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

Table of contents

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[411.] Experimentum 4.
[412.] Fonticulus Heronis.
[413.] Experimentum 5.
[414.] CAPUT XIX. De Aëris motu undulatorio, ubi de Sono.
[415.] Experimentum i.
[416.] Experimentum 2.
[417.] Experimentum 3.
[418.] Experimentum 4.
[419.] Experimentum 5.
[420.] Experimentum 6.
[421.] Experimentum 7.
[422.] Experimentum 8.
[423.] SCHOLIUM. 1. Demonſtrationes n. 1150. 1152.
[424.] SCHOLIUM 2. De Soni intenſitate.
[425.] FINIS. CORRIGENDA.
[426.] IN MARGINE
[427.] FINIS.
[428.] De quelques Livres nouveaux & autres, que PIERRE VANDER Aa a LEIDE a imprimé oureçu de divers endroits, & quiſe trouvent dans ſa Boutique.
[429.] ET AUTRES
[430.] PHYSICES ELEMENTA
[431.] MATHEMATICA, EXPERIMENTIS CONFIRMATA. Sive Introductio ad Philoſophiam
[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.
[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.
[434.] PRIVILEGIE.
[435.] INDEX CAPITUM. LIBER TERTIUS. Pars Prima. De Igne.
[436.] Pars Secunda. De Inflectione, Refractione, & Reflectione Luminis.
[437.] Pars Tertia. De Opaco & Coloribus. Cap. XVII. De corporum opacitate. # 75
[438.] INDEX CAPITUM. LIBER QUARTUS. Pars Prima. De Mundi Syſtemate.
[439.] Pars Secunda. Motuum Cœleſtium caulæ Phyſicæ.
[440.] PHYSICES ELEMENTA MATHEMATICA, EXPERIMENTIS CONFIRMATA. LIBER III. Pars I. De Igne. CAPUT I. De Ignis proprietatibus in genere.
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            <s xml:id="echoid-s10161" xml:space="preserve">
              <pb o="283" file="0383" n="418" rhead="MATHEMATICA. LIB. II. CAP XII."/>
            ce notantur, deteguntur altitudines ad quas pendulum ad-
              <lb/>
            ſcendit, ſi variis vicibus ab eadem altitudine dimittatur,
              <lb/>
            & </s>
            <s xml:id="echoid-s10162" xml:space="preserve">index alter mutetur, donec ad hunc pendulum in adſcen-
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            ſu appellat, ſed remoto indice ad ipſum non pertingat.</s>
            <s xml:id="echoid-s10163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10164" xml:space="preserve">Differentiæ arcuum adſcenſu & </s>
            <s xml:id="echoid-s10165" xml:space="preserve">deſcenſu deſcriptorum
              <lb/>
            erunt proxime inter ſe ut quadrata arcuum deſcenſu de-
              <lb/>
            ſcriptorum, ſi ad hoc attendamus æqualiter vibrationes ſin-
              <lb/>
            gulas eſſe minuendas, propter reſiſtentiam ex partium
              <lb/>
            cohæſione.</s>
            <s xml:id="echoid-s10166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10167" xml:space="preserve">Notandum autem pendulum non eſſe dimittendum niſi
              <lb/>
            quieſcente aquæ ſuperficie.</s>
            <s xml:id="echoid-s10168" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1433" type="section" level="1" n="348">
          <head xml:id="echoid-head479" xml:space="preserve">SCHOLIUM 1.
            <lb/>
          De Logarithmica.</head>
          <p>
            <s xml:id="echoid-s10169" xml:space="preserve">QUæ in ſcholiis ſequentibus de retardationibus corporum, in fluidis mo-
              <lb/>
            torum, demonſtrantur, lineæ logarithmicæ proprietates profundamen-
              <lb/>
            to habent. </s>
            <s xml:id="echoid-s10170" xml:space="preserve">Formationem ideò hujus curvæ, proprietatesque quibus in ſe-
              <lb/>
            quentibus indigemus, in hocſcholio exponam.</s>
            <s xml:id="echoid-s10171" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10172" xml:space="preserve">Sit AB recta, & </s>
            <s xml:id="echoid-s10173" xml:space="preserve">in hac partes infinite exiguæ AD, DF, FH, &</s>
            <s xml:id="echoid-s10174" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10175" xml:space="preserve">æ-
              <lb/>
              <note position="right" xlink:label="note-0383-01" xlink:href="note-0383-01a" xml:space="preserve">979.</note>
            quales inter ſe. </s>
            <s xml:id="echoid-s10176" xml:space="preserve">Sint præterea ad AB, perpendiculares AC, DE, FG,
              <lb/>
              <note position="right" xlink:label="note-0383-02" xlink:href="note-0383-02a" xml:space="preserve">TAB, XXXVII.
