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

Table of figures

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[111] Fig. 2.G B R F
[112] Fig. 3.A E C F B
[113] Fig. 4.A C E D F B
[114] Fig. 6.A B C G D L
[115] Fig. 5.H A O M R L N
[116] Pag. 166.TAB.XXV.Fig. 1.A O C G D L N
[117] Fig. 2.A B C G D L N
[118] Fig. 3.O C D A K B N E F C D L M
[119] Fig. 4.O A C D F E K B N C L D M
[120] Fig. 5.E A G F H K B D C
[121] Pag. 170.TAB. XXVI.Fig. 1.Ω O Ω A Z R F R N E N R G S V P Φ Δ V B D K C
[122] Fig. 2.L O A V P Φ Δ V B E C S H D
[123] Fig. 3.F G E G P A P K K L B D B S
[Figure 124]
[Figure 125]
[126] Pag. 188.TAB.XXVII.Fig. 1.O V VA M N D N B O E CE A G B D C F
[127] Fig. 2.S Z G F H Y
[128] Fig. 3.D A D M T C
[129] Fig. 4.A E N D C
[130] Fig. 5.K D B G A F E H
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
[138] Fig. 2.M B A E D L N H F O I G
[139] Fig. 4.O P M I B G Q N L R H A F D
[140] Fig. 5.B A D L N H I
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        <div xml:id="echoid-div327" type="section" level="1" n="118">
          <p>
            <s xml:id="echoid-s3628" xml:space="preserve">
              <pb o="161" file="0231" n="254" rhead="HOROLOG. OSCILLATOR."/>
            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>
        </div>
        <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-
              <lb/>
            dicularis à centro in latus, cum duodecima parte quadrati
              <lb/>
            lateris.</s>
            <s xml:id="echoid-s3636" xml:space="preserve"/>
          </p>
        </div>
        <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>
            <s xml:id="echoid-s3640" xml:space="preserve">
              <lb/>
            longitudine A B, invenire locum duorum ponderum æqua-
              <lb/>
            lium C, D, æqualiter ab A & </s>
            <s xml:id="echoid-s3641" xml:space="preserve">à perpendiculari A B diſtan-
              <lb/>
            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.
                <lb/>
              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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