Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of contents

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[101.] PROPOSITIO XI.
Page: 218 (137)
[102.] PROPOSITIO XII.
Page: 218 (137)
[103.] PROPOSITIO XIII.
Page: 221 (140)
[104.] PROPOSITIO XIV.
Page: 223 (142)
[105.] PROPOSITIO XV.
Page: 228 (144)
[106.] PROPOSITIO XVI.
Page: 232 (148)
[107.] PROPOSITIO XVII.
Page: 233 (149)
[108.] PROPOSITIO XVIII.
Page: 234 (150)
[109.] PROPOSITIO XIX.
Page: 237 (153)
[110.] PROPOSITIO XX.
Page: 238 (154)
[111.] PROPOSITIO XXI.
Page: 238 (154)
[112.] Centrum oſcillationis Circuli.
Page: 247 (157)
[113.] Centrum oſcillationis Rectanguli.
Page: 247 (157)
[114.] Centrum oſcillationis Trianguli iſoſcelis.
Page: 248 (158)
[115.] Centrum oſcillationis Parabolæ.
Page: 248 (158)
[116.] Centrum oſcillationis Sectoris circuli.
Page: 248 (158)
[117.] Centrum oſcillationis Circuli, aliter quam ſupra.
Page: 250 (160)
[118.] Centrum oſcillationis Peripheriæ circuli.
Page: 250 (160)
[119.] Centrum oſcillationis Polygonorum ordinatorum.
Page: 254 (161)
[120.] Loci plani & ſolidi uſus in hac Theoria.
Page: 254 (161)
[121.] PROPOSITIO XXII.
Page: 261 (165)
[122.] Centrum oſcillationis in Pyramide.
Page: 262 (166)
[123.] Centrum oſcillationis Coni.
Page: 266 (167)
[124.] Centrum oſcillationis Sphæræ.
Page: 266 (167)
[125.] Centrum oſcillationis Cylindri.
Page: 267 (168)
[126.] Centrum oſcillationis Conoidis Parabolici.
Page: 267 (168)
[127.] Centrum oſcillationis Conoidis Hyperbolici.
Page: 268 (169)
[128.] Centrum oſcillationis dimidii Coni.
Page: 268 (169)
[129.] PROPOSITIO XXIII.
Page: 274 (172)
[130.] PROPOSITIO XXIV.
Page: 279 (177)
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            <s xml:id="echoid-s1354" xml:space="preserve">Sint plana inclinata A C, A D quorum eadem elevatio
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                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
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            A B. </s>
            <s xml:id="echoid-s1355" xml:space="preserve">dico tempus deſcenſus per planum A C ad tempus
              <lb/>
              <note position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 5.</note>
            deſcenſus per A D eſſe ut longitudo A C ad A D. </s>
            <s xml:id="echoid-s1356" xml:space="preserve">Eſt enim
              <lb/>
            tempus per A C æquale tempori motus æquabilis per ean-
              <lb/>
            dem A C, cum celeritate dimidia ejus quæ acquiritur caſu
              <lb/>
            per A C . </s>
            <s xml:id="echoid-s1357" xml:space="preserve">Similiter tempus per A D eſt æquale
              <note symbol="*" position="left" xlink:label="note-0096-03" xlink:href="note-0096-03a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            motus æquabilis per ipſam A D, cum dimidia celeritate ejus
              <lb/>
            quæ acquiritur caſu per A D. </s>
            <s xml:id="echoid-s1358" xml:space="preserve">Eſt autem hæc dimidia celeri-
              <lb/>
            tas illi dimidiæ celerirati æqualis , ideoque dictum
              <note symbol="*" position="left" xlink:label="note-0096-04" xlink:href="note-0096-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            motus æquabilis per A C, ad tempus motus æquabilis per A D,
              <lb/>
            erit ut A C ad A D. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1360" xml:space="preserve">tempora ſingulis iſtis æqualia,
              <lb/>
            nimirum tempus deſcenſus per A C, ad tempus deſcenſus
              <lb/>
            per A D, eandem rationem habebunt, nempe quam A C
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            ad A D. </s>
            <s xml:id="echoid-s1361" xml:space="preserve">quod erat demonſtrandum.</s>
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            <s xml:id="echoid-s1363" xml:space="preserve">Eodem modo oſtendetur & </s>
            <s xml:id="echoid-s1364" xml:space="preserve">tempus deſcenſus per A C, ad
              <lb/>
            tempus caſus per A B perpendicularem, eſſe ut A C ad
              <lb/>
            A B longitudine.</s>
            <s xml:id="echoid-s1365" xml:space="preserve"/>
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          <head xml:id="echoid-head53" xml:space="preserve">PROPOSITIO VIII.</head>
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            <s xml:id="echoid-s1366" xml:space="preserve">SI ex altitudine eadem deſcendat mobile conti-
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            nuato motu per quotlibet ac quælibet plana con-
              <lb/>
            tigua, utcunque inclinata; </s>
            <s xml:id="echoid-s1367" xml:space="preserve">ſemper eandem in fine
              <lb/>
            velocitatem acquiret, quæ nimirum æqualis erit ei
              <lb/>
            quam acquireret cadendo perpendiculariter ex pa-
              <lb/>
            ri altitudine.</s>
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          <p>
            <s xml:id="echoid-s1369" xml:space="preserve">Sint plana contigua A B, B C, C D, quorum terminus
              <lb/>
              <note position="left" xlink:label="note-0096-05" xlink:href="note-0096-05a" xml:space="preserve">TAB VI.
                <lb/>
              Fig. 1.</note>
            A, ſupra horizontalem lineam D F per infimum terminum
              <lb/>
            D ductam, altitudinem habeat quanta eſt perpendicularis E F.
              <lb/>
            </s>
            <s xml:id="echoid-s1370" xml:space="preserve">deſcendatque mobile per plana illa ab A uſque in D. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Di-
              <lb/>
            co in D eam velocitatem habiturum quam, ex E cadens, ha-
              <lb/>
            beret in F.</s>
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            <s xml:id="echoid-s1373" xml:space="preserve">Producta enim C B occurrat rectæ A E in G. </s>
            <s xml:id="echoid-s1374" xml:space="preserve">Itemque
              <lb/>
            D C producta occurrat eidem A E in E. </s>
            <s xml:id="echoid-s1375" xml:space="preserve">Quoniam </s>
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