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

Page concordance

< >
Scan Original
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
41 11
42 12
43 13
44 14
45 15
46 16
47 17
48 18
49 19
50 20
51 21
52 22
53
54
55
56 23
57 24
58 25
59 26
60 27
< >
page |< < (19) of 824 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div126" type="section" level="1" n="49">
          <pb o="19" file="0049" n="49" rhead="MATHEMATICA. LIB. I. CAP. V."/>
        </div>
        <div xml:id="echoid-div130" type="section" level="1" n="50">
          <head xml:id="echoid-head89" xml:space="preserve">SCHOLIUM</head>
          <head xml:id="echoid-head90" style="it" xml:space="preserve">De efſectu attractionis vitri in aquam.</head>
          <p>
            <s xml:id="echoid-s1107" xml:space="preserve">Singulæ particulæ aqueæ ad exiguam a vitro diſtantiam ab hoc attrahuntur,
              <lb/>
              <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">73.</note>
            id eſt, per lineas rectas tendunt ad ſingulas vitri particulas, quarum diſtantia
              <lb/>
            non ſuperat illam ad quam vitrum & </s>
            <s xml:id="echoid-s1108" xml:space="preserve">aqua in ſe mutuo agere poſſunt. </s>
            <s xml:id="echoid-s1109" xml:space="preserve">Sit
              <lb/>
              <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 5.</note>
            vitri ſuperficies AB; </s>
            <s xml:id="echoid-s1110" xml:space="preserve">particula C; </s>
            <s xml:id="echoid-s1111" xml:space="preserve">hæc ad vitrum tendit per lineam CD, ad
              <lb/>
            ſuperficiem perpendicularem; </s>
            <s xml:id="echoid-s1112" xml:space="preserve">tendit etiam ad punctum e, ſed eodem tem-
              <lb/>
            pore æquali vi tendit ad omnia puncta in ſuperficie æqualiter cum e à D di-
              <lb/>
            ſtantia, id eſt in cir cumferentia circuli poſita, cujus diameter eſt e f: </s>
            <s xml:id="echoid-s1113" xml:space="preserve">propter
              <lb/>
            harum omnium virium æqualitatem non poterit punctum magis ad punctum u-
              <lb/>
            num ferri, quam ad aliud; </s>
            <s xml:id="echoid-s1114" xml:space="preserve">ideo, omnibus viribus ſimul agentibus, par-
              <lb/>
            ticula etiam trahitur per CD. </s>
            <s xml:id="echoid-s1115" xml:space="preserve">Similem demonſtrationem aliis particulis vitri
              <lb/>
            in aquæ particulam agentibus applicando conſtabit, hanc ad vitrum tendere per
              <lb/>
              <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">74.</note>
            lineam ad ſuperficiem bujus perpendicularem.</s>
            <s xml:id="echoid-s1116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1117" xml:space="preserve">Detur ſuper plano vitreo AB gutta G. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">Particulæ ſingulæ parum a vitro
              <lb/>
              <note position="right" xlink:label="note-0049-04" xlink:href="note-0049-04a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 6.</note>
            diſtantes ad hoc directe tendunt, particulaſque cum quibus cohærent ſecum
              <lb/>
            trahunt, unde in gutta oritur motus ſimilis illi, qui in gutta daretur, ſi plano
              <lb/>
            CD ad AB parallelo hoc verſus premeretur; </s>
            <s xml:id="echoid-s1119" xml:space="preserve">qua preſſione gutta ſeſe expan-
              <lb/>
            deret quaqua verſum, & </s>
            <s xml:id="echoid-s1120" xml:space="preserve">expanſio hæc eſt effectus attractionis.
              <lb/>
            </s>
            <s xml:id="echoid-s1121" xml:space="preserve">
              <note position="right" xlink:label="note-0049-05" xlink:href="note-0049-05a" xml:space="preserve">75.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1122" xml:space="preserve">Sit AB aquæ ſuperficies; </s>
            <s xml:id="echoid-s1123" xml:space="preserve">huic pro parte immergatur perpendiculariter
              <lb/>
              <note position="right" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">76.</note>
            vitreum planum FD, cujus craſſitiem hic repræſentamus. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">Aqua a plano at
              <lb/>
              <note position="right" xlink:label="note-0049-07" xlink:href="note-0049-07a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 7.</note>
            trahitur, quo premitur juxta directionem BD , & </s>
            <s xml:id="echoid-s1125" xml:space="preserve">conatur quaqua
              <note symbol="*" position="right" xlink:label="note-0049-08" xlink:href="note-0049-08a" xml:space="preserve">74.</note>
            ſuper plano ſeſe expandere ; </s>
            <s xml:id="echoid-s1126" xml:space="preserve">quo motu non poſſunt agitari niſi particulæ
              <note symbol="*" position="right" xlink:label="note-0049-09" xlink:href="note-0049-09a" xml:space="preserve">75.</note>
            D, motibus contrariis infra ſuperficiem ſeſe mutuo deſtruentibus; </s>
            <s xml:id="echoid-s1127" xml:space="preserve">elevabitur
              <lb/>
            ideo aqua, & </s>
            <s xml:id="echoid-s1128" xml:space="preserve">aſcendentem ſequetur illa, quæ cum ipſa cohæret, ſuſtinebi-
