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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              <pb o="67" file="0101" n="106" rhead="HOROLOG. OSCILLATOR."/>
            dem ſuperficiem vel aliam ſimilem ſimiliter que po-
              <lb/>
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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>
              .</note>
            ſitam feratur, æqualibus temporibus per idem ſpa-
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            tium deſcendet atque aſcendet.</s>
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          </p>
          <p>
            <s xml:id="echoid-s1420" xml:space="preserve">Velut ſi per ſuperficiem A B deſcendat mobile, atque, ubi
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 4.</note>
            ad B pervenerit, converſo motu ſurſum per eandem A B, vel
              <lb/>
            ei ſimilem & </s>
            <s xml:id="echoid-s1421" xml:space="preserve">reſpectu plani horizontalis ſimiliter poſitam
              <lb/>
            B C, aſcendat, conſtat ex ante demonſtratis, perventurum
              <lb/>
            ad eandem ex qua venit altitudinem. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Cum autem perpetuo,
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            in punctis quorum eadem altitudo, eandem velocitatem ha-
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            beat aſcendendo ac deſcendendo ; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">apparet eandem
              <note symbol="*" position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">Prop.
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              præced.</note>
            bis eadem velocitate ſingulis ſui partibus percurri: </s>
            <s xml:id="echoid-s1424" xml:space="preserve">unde & </s>
            <s xml:id="echoid-s1425" xml:space="preserve">
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            tempora utriusque motus æqualia eſſe neceſſe eſt; </s>
            <s xml:id="echoid-s1426" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
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          <head xml:id="echoid-head57" xml:space="preserve">PROPOSITIO XII.</head>
          <p style="it">
            <s xml:id="echoid-s1428" xml:space="preserve">ESto circulus A B C, diametro A C, cui ad an-
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 5.</note>
            gulos rectos ſit F G; </s>
            <s xml:id="echoid-s1429" xml:space="preserve">huic vero occurrat à ter-
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            mino diametri A educta A F extra circulum, quæ
              <lb/>
            quidem neceſſario ſecabit circumferentiam, puta
              <lb/>
            in B. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Dico arcum B D, lineis G F, A F inter-
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            ceptum, minorem eſſe recta D F.</s>
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            <s xml:id="echoid-s1432" xml:space="preserve">Jungatur enim B C, & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">ducatur ex B puncto tangens cir-
              <lb/>
            cumferentiam recta B E, quæ neceſſario occurret rectæ F G
              <lb/>
            inter F & </s>
            <s xml:id="echoid-s1434" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Eſt igitur angulus B A C in circulo æqualis
              <lb/>
            angulo E B C . </s>
            <s xml:id="echoid-s1436" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">angulus F B E, qui una
              <note symbol="*" position="right" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">Prop. 32.
                <lb/>
              Lib. 3. Eucl.</note>
            E B C conſtituit angulum rectum F B C, erit æqualis B C A.
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            </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Quia autem ſimilia ſunt triangula A B C, A G F, erit & </s>
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            angulus F æqualis angulo A C B. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">Ergo idem angulus F æ-
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            qualis angulo F B E. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">Itaque iſoſceles eſt triangulus F E B,
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            habens crura æqualia F E, E B. </s>
            <s xml:id="echoid-s1442" xml:space="preserve">Addita ergo utrique eo-
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            rum recta E D, fiet F D, æqualis duabus B E, E D. </s>
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            ce vero duas majores eſſe conſtat arcu B D, iisdem </s>
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