3.
[95.] Experimentum 4.
[96.] Experimentum 5.
[97.] Experimentum 6.
[98.] Experimentum 7. & 8.
[99.] Experimentum 9
[100.] CAPUT XI.
[101.] Definitio
[102.] Experimentum 1.
[103.] Experimentum 2.
[104.] CAPUT XII. De Trochlea, Machinarum ſimplicium tertia.
[105.] Experimentum 1.
[106.] Experimentum 2.
[107.] Experimentum 3. & 4
[108.] Experimentum 5.
[109.] CAPUT XIII. De Cuneo & Cocbleâ, Machinarum Simplicium quartâ, & quintâ.
[110.] Definitio I.
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          <p>
            <s xml:id="echoid-s1901" xml:space="preserve">Si axis rotæ ſit dentatus, valet ad movendam rotam, cu-
              <lb/>
              <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">TAB. VI.
                <lb/>
              fig. 7.</note>
            jus peripheria dentes habet, & </s>
            <s xml:id="echoid-s1902" xml:space="preserve">cujus axis tertiæ rotæ motum
              <lb/>
            communicare poteſt, & </s>
            <s xml:id="echoid-s1903" xml:space="preserve">ſic ulterius. </s>
            <s xml:id="echoid-s1904" xml:space="preserve">In eo caſu</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1905" xml:space="preserve">Ratio potentiæ ad pondus ut æquè polleant, eſt ratio compo-
              <lb/>
              <note position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">190.</note>
            ſita ex ratione diametri axis ultimæ rotæ, ad diametrum pri-
              <lb/>
            mæ & </s>
            <s xml:id="echoid-s1906" xml:space="preserve">ratione circumvolutionum ultimæ rotæ, ad circum-
              <lb/>
            volutiones primæ, eodem tempore.</s>
            <s xml:id="echoid-s1907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1908" xml:space="preserve">Cujus regulæ demonſtratio etiam ex comparatione viarum
              <lb/>
            percurſarum à pondere & </s>
            <s xml:id="echoid-s1909" xml:space="preserve">potentia deducitur.</s>
            <s xml:id="echoid-s1910" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div311" type="section" level="1" n="103">
          <head xml:id="echoid-head153" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          2.</head>
          <p>
            <s xml:id="echoid-s1911" xml:space="preserve">Rotæ AB potentia, quæ per pondus M repræſentatur,
              <lb/>
              <note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">191.</note>
            applicatur, pondus P axi rotæ FG; </s>
            <s xml:id="echoid-s1912" xml:space="preserve">axis illius diameter eſt
              <lb/>
              <note position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">TAB. VI.
                <lb/>
              fig. 7.</note>
            octava pars diametri rotæ AB, & </s>
            <s xml:id="echoid-s1913" xml:space="preserve">hæc rota quinquies cir-
              <lb/>
            cumvolvitur, dum rota FG ſemel: </s>
            <s xml:id="echoid-s1914" xml:space="preserve">ratio ergo potentiæ ad
              <lb/>
            pondus componitur ex rationibus 1. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">ad 8.</s>
            <s xml:id="echoid-s1916" xml:space="preserve">; & </s>
            <s xml:id="echoid-s1917" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">ad 5.</s>
            <s xml:id="echoid-s1919" xml:space="preserve">; eſt
              <lb/>
            ergo ratio 1. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">ad 40.</s>
            <s xml:id="echoid-s1921" xml:space="preserve">; ſemilibra ſuſtinet in eo caſu viginti li-
              <lb/>
            bras.</s>
            <s xml:id="echoid-s1922" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div313" type="section" level="1" n="104">
          <head xml:id="echoid-head154" xml:space="preserve">CAPUT XII.
            <lb/>
          De Trochlea, Machinarum ſimplicium tertia.</head>
          <p>
            <s xml:id="echoid-s1923" xml:space="preserve">MUltis in occaſionibus axis in peritrochio ad elevanda
              <lb/>
            pondera inſervire nequit; </s>
            <s xml:id="echoid-s1924" xml:space="preserve">trochleis in iis caſibus u-
              <lb/>
            tendum, & </s>
            <s xml:id="echoid-s1925" xml:space="preserve">Machina, quæ ex iſtis formatur, eſt admodum
              <lb/>
            compendioſa, & </s>
            <s xml:id="echoid-s1926" xml:space="preserve">facillime de loco in locum transfertur.</s>
            <s xml:id="echoid-s1927" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1928" xml:space="preserve">Quid ſit Trochlea, jam ante dictum .</s>
            <s xml:id="echoid-s1929" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">123.</note>
          <p>
            <s xml:id="echoid-s1930" xml:space="preserve">Si pondus trochleæ conjunctum ſit ita, ut cum ea traha-
              <lb/>
            tur, utraque extremitas funis ductarii ſuſtinet partem dimi-
              <lb/>
            diam ponderis. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">Quando ergo extremitas una, unco alliga-
              <lb/>
              <note position="left" xlink:label="note-0080-06" xlink:href="note-0080-06a" xml:space="preserve">192.</note>
            ta, aut aliter fixa eſt, vis movens alteri extremitati appli-
              <lb/>
            cata, quæ dimidium ponderis valet, pondus ſuſtinet.</s>
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          </p>
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        <div xml:id="echoid-div315" type="section" level="1" n="105">
          <head xml:id="echoid-head155" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          1.</head>
          <p>
            <s xml:id="echoid-s1933" xml:space="preserve">Pondus P, duarum librarum trochleæ conjungitur, ita ta-
              <lb/>
              <note position="left" xlink:label="note-0080-07" xlink:href="note-0080-07a" xml:space="preserve">193.</note>
            men, ut rotatio orbiculi eo non impediatur; </s>
            <s xml:id="echoid-s1934" xml:space="preserve">unco funis e f
              <lb/>
              <note position="left" xlink:label="note-0080-08" xlink:href="note-0080-08a" xml:space="preserve">TAB. VII.
                <lb/>
              fig. 1.</note>
            alligatur, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">altera funis extremitas cd circumit trochleam
              <lb/>
            fixam ad directionem mutandam ; </s>
            <s xml:id="echoid-s1936" xml:space="preserve">tunc pondus M,
              <note symbol="*" position="left" xlink:label="note-0080-09" xlink:href="note-0080-09a" xml:space="preserve">124.</note>
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