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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            <emph style="sc">De centro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
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        <div xml:id="echoid-div360" type="section" level="1" n="129">
          <head xml:id="echoid-head155" xml:space="preserve">PROPOSITIO XXIII.</head>
          <p style="it">
            <s xml:id="echoid-s3903" xml:space="preserve">HOrologiorum motum temperare, addito ponde-
              <lb/>
            re exiguo ſecundario, quod ſuper virga pen-
              <lb/>
            duli, certa ratione diviſa, ſurſum deorſumque
              <lb/>
            moveri poſſit.</s>
            <s xml:id="echoid-s3904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3905" xml:space="preserve">Ut hoc expediamus, primo penduli ipſius, ex virga gra-
              <lb/>
              <note position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">TAB. XXVII.
                <lb/>
              Fig. 3.</note>
            vitate prædita, & </s>
            <s xml:id="echoid-s3906" xml:space="preserve">appenſo parte ima pondere, compoſiti,
              <lb/>
            centrum oſcillationis inveniendum eſt.</s>
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            <s xml:id="echoid-s3908" xml:space="preserve">Sit virga, cum appenſo pondere, A C, cujus longitudo
              <lb/>
            dicatur a. </s>
            <s xml:id="echoid-s3909" xml:space="preserve">Intelligantur autem, tum virga ipſa, tum pondus
              <lb/>
            appenſum C, in particulas minimas æquales diviſa, earum-
              <lb/>
            que particularum virga habeat numerum b, pondus vero C
              <lb/>
            numerum c, ponendo nempe b ad c, ſicut gravitas virgæ ad
              <lb/>
            gravitatem appenſi ponderis. </s>
            <s xml:id="echoid-s3910" xml:space="preserve">Longitudo igitur penduli ſim-
              <lb/>
            plicis, dato iſochroni, habebitur, ſi ſumma quadratorum à
              <lb/>
            diſtantiis particularum omnium à puncto ſuſpenſionis A, di-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0248-03" xlink:href="note-0248-03a" xml:space="preserve">Prop. 6.
                <lb/>
              huj. in fine.</note>
            vidatur per ſummam earundem diſtantiarum . </s>
            <s xml:id="echoid-s3911" xml:space="preserve">Secetur A C bifariam in M; </s>
            <s xml:id="echoid-s3912" xml:space="preserve">tum vero in T, ut A T ſit dupla T C. </s>
            <s xml:id="echoid-s3913" xml:space="preserve">Quia
              <lb/>
            ergo M eſt centrum gravitatis lineæ A C, & </s>
            <s xml:id="echoid-s3914" xml:space="preserve">A T ſubcen-
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            trica cunei ſuper ipſa abſciſſi plano per A D, perpendicu-
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            larem ad A C; </s>
            <s xml:id="echoid-s3915" xml:space="preserve">qui cuneus hîc revera triangulum eſt; </s>
            <s xml:id="echoid-s3916" xml:space="preserve">erit ſum-
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            ma quadratorum, à diſtantiis particularum virgæ à puncto
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            A, æqualis rectangulo A M T, una cum quadrato A M;
              <lb/>
            </s>
            <s xml:id="echoid-s3917" xml:space="preserve">hoc eſt, rectangulo T A M, multiplici ſecundum numerum
              <lb/>
            particularum b; </s>
            <s xml:id="echoid-s3918" xml:space="preserve">hoc eſt, {1/3} a a b; </s>
            <s xml:id="echoid-s3919" xml:space="preserve">quia M A eſt {1/2} a, & </s>
            <s xml:id="echoid-s3920" xml:space="preserve">T A
              <lb/>
            {2/3} a, ac proinde rectangulum T A M = {1/3} a a. </s>
            <s xml:id="echoid-s3921" xml:space="preserve">Summa vero
              <lb/>
            quadratorum, à diſtantiis particularum ponderis C ab eo-
              <lb/>
            dem puncto A, æquabitur quadrato A C, multiplici ſecun-
              <lb/>
            dum numerum particularum ipſius ponderis; </s>
            <s xml:id="echoid-s3922" xml:space="preserve">hoc eſt, a a c. </s>
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            Adeoque ſumma quadratorum omnium, tam à diſtantiis par-
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            ticularum virgæ, quam ponderis C, erit {1/3} a a b + a a c.</s>
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            <s xml:id="echoid-s3925" xml:space="preserve">Porro, diſtantiæ omnes particularum virgæ A C à pun-
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            cto A, æquantur {1/2} b a; </s>
            <s xml:id="echoid-s3926" xml:space="preserve">longitudini ſcilicet virgæ ipſius, </s>
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