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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          <pb o="185" file="0263" n="287" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/>
          <p>
            <s xml:id="echoid-s7288" xml:space="preserve">Circa motum hunc abſolutum plurimorum corporum nota-
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">650.</note>
            mus, ipſum, actione reſpectivâ, qualis eſt omnis colliſio, non
              <lb/>
            mutari; </s>
            <s xml:id="echoid-s7289" xml:space="preserve">ideoque Centrum gravitatis commune variorum
              <lb/>
              <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">651.</note>
            corporum in eâdem lineâ, eâdem velocitate, ante & </s>
            <s xml:id="echoid-s7290" xml:space="preserve">poſt i-
              <lb/>
            ctum moveri. </s>
            <s xml:id="echoid-s7291" xml:space="preserve">Quod in omnibus colliſionibus ante explica-
              <lb/>
            tis obtineri demonſtrabimus.</s>
            <s xml:id="echoid-s7292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7293" xml:space="preserve">Sint A & </s>
            <s xml:id="echoid-s7294" xml:space="preserve">B centra gravitatis duorum corporum, ſi ad C,
              <lb/>
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">
                <emph style="sc">TA. XXV.</emph>
                <lb/>
              fig. 8.</note>
            centrum gravit atis commune, accedant ambo corpora, veloci-
              <lb/>
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">652.</note>
            tatibus quæ ſunt inter ſe ut diſtantiæ ſuæ à centro, nempeut
              <lb/>
            AC ad BC, id eſt, inverſe ut maſſæ ipſorum corporum
              <note symbol="*" position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">134. 143.</note>
            quieſcit in hoc motu centrum gravitatis; </s>
            <s xml:id="echoid-s7295" xml:space="preserve">nam dum eodem
              <lb/>
            tempore percurrunt A a, B b, quæ ſunt ut AC, BC,
              <lb/>
            reſtant a C, b C in eâdem ratione inverſa maſſarum, qua-
              <lb/>
            re & </s>
            <s xml:id="echoid-s7296" xml:space="preserve">in hoc ſitu C eſt commune gravitatis centrum ,
              <note symbol="*" position="right" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">134.</note>
            in motu hoc non fuit tranſlatum.</s>
            <s xml:id="echoid-s7297" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7298" xml:space="preserve">Eadem demonſtratio poteſt applicari ad motum corpo-
              <lb/>
              <note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">653.</note>
            rum à commune gravitatis centro recedentium, velocitati-
              <lb/>
            bus quæ ſunt inverſe ut maſſæ, in quo caſu ergo etiam cen-
              <lb/>
            trum hoc quieſcit.</s>
            <s xml:id="echoid-s7299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7300" xml:space="preserve">Si varia dentur corpora, ut A, B, D, & </s>
            <s xml:id="echoid-s7301" xml:space="preserve">hæc in eâdem
              <lb/>
              <note position="right" xlink:label="note-0263-08" xlink:href="note-0263-08a" xml:space="preserve">654.</note>
            lineâ mota, accedant omnia ad C commune gravitatis centrum,
              <lb/>
              <note position="right" xlink:label="note-0263-09" xlink:href="note-0263-09a" xml:space="preserve">
                <emph style="sc">TA. XXV.</emph>
                <lb/>
              fig. 9.</note>
            aut recedant ab hoc, velocitatibus quæ in ſingulis corpori-
              <lb/>
            bus ſunt ut diſtantiæ ab hoc centro quieſcit etiam hoc ipſum.
              <lb/>
            </s>
            <s xml:id="echoid-s7302" xml:space="preserve">Nam cum in ſitu A, B, D ſumma productorum maſſarum
              <lb/>
            per diſtantias a C ab una parte hujus puncti æqualis ſit ſimi-
              <lb/>
            li ſummæ ad aliam partem , & </s>
            <s xml:id="echoid-s7303" xml:space="preserve">hoc locum habebit
              <note symbol="*" position="right" xlink:label="note-0263-10" xlink:href="note-0263-10a" xml:space="preserve">141. 143.</note>
            tis omnibus diſtantiis, ut hîc fit, in eadem ratione, quare
              <lb/>
            C manet centrum commune gravitatis ; </s>
            <s xml:id="echoid-s7304" xml:space="preserve">quod ergo
              <note symbol="*" position="right" xlink:label="note-0263-11" xlink:href="note-0263-11a" xml:space="preserve">141.</note>
            ſcit.</s>
            <s xml:id="echoid-s7305" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s7306" xml:space="preserve">In hoc caſu, multiplicatis ſingulis maſſis per ſuas veloci-
              <lb/>
            tates, ſumma productorum ab una parte centri gravitatis,
              <lb/>
            æqualis eſt ſimili ſummæ ad aliam partem; </s>
            <s xml:id="echoid-s7307" xml:space="preserve">ponimus enim
              <lb/>
            velocitates ut diſtantias à centro hoc.</s>
            <s xml:id="echoid-s7308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7309" xml:space="preserve">Ex hiſce ſequentes deducimus concluſiones.</s>
            <s xml:id="echoid-s7310" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7311" xml:space="preserve">Corporum duorum, aut trium, in ſe mutuo directè incur-
              <lb/>
              <note position="right" xlink:label="note-0263-12" xlink:href="note-0263-12a" xml:space="preserve">655.</note>
            rentium ita, ut poſt ictum, ſi non ſint elaſtica, quieſcant, </s>
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