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

Table of contents

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[231.] Experimentum 12.
Page: 246 (159)
[232.] SCHOLIUM I. Uberior demonſtratio n. 558.
Page: 247 (160)
[233.] SCHOLIUM 2. Illuſtratio circa mutuam corporum elaſticorum actionem.
Page: 251 (161)
[234.] SCHOLIUM 3. Paradoxi explicatio.
Page: 256 (163)
[235.] CAPUT XXV. De motu compoſito.
Page: 257 (164)
[236.] CAPUT XXVI. De Percuſſione obliqua. Definitio 1.
Page: 261 (168)
[237.] Definitio. 2.
Page: 261 (168)
[238.] Machina.
Page: 262 (169)
[239.] Experimentum. I.
Page: 263 (170)
[240.] CAPUT XXVII. De Colliſione compoſita. Definitio.
Page: 268 (172)
[241.] Experimentum. 1
Page: 276 (177)
[242.] Experimentum 2.
Page: 276 (177)
[243.] Experimentum 3.
Page: 279 (180)
[244.] SCHOLIUM 1. Demonſtrationes n. 623. 625. 626. 627.
Page: 279 (180)
[245.] SCHOLIUM 2. Inveſtigatio motus memorati in n. 633.
Page: 284 (182)
[246.] SCHOLIUM 3. Demonſtratio n. 637.
Page: 286 (184)
[247.] CAPUT XXVIII. De Motu Centri gravitatis.
Page: 286 (184)
[248.] Definitio.
Page: 286 (184)
[249.] SCHOLIUM 1. Demonſtratio n. 660.
Page: 289 (187)
[250.] SCHOLIUM 2. Demonſtrationes n. 658. ut & 648.
Page: 290 (188)
[251.] SCHOLIUM 3.
Page: 291 (189)
[252.] CAPUT XXIX. De Legibus Elaſticitatis.
Page: 292 (190)
[253.] Definitio.
Page: 296 (191)
[254.] Machina Qua Experimenta de Elaſticitate inſtituuntur.
Page: 297 (192)
[255.] Experimentum. i.
Page: 297 (192)
[256.] Experimentum 2.
Page: 299 (194)
[257.] Experimentum 3.
Page: 299 (194)
[258.] Experimentum 4.
Page: 300 (195)
[259.] Experimentum 5.
Page: 302 (197)
[260.] Experimentum 6.
Page: 304 (199)
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            in eadem ſunt ratione cum lineis cB, cB, CB. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">Punctum
              <lb/>
            ideo C verſus B & </s>
            <s xml:id="echoid-s7603" xml:space="preserve">A ſemper trahitur, viribus lineæ CB
              <lb/>
            aut CA proportionalibus; </s>
            <s xml:id="echoid-s7604" xml:space="preserve">& </s>
            <s xml:id="echoid-s7605" xml:space="preserve">vis qua chorda inflectitur, cu-
              <lb/>
            jus directio eſt per c C, duplicatæ ſagittæ rationem ſequi-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">220, 231.</note>
            tur , & </s>
            <s xml:id="echoid-s7606" xml:space="preserve">eſt ut ipſa ſagitta. </s>
            <s xml:id="echoid-s7607" xml:space="preserve">In omnibus ergo chordæ
              <note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">678.</note>
            juſcunque inflexionibus minimis, ſagitta creſcit & </s>
            <s xml:id="echoid-s7608" xml:space="preserve">minuitur
              <lb/>
            in eadem ratione cum vi qua chorda inflectitur.</s>
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        <div xml:id="echoid-div1051" type="section" level="1" n="256">
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            <emph style="sc">Experimentum</emph>
          2.</head>
          <p>
            <s xml:id="echoid-s7610" xml:space="preserve">Chorda AB, pondere quocunque tenſa, inflectitur pon-
              <lb/>
              <note position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">679.</note>
            deribus unius unciæ, duarum, & </s>
            <s xml:id="echoid-s7611" xml:space="preserve">trium unciarum, deſcen-
              <lb/>
              <note position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 2.</note>
            ſus puncti g, id eſt, ipſæ ſagittæ, ſunt inter ſe ut unum,
              <lb/>
            duo, & </s>
            <s xml:id="echoid-s7612" xml:space="preserve">tria.</s>
            <s xml:id="echoid-s7613" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7614" xml:space="preserve">In chordis ejuſdem generis, craſſitiei, & </s>
            <s xml:id="echoid-s7615" xml:space="preserve">æqualiter tenſis,
              <lb/>
              <note position="left" xlink:label="note-0274-05" xlink:href="note-0274-05a" xml:space="preserve">680.</note>
            ſed diverſæ longitudinis, productiones, quæ ex ſuperadditis
              <lb/>
            æqualibus ponderibus oriuntur, ſunt inter ſe ut chor darum
