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

Table of contents

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[221.] Experimentum 2.
Page: 242 (155)
[222.] Experimentum 3.
Page: 242 (155)
[223.] Experimentum 4.
Page: 242 (155)
[224.] Experimentum 5.
Page: 243 (156)
[225.] Experimentum 6.
Page: 243 (156)
[226.] Experimentum 7.
Page: 243 (156)
[227.] Experimentum 8.
Page: 244 (157)
[228.] Experimentum 9.
Page: 244 (157)
[229.] Experimentum 10.
Page: 244 (157)
[230.] Experimentum 11.
Page: 245 (158)
[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)
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              <pb o="167" file="0239" n="260" rhead="MATHEMATICA. LIB. I. CAP. XXV."/>
            communicandam eſſe vim, quæ proportionalis ſit quadrato
              <lb/>
            A f, & </s>
            <s xml:id="echoid-s6595" xml:space="preserve">impreſſionem, qua agitatur, ulterius tantum valere
              <lb/>
            debere, ut quantitate A g poſſit minuere velocitatem AD,
              <lb/>
            in hoc caſu corpus juxta directionem AD tantum ſuperſti-
              <lb/>
            tem habebit vim proportionalem quadrato A b , cui ſi
              <note symbol="*" position="right" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">598.</note>
            datur vis proportionalis quadrato A f, habemus vim
              <note symbol="*" position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">601.</note>
            tionalem quadrato AB; </s>
            <s xml:id="echoid-s6596" xml:space="preserve">quod iterum cum ante demonſtra-
              <lb/>
            tis congruit .</s>
            <s xml:id="echoid-s6597" xml:space="preserve"/>
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          <note symbol="*" position="right" xml:space="preserve">246 447.</note>
          <p>
            <s xml:id="echoid-s6598" xml:space="preserve">Propoſitionem hanc, vim ſequi proportionem quadrati
              <lb/>
              <note position="right" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">607.</note>
            velocitatis, non poſſe referri ad illam cum qua alia in ea-
              <lb/>
            dem linea agit, facile ex ante demonſtratis ſequitur ,
              <note symbol="*" position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">598. 599</note>
            de causâ ubi vim in duas reſolvimus, hæ quadratis veloci-
              <lb/>
            tatum proportionales non erunt, niſi ambarum directiones
              <lb/>
            angulum rectum contineant ne aliter pro parte conſpirent
              <lb/>
            aut contrarie agant . </s>
            <s xml:id="echoid-s6599" xml:space="preserve">Ex quibus deducimus vim
              <note symbol="*" position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">601.</note>
            tam non iterum poſſe reſolvi. </s>
            <s xml:id="echoid-s6600" xml:space="preserve">Motus per AB reſolvitur
              <lb/>
            in duos motus ejuſdem corporis per AD & </s>
            <s xml:id="echoid-s6601" xml:space="preserve">AE, & </s>
            <s xml:id="echoid-s6602" xml:space="preserve">vires
              <lb/>
              <note position="right" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig 54.</note>
            quadratis velociratum ſunt proportionales; </s>
            <s xml:id="echoid-s6603" xml:space="preserve">ſed ſi motus per
              <lb/>
            AE iterum in duos per AF & </s>
            <s xml:id="echoid-s6604" xml:space="preserve">AG angulum rectum con-
              <lb/>
            tinentes ſeparetur, non erunt hæ ultimæ quadratis veloci-
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            tatum proportionales, & </s>
            <s xml:id="echoid-s6605" xml:space="preserve">non poterit hîc applicari n. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">604,
              <lb/>
            in quo agitur de viribus, quæ non modo inter ſe non con-
              <lb/>
            fpirant, neque contrarie agunt, ſed quæ cum tertiâ nil
              <lb/>
            commune habent. </s>
            <s xml:id="echoid-s6607" xml:space="preserve">Hîc autem ipſe motus corporis per
              <lb/>
            AB in tres motus reſolvitur per AD, AF & </s>
            <s xml:id="echoid-s6608" xml:space="preserve">AG, in qui-
              <lb/>
            bus AF & </s>
            <s xml:id="echoid-s6609" xml:space="preserve">AD pro parte conſpirant, AD & </s>
            <s xml:id="echoid-s6610" xml:space="preserve">AG partim
              <lb/>
            contrariè agunt; </s>
            <s xml:id="echoid-s6611" xml:space="preserve">& </s>
            <s xml:id="echoid-s6612" xml:space="preserve">reſolutio quæ ad velocitates poteſtappli-
              <lb/>
            cari, cùm demonſtratio n. </s>
            <s xml:id="echoid-s6613" xml:space="preserve">246. </s>
            <s xml:id="echoid-s6614" xml:space="preserve">eadem ſit, ſive motus in re-
              <lb/>
            folutione conſpirent, ſive contrarie agunt, ad vires non poſſe
              <lb/>
            referri ex ante demonſtratis clarum eſt .</s>
            <s xml:id="echoid-s6615" xml:space="preserve">
              <note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">440. 443.</note>
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            <s xml:id="echoid-s6616" xml:space="preserve">In n. </s>
            <s xml:id="echoid-s6617" xml:space="preserve">605. </s>
            <s xml:id="echoid-s6618" xml:space="preserve">606. </s>
            <s xml:id="echoid-s6619" xml:space="preserve">motum per AB compoſitum habemus ex
              <lb/>
              <note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">608.</note>
            duobus, quorum unum in alios reſolvimus, ſed ita, ut poſt
              <lb/>
              <note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 4. 5.</note>
            reſolutionem omnes motus darentur in duabus lineis, angu-
              <lb/>
            lum rectum continentibus: </s>
            <s xml:id="echoid-s6620" xml:space="preserve">quare motus in ſingulis lineis,
              <lb/>
            ſeparatim conſiderari potuere, quod nunquam fieri poteſt
              <lb/>
            ubi motus varii in pluribus quàm duabus lineis dantur, </s>
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