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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            numerum particularum ſolidi A B C, æquale quadratis di-
              <lb/>
              <note position="right" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS.</emph>
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            ſtantiarum à plano A D . </s>
            <s xml:id="echoid-s3793" xml:space="preserve">Apparet autem, fieri ſpatium
              <note symbol="*" position="right" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">Prop. 15.
                <lb/>
              huj.</note>
            æquale {1/20} quadrati B C.</s>
            <s xml:id="echoid-s3794" xml:space="preserve"/>
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            <s xml:id="echoid-s3795" xml:space="preserve">Itaque, totum ſpatium applicandum, æquatur hic {3/80} qua-
              <lb/>
            drati A D, cum {1/20} quadrati B C. </s>
            <s xml:id="echoid-s3796" xml:space="preserve">Unde, ſi ſuſpenſio, ut
              <lb/>
            hic, poſita fuerit in A, vertice pyramidis, ideoque diſtan-
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            tia, ad quam applicatio facienda, A E æqualis {3/4} A D; </s>
            <s xml:id="echoid-s3797" xml:space="preserve">fiet
              <lb/>
            hinc E S, intervallum quo centrum agitationis inferius eſt
              <lb/>
            centro gravitatis, æquale {1/20} A D, atque inſuper {1/15} tertiæ
              <lb/>
            proportionalis duabus A D, B C. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">ſive tota A S æqualis {4/5}
              <lb/>
            A D, præter dictam {1/15} tertiæ proportionialis.</s>
            <s xml:id="echoid-s3799" xml:space="preserve"/>
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        <div xml:id="echoid-div348" type="section" level="1" n="123">
          <head xml:id="echoid-head149" style="it" xml:space="preserve">Centrum oſcillationis Coni.</head>
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            <s xml:id="echoid-s3800" xml:space="preserve">Quod ſi A B C conus fuerit, omnia eodem modo @e habe-
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            bunt, niſi quod ſpatium Z hic fit æquale rectangulo Δ Ρ Φ
              <note symbol="*" position="right" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">Prop. 15.
                <lb/>
              huj.</note>
            hoc eſt {3/2@} quadrati P V vel B D, ſive {3/80} quadrati B C.
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            </s>
            <s xml:id="echoid-s3801" xml:space="preserve">Quare, totum ſpatium applicandum, in cono erit {3/80} qua-
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            drati A D, una cum {3/80} quadrati B C. </s>
            <s xml:id="echoid-s3802" xml:space="preserve">Ac proinde, poſita
              <lb/>
            ſuſpenſione ex vertice A, fiet E S, qua centrum agitationis
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            inferius eſt centro gravitatis, æqualis {1/20} A D, & </s>
            <s xml:id="echoid-s3803" xml:space="preserve">{1/20} tertiæ
              <lb/>
            proportionalis duabus A D, B C. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">ſive tota A S æqualis {4/5}
              <lb/>
            A D, una cum {1/5} tertiæ proportionalis duabus A D, D B. </s>
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            Atque hinc manifeſtum eſt, ſi A D, D B æquales ſint, hoc
              <lb/>
            eſt, ſi conus A B C ſit rectangulus, fieri A S æqualem axi
              <lb/>
            A D.</s>
            <s xml:id="echoid-s3806" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3807" xml:space="preserve">Sequitur quoque porro, ex propoſitione 20, conum hunc
              <lb/>
            rectangulum, ſi ex D centro baſeos ſuſpendatur, iſochro-
              <lb/>
            num fore ſibi ipſi ex vertice A ſuſpenſo, quemadmodum & </s>
            <s xml:id="echoid-s3808" xml:space="preserve">
              <lb/>
            de triangulo rectangulo ſupra oſtenſum fuit.</s>
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        <div xml:id="echoid-div350" type="section" level="1" n="124">
          <head xml:id="echoid-head150" style="it" xml:space="preserve">Centrum oſcillationis Sphæræ.</head>
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            <s xml:id="echoid-s3810" xml:space="preserve">Si A B C ſit ſphæra, erit figura plana proportionalis, à
              <lb/>
              <note position="right" xlink:label="note-0241-04" xlink:href="note-0241-04a" xml:space="preserve">TAB. XXVI.
                <lb/>
              Fig. 2.</note>
            latere adponenda, O V H, ex parabolis compoſita, qua-
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            rum baſis communis O H, æqualis ſphæræ diametro A D.
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            </s>
            <s xml:id="echoid-s3811" xml:space="preserve">Sectâ vero ſphærâ planis per centrum E, quorum B C </s>
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