              <lb/>
            longitudines. </s>
            <s xml:id="echoid-s7616" xml:space="preserve">Ex eo hoc patet, quod chorda in omnibus
              <lb/>
            punctis ſit æque tenſa; </s>
            <s xml:id="echoid-s7617" xml:space="preserve">productio ergo integræ chordæ eſt
              <lb/>
            dupla productionis dimidiæ partis, aut chordæ dimidiæ lon-
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            gitudinis.</s>
            <s xml:id="echoid-s7618" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7619" xml:space="preserve">Quod ad inflexionem harum chordarum attinet, ſint
              <lb/>
              <note position="left" xlink:label="note-0274-06" xlink:href="note-0274-06a" xml:space="preserve">681.</note>
            AB, ab, chordæ ejuſdem generis & </s>
            <s xml:id="echoid-s7620" xml:space="preserve">craſſitiei, ſed diverſæ
              <lb/>
              <note position="left" xlink:label="note-0274-07" xlink:href="note-0274-07a" xml:space="preserve">
                <emph style="sc">TA. XXVI.</emph>
                <lb/>
              fig. 4.</note>
            longitudinis, æque tenſæ & </s>
            <s xml:id="echoid-s7621" xml:space="preserve">ita inflexæ, ut ACB ſit ſitus
              <lb/>
            illius; </s>
            <s xml:id="echoid-s7622" xml:space="preserve">adb hujus inflexio; </s>
            <s xml:id="echoid-s7623" xml:space="preserve">& </s>
            <s xml:id="echoid-s7624" xml:space="preserve">ſint triangula BCc & </s>
            <s xml:id="echoid-s7625" xml:space="preserve">bDd ſi-
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            milia: </s>
            <s xml:id="echoid-s7626" xml:space="preserve">cB eſt ad Db, id eſt, ſunt chordarum longitudines,
              <lb/>
            ut CB ad db; </s>
            <s xml:id="echoid-s7627" xml:space="preserve">chordæ ergo proportionaliter ad longitudi-
              <lb/>
            nes producuntur, & </s>
            <s xml:id="echoid-s7628" xml:space="preserve">ideo viribus æqualibus, juxta directio-
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            nes bd, ad, BC, AC trahuntur ; </s>
            <s xml:id="echoid-s7629" xml:space="preserve">propter
              <note symbol="*" position="left" xlink:label="note-0274-08" xlink:href="note-0274-08a" xml:space="preserve">680.</note>
            autem triangulorum ſtatim memoratorum vires etiam juxta
              <lb/>
            cC & </s>
            <s xml:id="echoid-s7630" xml:space="preserve">Dd agentes ſunt æquales inter ſe , & </s>
            <s xml:id="echoid-s7631" xml:space="preserve">ſagittæ
              <note position="left" xlink:label="note-0274-09" xlink:href="note-0274-09a" xml:space="preserve">682.</note>
            Dd ſunt ut chordarum longitudines; </s>
            <s xml:id="echoid-s7632" xml:space="preserve">quod igitur, cæteris
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0274-10" xlink:href="note-0274-10a" xml:space="preserve">200. 232.</note>
            paribus, in chordis inæqualibus & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">inflexis ſemper obti-
              <lb/>
            net.</s>
            <s xml:id="echoid-s7634" xml:space="preserve"/>
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        <div xml:id="echoid-div1055" type="section" level="1" n="257">
          <head xml:id="echoid-head365" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          3.</head>
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            <s xml:id="echoid-s7635" xml:space="preserve">Chorda A B pondere quocunque tenditur, applicatis
              <lb/>
              <note position="left" xlink:label="note-0274-11" xlink:href="note-0274-11a" xml:space="preserve">683.</note>
            Priſmatibus H, H, ab utraque parte ad ſextam diviſionem;
              <lb/>
            </s>
            <s xml:id="echoid-s7636" xml:space="preserve">
              <note position="left" xlink:label="note-0274-12" xlink:href="note-0274-12a" xml:space="preserve">
                <emph style="sc">TA. XXVI</emph>
                <lb/>
              fig. a.</note>
            inflectatur pondere quocunque, ita ut ſagitta ſit ſex </s>
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