              <lb/>
            turque ita aqua a vitro, ut pondus aquæ elevatæ valeat vim qua elevatur.</s>
            <s xml:id="echoid-s1129" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1130" xml:space="preserve">Sit altitudo hæc, quam juſto majorem repræſentamus, DC; </s>
            <s xml:id="echoid-s1131" xml:space="preserve">ſuſtinetur autem
              <lb/>
            aqua in CDG ſolâ vi qua particulæ in C ſurſum pelluntur: </s>
            <s xml:id="echoid-s1132" xml:space="preserve">nam ubi aqua
              <lb/>
            quieſcit, vires, quibus aqua inter C & </s>
            <s xml:id="echoid-s1133" xml:space="preserve">D ſeſe quaqua verſum expandere cona-
              <lb/>
            tur , ſeſe mutuo deſtruunt: </s>
            <s xml:id="echoid-s1134" xml:space="preserve">particula ex. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">in e æqualiter ſurſum & </s>
            <s xml:id="echoid-s1137" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0049-10" xlink:href="note-0049-10a" xml:space="preserve">75.</note>
            ſum pellitur. </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Vis ergo quæ ſuſtinet aquam, proportionem ſequitur latitudinis
              <lb/>
              <note position="right" xlink:label="note-0049-11" xlink:href="note-0049-11a" xml:space="preserve">77.</note>
            ſuperficiei juxta quam aqua adſcendit, menſuratæ, ad altitudinem ad quam aqua
              <lb/>
            pertingit, in linea ad ſuperficiem ipſius aquæ parallela: </s>
            <s xml:id="echoid-s1139" xml:space="preserve">quam eandem rationem
              <lb/>
            ſequitur pondus aquæ elevatæ.</s>
            <s xml:id="echoid-s1140" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div135" type="section" level="1" n="51">
          <head xml:id="echoid-head91" style="it" xml:space="preserve">De Tubis Capillaribus.</head>
          <p>
            <s xml:id="echoid-s1141" xml:space="preserve">Aquam in tubos vitreos minores ſponte adſcendere debere, ex explicatis
              <lb/>
            facile deducitur. </s>
            <s xml:id="echoid-s1142" xml:space="preserve">Quantitas autem aquæ, quæ ſuſtinetur, ſequitur rationem o-
              <lb/>
              <note position="right" xlink:label="note-0049-12" xlink:href="note-0049-12a" xml:space="preserve">78.</note>
            ræ aquæ elevatæ ; </s>
            <s xml:id="echoid-s1143" xml:space="preserve">& </s>
            <s xml:id="echoid-s1144" xml:space="preserve">orahæc, ſiagatur detubis cylindricis, perpendiculariter
              <note symbol="*" position="right" xlink:label="note-0049-13" xlink:href="note-0049-13a" xml:space="preserve">77.</note>
            merſis ad inſtar diametri creſcit aut minuitur.</s>
            <s xml:id="echoid-s1145" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1146" xml:space="preserve">Sint duo tubi quorum diametri dicantur D, d; </s>
            <s xml:id="echoid-s1147" xml:space="preserve">altitudines aquæ A, a;
              <lb/>
            </s>
            <s xml:id="echoid-s1148" xml:space="preserve">quantitates aquæ ergo erunt inter ſe ut D
              <emph style="super">q</emph>
            x A ad d
              <emph style="super">q</emph>
            x a ; </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ideo D
              <emph style="super">q</emph>
            x A, d
              <emph style="super">q</emph>
            x
              <note symbol="*" position="right" xlink:label="note-0049-14" xlink:href="note-0049-14a" xml:space="preserve">2. II. 14.
                <lb/>
              El. XII.</note>
            :</s>
            <s xml:id="echoid-s1150" xml:space="preserve">: D, d; </s>
            <s xml:id="echoid-s1151" xml:space="preserve">dividendo antecedentia per D
              <emph style="super">q</emph>
            , & </s>
            <s xml:id="echoid-s1152" xml:space="preserve">conſequentia per dq
              <note symbol="*" position="right" xlink:label="note-0049-15" xlink:href="note-0049-15a" xml:space="preserve">78.</note>
            A, a :</s>
            <s xml:id="echoid-s1153" xml:space="preserve">: {1/D}, {1/d}, id eſt altitudines ſunt inverſe ut diametri.
              <lb/>
            </s>
            <s xml:id="echoid-s1154" xml:space="preserve">
              <note position="right" xlink:label="note-0049-16" xlink:href="note-0049-16a" xml:space="preserve">79.</note>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div138" type="section" level="1" n="52">
          <head xml:id="echoid-head92" style="it" xml:space="preserve">De aſcènſu aquæ inter plana, de quo in n. 58.</head>
          <p>
            <s xml:id="echoid-s1155" xml:space="preserve">Sint AC, BC, lineæ repræſentantes planorum ſectionem horizontalem a
              <lb/>
              <note position="right" xlink:label="note-0049-17" xlink:href="note-0049-17a" xml:space="preserve">80.</note>
            ſuperficie aquæ; </s>
            <s xml:id="echoid-s1156" xml:space="preserve">ponamus ſpatium, angulo ACB contentum, dividi lineis
              <lb/>
              <note position="right" xlink:label="note-0049-18" xlink:href="note-0049-18a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 7.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum