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

Table of contents

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[91.] PROPOSITIO III.
Page: 200 (125)
[92.] PROPOSITIO IV.
Page: 201 (126)
[93.] PROPOSITIO V.
Page: 202 (127)
[94.] PROPOSITIO VI.
Page: 208 (130)
[95.] DEFINITIO XIV.
Page: 210 (132)
[96.] DEFINITIO XV.
Page: 210 (132)
[97.] PROPOSITIO VII.
Page: 210 (132)
[98.] PROPOSITIO VIII.
Page: 211 (133)
[99.] PROPOSITIO IX.
Page: 213 (135)
[100.] PROPOSITIO X.
Page: 214 (136)
[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)
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            rum quæ ex paraboloidibus naſcuntur conſtructionem, du-
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUMCUR.</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            cendæ ſunt lineæ D B Z, quæ ad datum punctum B ſecent
              <lb/>
            curvas A B, ſive ipſarum tangentes B H, ad angulos re-
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            ctos; </s>
            <s xml:id="echoid-s2701" xml:space="preserve">dicemus in univerſum quomodo hæ tangentes inve-
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            niantur. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">In æquatione itaque, quæ cujusque curvæ naturam
              <lb/>
            explicat, quales æquationes duabus tabellis præcedentibus
              <lb/>
            exponuntur, conſiderare oportet quæ ſint exponentes pote-
              <lb/>
            ſtatum x & </s>
            <s xml:id="echoid-s2703" xml:space="preserve">y, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">facere ut, ſicut exponens poteſtatis x ad
              <lb/>
            exponentem poteſtatis y, ita ſit S K ad K H. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Juncta enim
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            H B curvam in B continget. </s>
            <s xml:id="echoid-s2706" xml:space="preserve">Velut in tertia hyperboloide,
              <lb/>
            cujus æquatio eſt x y
              <emph style="super">2</emph>
            = a
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s2707" xml:space="preserve">quia exponens poteſtatis x eſt
              <lb/>
            1, poteſtatis autem y exponens 2; </s>
            <s xml:id="echoid-s2708" xml:space="preserve">oportet eſſe ut 1 ad 2 ita
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            S K ad K H. </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Horum autem demonſtrationem noverunt
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            analyticæ artis periti, qui jam pridem omnes has lineas con-
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            templari cœperunt; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">& </s>
            <s xml:id="echoid-s2711" xml:space="preserve">non ſolum paraboloidum iſtarum,
              <lb/>
            ſed & </s>
            <s xml:id="echoid-s2712" xml:space="preserve">ſpatiorum quorundam infinitorum, inter hyperboloi-
              <lb/>
            des & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">aſymptotos interjectorum, plana ſolidaque dimenſi
              <lb/>
            ſunt. </s>
            <s xml:id="echoid-s2714" xml:space="preserve">Quod quidem & </s>
            <s xml:id="echoid-s2715" xml:space="preserve">nos, facili atque univerſali metho-
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            do, expedire poſſemus, ex ſola tangentium proprietate ſum-
              <lb/>
            pta demonſtratione. </s>
            <s xml:id="echoid-s2716" xml:space="preserve">Sed illa non ſunt hujus loci.</s>
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        <div xml:id="echoid-div212" type="section" level="1" n="72">
          <head xml:id="echoid-head96" xml:space="preserve">HOROLOGII OSCILLATORII
            <lb/>
          PARS QUARTA.</head>
          <head xml:id="echoid-head97" style="it" xml:space="preserve">De centro Oſcillationis.</head>
          <p>
            <s xml:id="echoid-s2718" xml:space="preserve">CEntrorum Oſcillationis, ſeu Agitationis, inveſtigatio-
              <lb/>
            nem olim mihi, fere adhuc puero, aliiſque multis, do-
              <lb/>
            ctiſſimus Merſennus propoſuit, celebre admodum inter illius
              <lb/>
            temporis Geometras problema, prout ex litteris ejus ad me
              <lb/>
            datis colligo, nec non ex Carteſii haud pridem editis, qui-
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            bus ad Merſennianas ſuper his rebus reſponſum continetur.
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            <s xml:id="echoid-s2719" xml:space="preserve">Poſtulabat autem centra illa ut invenirem in circuli </s>
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