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

Table of contents

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[41.] Experimentum 2.
Page: 44 (14)
[42.] Experimentum 3.
Page: 45 (15)
[43.] Experimentum 4.
Page: 45 (15)
[44.] Experimentum 5.
Page: 45 (15)
[45.] Experimentum 6.
Page: 46 (16)
[46.] Experimentum 7.
Page: 46 (16)
[47.] Experimentum 8.
Page: 46 (16)
[48.] Experimentum 9. 10. 11. 12. 13.
Page: 47 (17)
[49.] Definitio 5.
Page: 48 (18)
[50.] SCHOLIUM De efſectu attractionis vitri in aquam.
Page: 49 (19)
[51.] De Tubis Capillaribus.
Page: 49 (19)
[52.] De aſcènſu aquæ inter plana, de quo in n. 58.
Page: 49 (19)
[53.] De motu guttæ in n. 59,
Page: 50 (20)
[54.] CAPUT VI. De Motu in genere, ubi de Loco & Tempore.
Page: 51 (21)
[55.] Definitio 1.
Page: 51 (21)
[56.] Definitio 2.
Page: 51 (21)
[57.] Definitio 3.
Page: 51 (21)
[58.] Definitio 4.
Page: 52 (22)
[59.] Definitio 5.
Page: 52 (22)
[60.] Definitio 6.
Page: 52 (22)
[61.] LIBRI I. PARS II. De Actionibus Potentiarum. CAPUT VII. De Actionibus Potentiarum comparandis.
Page: 52 (22)
[62.] Definitio.
Page: 56 (23)
[63.] CAPUT VIII. Generalia circa Gravitatem. Phænomenon i.
Page: 57 (24)
[64.] Definitio. 1.
Page: 57 (24)
[65.] Definitio 2.
Page: 57 (24)
[66.] Phænomenon 2.
Page: 58 (25)
[67.] Phænomenon 3.
Page: 58 (25)
[68.] Machina
Page: 58 (25)
[69.] Experimentum
Page: 60 (27)
[70.] CAPUT IX.
Page: 61 (28)
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            <s xml:id="echoid-s1156" xml:space="preserve">
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            ut de, fg, hi, l m, &</s>
            <s xml:id="echoid-s1157" xml:space="preserve">c parum admodum, ſed æqualiter, a ſe mutuo di-
              <lb/>
            ſtantibus; </s>
            <s xml:id="echoid-s1158" xml:space="preserve">manifeſtum eſt æquales aquæ quantitates in ſpatiis dfeg, himl,
              <lb/>
            elevari ; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">ibique ideo dari priſmata æqualia, quorum altitudines ſunt
              <note symbol="*" position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve">77.</note>
            ut baſes ; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">hæ autem, quia pro parallelogrammis haberi poſſunt, & </s>
            <s xml:id="echoid-s1161" xml:space="preserve">propter
              <note symbol="*" position="left" xlink:label="note-0050-02" xlink:href="note-0050-02a" xml:space="preserve">34. El.
                <emph style="sc">XI</emph>
              .</note>
            titudines df, hl, æquales, ſunt inter ſe ut de ad hi ; </s>
            <s xml:id="echoid-s1162" xml:space="preserve">quæ ſunt ut d C ad h C.</s>
            <s xml:id="echoid-s1163" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">1. El.
                <emph style="sc">VI</emph>
              .</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1164" xml:space="preserve">Deducimus ex his curvam efg eſſe Hyperbolam cujus Aſymptoti ſunt lineæ
              <lb/>
              <note position="left" xlink:label="note-0050-04" xlink:href="note-0050-04a" xml:space="preserve">81.</note>
            AB, in qua vitra ſeſe mutuo tangunt, & </s>
            <s xml:id="echoid-s1165" xml:space="preserve">BC, ſuperficies aquæ ; </s>
            <s xml:id="echoid-s1166" xml:space="preserve">
              <note position="left" xlink:label="note-0050-05" xlink:href="note-0050-05a" xml:space="preserve">TAB. II.