                <lb/>
              fig. 1.</note>
            HI, &</s>
            <s xml:id="echoid-s10177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10178" xml:space="preserve">infinite parum differentes, & </s>
            <s xml:id="echoid-s10179" xml:space="preserve">quæ ſint progreſſione continua ge-
              <lb/>
            ometrica. </s>
            <s xml:id="echoid-s10180" xml:space="preserve">Si nunc curva tranſeat per extremitates C, E, G, I, &</s>
            <s xml:id="echoid-s10181" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10182" xml:space="preserve">erit hæc
              <lb/>
            logarithmica, cujus Aſymtotos erit AB, ad quam continuo curva acce-
              <lb/>
            dit, & </s>
            <s xml:id="echoid-s10183" xml:space="preserve">ad quam nunquam pertingere poteſt.</s>
            <s xml:id="echoid-s10184" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10185" xml:space="preserve">Eadem datur ratio inter ordinatas duas quaſcunque, ſi inter ipſas eadem detur
              <lb/>
              <note position="right" xlink:label="note-0383-03" xlink:href="note-0383-03a" xml:space="preserve">983.</note>
            diſtantia. </s>
            <s xml:id="echoid-s10186" xml:space="preserve">AB ſe habet HI, ut LM ad RS, ſi diſtantia AH diſtantiæ LR
              <lb/>
            fuerit æqualis. </s>
            <s xml:id="echoid-s10187" xml:space="preserve">Ratio enim quæ datur inter AC & </s>
            <s xml:id="echoid-s10188" xml:space="preserve">HI componitur ex ra-
              <lb/>
            tionibus AC ad DE, DE ad FG, & </s>
            <s xml:id="echoid-s10189" xml:space="preserve">FG ad HI; </s>
            <s xml:id="echoid-s10190" xml:space="preserve">ratio LM ad RS,
              <lb/>
            componitur ex rationibus LM ad NO, NO ad PQ, & </s>
            <s xml:id="echoid-s10191" xml:space="preserve">PQ ad RS: </s>
            <s xml:id="echoid-s10192" xml:space="preserve">ra-
              <lb/>
            tiones componentes ſingulæ ſunt æquales inter ſe ,
              <note symbol="*" position="right" xlink:label="note-0383-04" xlink:href="note-0383-04a" xml:space="preserve">979.</note>
            componentium in utroque caſu idem eſt, propter æquales diſtantias AH,
              <lb/>
            LR; </s>
            <s xml:id="echoid-s10193" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s10194" xml:space="preserve">æquales ſunt rationes compoſitæ. </s>
            <s xml:id="echoid-s10195" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s10196" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10197" xml:space="preserve">E.</s>
            <s xml:id="echoid-s10198" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1436" type="section" level="1" n="349">
          <head xml:id="echoid-head480" xml:space="preserve">
            <emph style="sc">Definitio</emph>
          1.</head>
          <p style="it">
            <s xml:id="echoid-s10199" xml:space="preserve">Logarithmus ordinatæ cujuſcunque dicitur abſciſſa ipſi reſpondens, ubicunque ini-
              <lb/>
              <note position="right" xlink:label="note-0383-05" xlink:href="note-0383-05a" xml:space="preserve">981.</note>
            tium abſciſſarum ponatur.</s>
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          </p>
        </div>
        <div xml:id="echoid-div1438" type="section" level="1" n="350">
          <head xml:id="echoid-head481" xml:space="preserve">
            <emph style="sc">Definitio</emph>
          2.</head>
          <p style="it">
            <s xml:id="echoid-s10201" xml:space="preserve">Diſtantia inter duas ordinatas vocatur logarithmus rationis quæ inter ipſas da-
              <lb/>
              <note position="right" xlink:label="note-0383-06" xlink:href="note-0383-06a" xml:space="preserve">982.</note>
            tur. </s>
            <s xml:id="echoid-s10202" xml:space="preserve">Eſtque differentia logarithmorum ipſarum ordinatarum.</s>
            <s xml:id="echoid-s10203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10204" xml:space="preserve">Poſitis iterum AH & </s>
            <s xml:id="echoid-s10205" xml:space="preserve">LR æqualibus habemus</s>
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        <div xml:id="echoid-div1440" type="section" level="1" n="351">
          <head xml:id="echoid-head482" xml:space="preserve">AC, HI :: LM, RS ; & dividendo</head>
          <note symbol="*" position="right" xml:space="preserve">982.</note>
          <p>
            <s xml:id="echoid-s10206" xml:space="preserve">AC - HI = TC, AC :</s>
            <s xml:id="echoid-s10207" xml:space="preserve">: LM - RS = VM, LM. </s>
            <s xml:id="echoid-s10208" xml:space="preserve">Quare eſt</s>
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