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

Table of contents

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[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)
[261.] SCHOLIUM.
Page: 304 (199)
[262.] FINIS LIBRI PRIMI.
Page: 304 (199)
[263.] PHYSICES ELEMENTA MATHEMATICA EXPERIMENTIS CONFIRMATA. LIBER II. Pars I. de Gravitate, & Preſſione Fluidorum. CAPUT I. De Gravitate partium Fluidorum, & illius Effectu in ipſis Fluidis.
Page: 305 (200)
[264.] Bilanx Hydrostatica.
Page: 309 (201)
[265.] Experimentum 1.
Page: 309 (201)
[266.] Experimentum 2.
Page: 310 (202)
[267.] Experimentum 3.
Page: 311 (203)
[268.] Experimentum 4.
Page: 311 (203)
[269.] Experimentum. 5.
Page: 312 (204)
[270.] Experimentum 6.
Page: 312 (204)
[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)
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          <pb o="161" file="0231" n="251" rhead="MATHEMATICA. LIB. I. CAP XXIV."/>
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        <div xml:id="echoid-div907" type="section" level="1" n="233">
          <head xml:id="echoid-head326" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head327" style="it" xml:space="preserve">Illuſtratio circa mutuam corporum elaſticorum
            <lb/>
          actionem.</head>
          <p>
            <s xml:id="echoid-s6366" xml:space="preserve">Licet circa ſummæ virium æqualitatem ante & </s>
            <s xml:id="echoid-s6367" xml:space="preserve">poſt ictum dubium ſapereſſe
              <lb/>
              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">589.</note>
            nullum poſſit, cum hæc ex ipſa perſecta claſticitate ſequatur , & </s>
            <s xml:id="echoid-s6368" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">557.</note>
            utin præcedenti ſcholio fecimus, ex regulis computationis deducatur, obſcurum
              <lb/>
            quid nihilominus in hiſce dari non diffiteor; </s>
            <s xml:id="echoid-s6369" xml:space="preserve">cum ex demonſtratis non pa-
              <lb/>
            teat, quomodo elaſterium, quod dum ſe inter corpora expandit, & </s>
            <s xml:id="echoid-s6370" xml:space="preserve">ad partes
              <lb/>
            oppoſitas vires, quæ ſuntinverſè ut maſſæ, communicat , poſſit ſæpe
              <note symbol="*" position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">561.</note>
            corpori integram non modo, qua ſe expandit, imprimere vim; </s>
            <s xml:id="echoid-s6371" xml:space="preserve">ſed præter-
              <lb/>
            ea quantum ex vi aliûs corporis tollit. </s>
            <s xml:id="echoid-s6372" xml:space="preserve">Si Ex. </s>
            <s xml:id="echoid-s6373" xml:space="preserve">C. </s>
            <s xml:id="echoid-s6374" xml:space="preserve">corpus A duobus gradi-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">470.</note>
            bus velocitatis, id eſt, cum quatuor grad. </s>
            <s xml:id="echoid-s6375" xml:space="preserve">vis , incurrat in corpus B æquale quieſcens, poſt ictum, ſepoſita elaſticitate, ambo unico gradu velocitatis gau-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">519.</note>
            dent & </s>
            <s xml:id="echoid-s6376" xml:space="preserve">ſingula unicum gradum vis habent , id eſt, amborum vis valet
              <note symbol="*" position="right" xlink:label="note-0231-06" xlink:href="note-0231-06a" xml:space="preserve">470.</note>
            & </s>
            <s xml:id="echoid-s6377" xml:space="preserve">duobus reliquis gradibus vis partes fuere compreſſæ ; </s>
            <s xml:id="echoid-s6378" xml:space="preserve">id eſt, ſi
              <note symbol="*" position="right" xlink:label="note-0231-07" xlink:href="note-0231-07a" xml:space="preserve">488.</note>
            ſint elaſtica, hac ipſa vielaſterium fuit flexum, & </s>
            <s xml:id="echoid-s6379" xml:space="preserve">eadem vi ſeſe expandit :</s>
            <s xml:id="echoid-s6380" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0231-08" xlink:href="note-0231-08a" xml:space="preserve">557.</note>
            Poſt ictum verò corpus B duos habet gradus velocitatis , id eſt vim
              <note symbol="*" position="right" xlink:label="note-0231-09" xlink:href="note-0231-09a" xml:space="preserve">576.</note>
            tuor , & </s>
            <s xml:id="echoid-s6381" xml:space="preserve">quieſcit A; </s>
            <s xml:id="echoid-s6382" xml:space="preserve">Elaſterium ergo ipſi B tres gradus vis
              <note symbol="*" position="right" xlink:label="note-0231-10" xlink:href="note-0231-10a" xml:space="preserve">470.</note>
            & </s>
            <s xml:id="echoid-s6383" xml:space="preserve">gradum unum ex A ſuſtulit; </s>
            <s xml:id="echoid-s6384" xml:space="preserve">quamvis duobus tantum gradibus vis fuerit
              <lb/>
            flexum; </s>
            <s xml:id="echoid-s6385" xml:space="preserve">& </s>
            <s xml:id="echoid-s6386" xml:space="preserve">licet propter corpora æqualia, æquales impreſſiones ab utraque