                <lb/>
              fig. 7.</note>
            angulum rectum ABC Hyperbola eſt æquilatera ; </s>
            <s xml:id="echoid-s1167" xml:space="preserve">examinavimus
              <note symbol="*" position="left" xlink:label="note-0050-06" xlink:href="note-0050-06a" xml:space="preserve">La Hire
                <lb/>
                <emph style="sc">S. C</emph>
              . l.
                <emph style="sc">IV</emph>
              .
                <lb/>
              p. 2.</note>
            caſum in quo linea, in qua vitra ſeſe mutuo tangunt, ad ſuperficiem aquæ
              <lb/>
            perpendicularis eſt.</s>
            <s xml:id="echoid-s1168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1169" xml:space="preserve">Facile etiam confertur altitudo in tubo cum altitudine inter plana.</s>
            <s xml:id="echoid-s1170" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">ibid. l.
            <emph style="sc">V</emph>
          .
            <lb/>
          p. 13.</note>
          <p>
            <s xml:id="echoid-s1171" xml:space="preserve">Sit tubi cylindrici ſectio M, cujus ſemidiameter æqualis eſt diſtantiæ e d inter
              <lb/>
            plana. </s>
            <s xml:id="echoid-s1172" xml:space="preserve">Clarum eſt vim, quæ ſuſtinet priſma aqueum cujus baſis eſt def pro-
              <lb/>
              <note position="left" xlink:label="note-0050-08" xlink:href="note-0050-08a" xml:space="preserve">82.</note>
            portionem ſequi lineæ df; </s>
            <s xml:id="echoid-s1173" xml:space="preserve">ambabus enim df & </s>
            <s xml:id="echoid-s1174" xml:space="preserve">eg proportionalis eſt vis quæ pa-
              <lb/>
              <note position="left" xlink:label="note-0050-09" xlink:href="note-0050-09a" xml:space="preserve">TAB I.
                <lb/>
              fig. 7.</note>
            rallelopipedum, cujus baſis eſt dfeg, ſuſtinet .</s>
            <s xml:id="echoid-s1175" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0050-10" xlink:href="note-0050-10a" xml:space="preserve">77.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1176" xml:space="preserve">In tubo vis quæ ſuſtinet priſma, cujus baſis eſt nop, proportionalis eſt ipſi np;
              <lb/>
            </s>
            <s xml:id="echoid-s1177" xml:space="preserve">quia tota circumferentia proportionalis eſt illi quæ integrum aqueum cylin-
              <lb/>
            drum vitro contentum ſuſtinet. </s>
            <s xml:id="echoid-s1178" xml:space="preserve">Si np & </s>
            <s xml:id="echoid-s1179" xml:space="preserve">df fuerint æquales; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">vires quæ pri-
              <lb/>
            ſmata ſuſtinent æquales ſunt; </s>
            <s xml:id="echoid-s1181" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s1182" xml:space="preserve">ipſa priſmata æqualia; </s>
            <s xml:id="echoid-s1183" xml:space="preserve">ſunt etiam
              <lb/>
            in hoc caſu baſes nop, def, æquales, quare priſmatum altitudines non
              <lb/>
            difterunt, & </s>
            <s xml:id="echoid-s1184" xml:space="preserve">aqua in tubum & </s>
            <s xml:id="echoid-s1185" xml:space="preserve">inter plana ad eandem adſcendit altitudinem.</s>
            <s xml:id="echoid-s1186" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1187" xml:space="preserve">Variarimultis modis poteſt experimentum de adſcenſu aquæ inter plana.</s>
            <s xml:id="echoid-s1188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1189" xml:space="preserve">Nimium longum & </s>
            <s xml:id="echoid-s1190" xml:space="preserve">ſatis inutile foret, omnia quæ huc ſpectant perpendere;
              <lb/>
            </s>
            <s xml:id="echoid-s1191" xml:space="preserve">ſatis eſt caſum præcipuum examinaſſe; </s>
            <s xml:id="echoid-s1192" xml:space="preserve">Circa duos alios in quibus angulus
              <lb/>
              <note position="left" xlink:label="note-0050-11" xlink:href="note-0050-11a" xml:space="preserve">83.</note>
            ABC, quem linea, in qua vitra junguntur, cum ſuperficie aquæ efficit, eſt
              <lb/>
              <note position="left" xlink:label="note-0050-12" xlink:href="note-0050-12a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 8. 9.</note>
