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

Table of contents

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[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)
[131.] PROPOSITIO XXV.
Page: 280 (178)
[132.] PROPOSITIO XXVI.
Page: 284 (182)
[133.] HOROLOGII OSCILLATORII PARS QUINTA.
Page: 287 (185)
[134.] Horologii ſecundi conſtructio.
Page: 288 (186)
[135.] DE VI CENTRIFUGA ex motu circulari, Theoremata. I.
Page: 290 (188)
[136.] II.
Page: 290 (188)
[137.] III.
Page: 290 (188)
[138.] IV.
Page: 294 (189)
[139.] V.
Page: 294 (189)
[140.] VI.
Page: 294 (189)
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            <s xml:id="echoid-s3628" xml:space="preserve">
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            earum particularum ad centrum B. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">Quare quadratum B R
              <lb/>
              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            erit hic ſpatium applicandum . </s>
            <s xml:id="echoid-s3630" xml:space="preserve">Patetque hinc, ſi
              <note symbol="*" position="right" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">Prop. 18.
                <lb/>
              huj.</note>
            ſit ex G, puncto circumferentiæ, penduli iſochroni longitu-
              <lb/>
            dinem æquari diametro G F.</s>
            <s xml:id="echoid-s3631" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div329" type="section" level="1" n="119">
          <head xml:id="echoid-head145" style="it" xml:space="preserve">Centrum oſcillationis Polygonorum ordinatorum.</head>
          <p>
            <s xml:id="echoid-s3632" xml:space="preserve">Haud abſimiliter & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">polygono cuivis ordinato, ut A B C,
              <lb/>
              <note position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">TAB XXIV.
                <lb/>
              Fig. 3.</note>
            pendulum iſochronum invenitur. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">Fit enim, ſpatium appli-
              <lb/>
            candum, æquale ſemiſſi quadrati perpendicularis ex centro
              <lb/>
            in latus polygoni, una cum vigefima quarta parte quadrati
              <lb/>
            lateris. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">At, ſi perimetro polygoni pendulum iſochronum
              <lb/>
            quæratur, fit ſpatium applicandum æquale quadrato perpen-
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            dicularis à centro in latus, cum duodecima parte quadrati
              <lb/>
            lateris.</s>
            <s xml:id="echoid-s3636" xml:space="preserve"/>
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        <div xml:id="echoid-div331" type="section" level="1" n="120">
          <head xml:id="echoid-head146" style="it" xml:space="preserve">Loci plani & ſolidi uſus in hac Theoria.</head>
          <p>
            <s xml:id="echoid-s3637" xml:space="preserve">Eſt præterea & </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Locorum contemplatio in his non injucun-
              <lb/>
              <note position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">TAB.XXIV.
                <lb/>
              Fig. 4.</note>
            da. </s>
            <s xml:id="echoid-s3639" xml:space="preserve">Ut ſi propoſitum ſit, dato puncto ſuſpenſionis A, & </s>
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            longitudine A B, invenire locum duorum ponderum æqua-
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            lium C, D, æqualiter ab A & </s>
            <s xml:id="echoid-s3641" xml:space="preserve">à perpendiculari A B diſtan-
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            tium, quæ agitata circa axem in A, perpendicularem plano
              <lb/>
            per A C D, iſochrona ſint pendulo ſimplici longitudinis
              <lb/>
            A B.</s>
            <s xml:id="echoid-s3642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3643" xml:space="preserve">Ponatur A B = a, ductâque C D, quæ ſecet A B ad
              <lb/>
            angulos rectos in E, ſit A E indeterminata = x: </s>
            <s xml:id="echoid-s3644" xml:space="preserve">E C vel
              <lb/>
            E D = y. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">Ergo quadratum A C = x x + y y. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">Hoc vero
              <lb/>
            multiplex ſecundum numerum particularum ponderum C, D,
              <lb/>
            quæ hic minima intelliguntur, æquatur quadratis diſtantia-
              <lb/>
            rum earundem particularum ab axe ſuſpenſionis A. </s>
            <s xml:id="echoid-s3647" xml:space="preserve">Ergo
              <lb/>
            quadratum A C, ſive x x + y y, applicatum ad diſtantiam
              <lb/>
            A E, quæ nempe eſt inter axem ſuſpenſionis & </s>
            <s xml:id="echoid-s3648" xml:space="preserve">centrum gra-
              <lb/>
            vitatis ponderum C, D, efficiet {xx + yy/x}, longitudinem pen-
              <lb/>
            duli iſochroni ; </s>
            <s xml:id="echoid-s3649" xml:space="preserve">quam propterea oportet æqualem eſſe A
              <note symbol="*" position="right" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">Prop. 17.
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              huj.</note>
            ſive a. </s>
            <s xml:id="echoid-s3650" xml:space="preserve">Itaque {x x + y y/x} = a. </s>
            <s xml:id="echoid-s3651" xml:space="preserve">Et y y = a x - x x. </s>
            <s xml:id="echoid-s3652" xml:space="preserve">Unde patet,
              <lb/>
            locum punctorum C & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">D, eſſe circumferentiam circuli, </s>
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