              <lb/>
            parte exeruerit.</s>
            <s xml:id="echoid-s6387" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6388" xml:space="preserve">Ut hæc tollatur difficultas, inter vim abſolutam & </s>
            <s xml:id="echoid-s6389" xml:space="preserve">relativam diſtinguen-
              <lb/>
              <note position="right" xlink:label="note-0231-11" xlink:href="note-0231-11a" xml:space="preserve">590.</note>
            dum. </s>
            <s xml:id="echoid-s6390" xml:space="preserve">Elaſterium inter corpora poſitum vires ipſis communicat, quæ ſuut inverſè
              <lb/>
            ut maſſæ, ſi inter corpora quieſcat ; </s>
            <s xml:id="echoid-s6391" xml:space="preserve">id eſt, ſi, translatis corporibus,
              <note symbol="*" position="right" xlink:label="note-0231-12" xlink:href="note-0231-12a" xml:space="preserve">561.</note>
            motu cum hiſce feratur; </s>
            <s xml:id="echoid-s6392" xml:space="preserve">quales ideò motus corporibus communicantur in
              <lb/>
            nave quæ eadem velocitate cum corporibus fertur, & </s>
            <s xml:id="echoid-s6393" xml:space="preserve">in qua idcirco hæc cum e-
              <lb/>
            laſterio quieſcunt ; </s>
            <s xml:id="echoid-s6394" xml:space="preserve">ſed propoſitio hæc ad motus abſolutos referrinon debet,
              <note symbol="*" position="right" xlink:label="note-0231-13" xlink:href="note-0231-13a" xml:space="preserve">564.</note>
            rum unus acceleratur, alter retardatur, translato jam ipſo elaſterio ante hu-
              <lb/>
            jus actionem, ad caſum ita conſideratum demonſtratio propoſitionis appli-
              <lb/>
            cari nequit.</s>
            <s xml:id="echoid-s6395" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6396" xml:space="preserve">Circa vires abſolutas notandum, has corpori ſæpe communicari, cauſâ mo-
              <lb/>
            venti quæ ipſa transfertur, in quo caſu non ſola cauſa movens in corpus agit,
              <lb/>
              <note position="right" xlink:label="note-0231-14" xlink:href="note-0231-14a" xml:space="preserve">591.</note>
            ſed & </s>
            <s xml:id="echoid-s6397" xml:space="preserve">in corpus datur actio illa quæ ipſam transfert canſam moventem, corporique
              <lb/>
            communicatur vis, quæ valet ſummam barum actionem ; </s>
            <s xml:id="echoid-s6398" xml:space="preserve">nam vis hæc eſt
              <note symbol="*" position="right" xlink:label="note-0231-15" xlink:href="note-0231-15a" xml:space="preserve">249.</note>
            fectus ambarum actionum conjunctarum; </s>
            <s xml:id="echoid-s6399" xml:space="preserve">agitur enim de caſu in quo hæ a-
              <lb/>
            lium nullum effectum edunt. </s>
            <s xml:id="echoid-s6400" xml:space="preserve">Hæc jam alia occaſione notavimus .</s>
            <s xml:id="echoid-s6401" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">446.</note>
          <p>
            <s xml:id="echoid-s6402" xml:space="preserve">Quando elaſterium obſtaculo inſiſtit quod ad partem oppoſitam non cedit,
              <lb/>
            totam vim qua fuit infiexum corpori quod ab obſtaculo repellit communicat,
              <lb/>
            ut hoc antea notavimus , & </s>
            <s xml:id="echoid-s6403" xml:space="preserve">ſequitur ex demonſtrationen. </s>
            <s xml:id="echoid-s6404" xml:space="preserve">561. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">& </s>
            <s xml:id="echoid-s6406" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0231-17" xlink:href="note-0231-17a" xml:space="preserve">441.</note>
            experimentis memoratis addita propoſitione n. </s>
            <s xml:id="echoid-s6407" xml:space="preserve">559; </s>
            <s xml:id="echoid-s6408" xml:space="preserve">quæ, poſitâ perfectâ
              <note symbol="*" position="right" xlink:label="note-0231-18" xlink:href="note-0231-18a" xml:space="preserve">492.</note>
            ſticitate, in dubium a nemine vocatur, neque vocari poteſt.</s>
            <s xml:id="echoid-s6409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6410" xml:space="preserve">Si autem elaſterium quod ab una parte inſiſtit obſtaculo quod non cedit
              <lb/>
            totam ſuam ad oppoſitam partem vim exerat, multo magis Elaſterium quod
              <lb/>
              <note position="right" xlink:label="note-0231-19" xlink:href="note-0231-19a" xml:space="preserve">592.</note>
            ad illam transſertur partem ad quam agit, integram vim, quarelaxatur, corpori com-
              <lb/>
            municabit, cui etiam imprimet vim quæ valet actionem, quæ ipſum transfert ela-
              <lb/>
            ſterium dum relaxatur .</s>
            <s xml:id="echoid-s6411" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">591.</note>
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