            acutus aut obtuſus, manentibus planis vitreis ad aquæ ſuperficiem perpendi-
              <lb/>
            cularibus, notabo, aquam etiam terminari Hyperbolica linea, cujus aſym-
              <lb/>
            ptos una eſt aquæ ſuperficies, altera habetur erigendo perpendicularem BF
              <lb/>
            ad CB, in puncto B, aſvmptos quæſita erit BE, quæ dividit bifariam FD,
              <lb/>
            perpendicularem in puncto quocunque ad BF, & </s>
            <s xml:id="echoid-s1193" xml:space="preserve">terminatam linea BA.</s>
            <s xml:id="echoid-s1194" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1195" xml:space="preserve">Si DF per punctum D Hyperbolæ tranſect, BF erit ſemidiameter con-
              <lb/>
            jugata cum ſemidiametro BD.</s>
            <s xml:id="echoid-s1196" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1197" xml:space="preserve">In Fig. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">ultra F Hyperbola non continuatur; </s>
            <s xml:id="echoid-s1200" xml:space="preserve">aqua tamen ulterius adſcen-
              <lb/>
            dit, ſed aliâ terminatur Curvâ.</s>
            <s xml:id="echoid-s1201" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1202" xml:space="preserve">In Fig. </s>
            <s xml:id="echoid-s1203" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">licet Hyperbola vitrorum latera juncta ſecet in D non ibi ad-
              <lb/>
            ſcenſus aquæ terminatur, ſed ad certam, & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">quidem pro diverſo, quem in-
              <lb/>
            ter ſe vitra continent, angulo, diverſam ab AB diſtantiam, ab Hyperbola
              <lb/>
            deflectitur curva, adſcenſuſque juxta BA continuatur. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">Ubi enim exigua
              <lb/>
              <note position="left" xlink:label="note-0050-13" xlink:href="note-0050-13a" xml:space="preserve">84.</note>
            admodum eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo juvant, quo au-
              <lb/>
            getur aquæ adſcenſus. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">Simile augmentum actionis in n ſequenti memoratur;
              <lb/>
            </s>
            <s xml:id="echoid-s1208" xml:space="preserve">in luminis attractione a corporibus etiam locum habet, ut notamus in nume-
              <lb/>
            ro ultimo cap. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">3.</s>
            <s xml:id="echoid-s1212" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div144" type="section" level="1" n="53">
          <head xml:id="echoid-head93" style="it" xml:space="preserve">De motu guttæ in n. 59,</head>
          <p>
            <s xml:id="echoid-s1213" xml:space="preserve">Concipiamus plana, inter quæ gutta movetur, ſecari plano ad plana, & </s>
            <s xml:id="echoid-s1214" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0050-14" xlink:href="note-0050-14a" xml:space="preserve">85.</note>
            lineam in qua junguntur perpendicularem: </s>
            <s xml:id="echoid-s1215" xml:space="preserve">repræſentatur ſectio hæc; </s>
            <s xml:id="echoid-s1216" xml:space="preserve">ſed, cum
              <lb/>
              <note position="left" xlink:label="note-0050-15" xlink:href="note-0050-15a" xml:space="preserve">TAB. I.
                <lb/>
              fig. 10.</note>
            motus ab inclinatione planorum ad ſe invicem pendeat, hanc juſto majorem
              <lb/>
            repræſentamus, ut & </s>
            <s xml:id="echoid-s1217" xml:space="preserve">diſtantiam inter vitra, & </s>
            <s xml:id="echoid-s1218" xml:space="preserve">diſtantiam ad quam vitrum in
              <lb/>
            oleum agit.</s>
            <s xml:id="echoid-s1219" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1220" xml:space="preserve">Sint plana AB, CD; </s>
            <s xml:id="echoid-s1221" xml:space="preserve">gutta e eff; </s>
            <s xml:id="echoid-s1222" xml:space="preserve">gh diſtantia ad quam vitrum oleum tra-
              <lb/>
            hit: </s>
            <s xml:id="echoid-s1223" xml:space="preserve">omne ergo oleum inter iehf ad planum trahitur, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">conatur ſeſe </s>
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