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

Table of contents

< >
[421.] Experimentum 7.
Page: 503 (338)
[422.] Experimentum 8.
Page: 509 (341)
[423.] SCHOLIUM. 1. Demonſtrationes n. 1150. 1152.
Page: 510 (342)
[424.] SCHOLIUM 2. De Soni intenſitate.
Page: 512 (344)
[425.] FINIS. CORRIGENDA.
Page: 516 (345)
[426.] IN MARGINE
Page: 517
[427.] FINIS.
Page: 517
[428.] De quelques Livres nouveaux & autres, que PIERRE VANDER Aa a LEIDE a imprimé oureçu de divers endroits, & quiſe trouvent dans ſa Boutique.
Page: 518
[429.] ET AUTRES
Page: 520
[430.] PHYSICES ELEMENTA
Page: 522
[431.] MATHEMATICA, EXPERIMENTIS CONFIRMATA. Sive Introductio ad Philoſophiam
Page: 522
[432.] NEWTONIANAM. Auctore GULIELMO JACOB ’s GRAVESANDE, A. L. M. Jur. Vtr. & Phil. Doctore, Regiæ Societ. Lond. Socio, Aſtron. & Math. in Acad. Lugd. Bat. Profeſſore ordinario. Tomus Secundus.
Page: 522
[433.] LUGDUNI BATAVORUM, Apud{PETRUM VANDER Aa,\\ Typographum Academiæ atque Civitatis,\\-&\\B. & P. JANSSONIOS VANDER Aa.}Bibliop. MDCC XXI. Cum Privilegio Præpotent. Ordd. Hollandiæ & Weſt-Friſiæ.
Page: 522
[434.] PRIVILEGIE.
Page: 524
[435.] INDEX CAPITUM. LIBER TERTIUS. Pars Prima. De Igne.
Page: 528
[436.] Pars Secunda. De Inflectione, Refractione, & Reflectione Luminis.
Page: 528
[437.] Pars Tertia. De Opaco & Coloribus. Cap. XVII. De corporum opacitate. # 75
Page: 528
[438.] INDEX CAPITUM. LIBER QUARTUS. Pars Prima. De Mundi Syſtemate.
Page: 529
[439.] Pars Secunda. Motuum Cœleſtium caulæ Phyſicæ.
Page: 529
[440.] PHYSICES ELEMENTA MATHEMATICA, EXPERIMENTIS CONFIRMATA. LIBER III. Pars I. De Igne. CAPUT I. De Ignis proprietatibus in genere.
Page: 530 ((1))
[441.] CAPUT II.
Page: 531 ((2))
[442.] Definitio.
Page: 531 ((2))
[443.] Experimentum 1.
Page: 531 ((2))
[444.] Experimentum 2.
Page: 531 ((2))
[445.] Experimentum 3.
Page: 531 ((2))
[446.] Experimentum 4. & 5.
Page: 533 ((4))
[447.] Experimentum 6.
Page: 533 ((4))
[448.] Experimentum. 7.
Page: 533 ((4))
[449.] Experimentum 8.
Page: 536 ((7))
[450.] Experimentum 9.
Page: 537 ((8))
< >
page |< < (291) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1494" type="section" level="1" n="359">
          <pb o="291" file="0393" n="429" rhead="MATHEMATICA. LIB. II. CAP. XII."/>
          <p>
            <s xml:id="echoid-s10562" xml:space="preserve">Ratio retardationis ex cohæſione, quæ æquabilis eſt , ad retardationem
              <note symbol="*" position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">950.</note>
            inertia, in velocitate data, eſt compoſita ex ratione retardationis primæ ad
              <lb/>
            retardationem ex pondere reſpectivo, & </s>
            <s xml:id="echoid-s10563" xml:space="preserve">ratione retardationis hujus ad ſe-
              <lb/>
            cundam. </s>
            <s xml:id="echoid-s10564" xml:space="preserve">Vidimus rationes componentes dari, datur ergo & </s>
            <s xml:id="echoid-s10565" xml:space="preserve">compoſita, id
              <lb/>
              <note position="right" xlink:label="note-0393-02" xlink:href="note-0393-02a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 4.</note>
            eſt ſi hoc applicemus ad demonſtrata in ſcholio præcedenti , datur ratio AB ad BI; </s>
            <s xml:id="echoid-s10566" xml:space="preserve">unde deducitur ratio BI ad PR ; </s>
            <s xml:id="echoid-s10567" xml:space="preserve">qua data detegitur BP
              <note symbol="*" position="right" xlink:label="note-0393-03" xlink:href="note-0393-03a" xml:space="preserve"> 1013. 1014.</note>
            ſpatium quæſitum.</s>
            <s xml:id="echoid-s10568" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">1015. 1014.</note>
          <p>
            <s xml:id="echoid-s10569" xml:space="preserve">Corpus fluido ſpecifice levius, eodem modo in hoc ſurſum fertur, acgra-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0393-05" xlink:href="note-0393-05a" xml:space="preserve">1009.</note>
            vius fundum petit; </s>
            <s xml:id="echoid-s10570" xml:space="preserve">quare demonſtrata in hoc ſcholio, ad corpora fluidis ſpe-
              <lb/>
              <note position="right" xlink:label="note-0393-06" xlink:href="note-0393-06a" xml:space="preserve">1028.</note>
            cifice leviora, & </s>
            <s xml:id="echoid-s10571" xml:space="preserve">in his motu impreſſo deſcendentia referri debent.</s>
            <s xml:id="echoid-s10572" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1505" type="section" level="1" n="360">
          <head xml:id="echoid-head496" xml:space="preserve">SCHOLIUM. 7.</head>
          <head xml:id="echoid-head497" style="it" xml:space="preserve">De Corporibus in Fluidis cadentibus.</head>
          <p>
            <s xml:id="echoid-s10573" xml:space="preserve">COrpus quod in fluido ſponte cadit, continuo æquabiliter acceleratur , dum
              <note position="right" xlink:label="note-0393-07" xlink:href="note-0393-07a" xml:space="preserve">1029.</note>
            ſiſtentiam patitur, quæ eſt ut quadratum velocitatis .</s>
            <s xml:id="echoid-s10574" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">251. 950.</note>
          <p>
            <s xml:id="echoid-s10575" xml:space="preserve">Quæ motum hunc ſpectant etiam parabolâ, & </s>
            <s xml:id="echoid-s10576" xml:space="preserve">logarithmicâ exhiben-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0393-09" xlink:href="note-0393-09a" xml:space="preserve">954.</note>
            tur.</s>
            <s xml:id="echoid-s10577" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10578" xml:space="preserve">Sit QAR logarithmicæ BDH aſymtos; </s>
            <s xml:id="echoid-s10579" xml:space="preserve">ordinata hujus curvæ ad Aſymto-
              <lb/>
              <note position="right" xlink:label="note-0393-10" xlink:href="note-0393-10a" xml:space="preserve">1030.</note>
            ton perpendicularis AB; </s>
            <s xml:id="echoid-s10580" xml:space="preserve">quæ etiam eſt axis parabolæ BFQ, cujus para-
              <lb/>
              <note position="right" xlink:label="note-0393-11" xlink:href="note-0393-11a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 5.</note>
            metrum ponimus AB.</s>
            <s xml:id="echoid-s10581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10582" xml:space="preserve">Si AR repræſentat ſpatium cadendo percurſum, poſito in A puncto ex
              <lb/>
            quo corpus dimittitur, determinatur velocitas in puncto quocunque ut C,
              <lb/>
            ductâ CD ad AB parallelâ, &</s>
            <s xml:id="echoid-s10583" xml:space="preserve">per D ad RAQ parallelâ DEF, velocitatem
              <lb/>
            quæſitam deſignabit parabolæ ordinata EF, dum AQ velocitatem maxi-
              <lb/>
            mam exprimit, ad quam corpus non pertingit, niſi poſt percurſum ſpatium
              <lb/>
            AR in infinitum productum.</s>
            <s xml:id="echoid-s10584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10585" xml:space="preserve">Hæc patebunt ſi, ſumtis ad libitum ſpatiolis æqualibus infinite exiguis,
              <lb/>
            C c, G g demonſtremus augmenta velocitatum, quæ hìc f L & </s>
            <s xml:id="echoid-s10586" xml:space="preserve">k M expri-
              <lb/>
            munt, eſſe inter ſe inverſè ut lineæ FE & </s>
            <s xml:id="echoid-s10587" xml:space="preserve">KI, quas velocitates exprimere
              <lb/>
            dicimus, ſublatis partibus quæ ſunt ut ipſæ hæ lineæ FE & </s>
            <s xml:id="echoid-s10588" xml:space="preserve">KI .</s>
            <s xml:id="echoid-s10589" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">991. 993.
            <lb/>
          1029.</note>
        </div>
        <div xml:id="echoid-div1509" type="section" level="1" n="361">
          <head xml:id="echoid-head498" xml:space="preserve">f L, k M :: {E e/FE}, {Ii/KI} :: {CD/FE} = {BA/FE} -{BE/FE}, {GH/KI} = {BA/KI} - {BI/KI}</head>
          <note symbol="*" position="right" xml:space="preserve">995.</note>
          <note symbol="*" position="right" xml:space="preserve">983.</note>
          <p>
            <s xml:id="echoid-s10590" xml:space="preserve">Sed BE x BA = FE x FE; </s>
            <s xml:id="echoid-s10591" xml:space="preserve">ergo {BE/FE} = {FE/BA}. </s>
            <s xml:id="echoid-s10592" xml:space="preserve">Eodem modo
              <note symbol="*" position="right" xlink:label="note-0393-15" xlink:href="note-0393-15a" xml:space="preserve">la Hire
                <lb/>
              ſect. con.
                <lb/>
              lib. 3.
                <lb/>
              prop. 2.</note>
            = KI/BA}. </s>
            <s xml:id="echoid-s10593" xml:space="preserve">Idcirco</s>
          </p>
        </div>
        <div xml:id="echoid-div1511" type="section" level="1" n="362">
          <head xml:id="echoid-head499" xml:space="preserve">fL, kM :: {BA/FE}-{FE/BA}, {BA/KI} = {KI/BA}</head>
          <p>
            <s xml:id="echoid-s10594" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s10595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10596" xml:space="preserve">Ut figurâ hac in computatione utamur, velocitas maxima ad quam corpus
              <lb/>
              <note position="right" xlink:label="note-0393-16" xlink:href="note-0393-16a" xml:space="preserve">1031.</note>
            pertingere poteſt, & </s>
            <s xml:id="echoid-s10597" xml:space="preserve">quæ QA repræſentatur, determinanda eſt:</s>
            <s xml:id="echoid-s10598" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10599" xml:space="preserve">Quærimus igitur velocitatem, qua conceſſa, retardatio ex ſecunda </s>
          </p>
        </div>
      </text>
    </echo>
Impressum