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

Table of figures

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[101] Fig. 5.D D D E F E B A C H K
[102] Pag. 160.Fig. 1.F D D @ N A L C H K M
[103] Fig. 2.D D D F B A L C H K
[104] Fig. 3.C A B
[105] Fig. 4.B A K C E D G
[106] G D E C A K B
[107] G D K C A B
[108] Fig. 5.K B K A C E D F
[109] Fig. 6.Q B Q O N A C E D R P F
[110] Pag. 164.Fig. 1.G B O N C R P F
[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
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        <div xml:id="echoid-div244" type="section" level="1" n="93">
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            <s xml:id="echoid-s2955" xml:space="preserve">
              <pb o="130" file="0190" n="208" rhead="CHRISTIANI HUGENII"/>
            titudinibus iſtis in ſua pondera, erit ſumma productorum
              <lb/>
              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
              </note>
            major quam {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2956" xml:space="preserve">quæ proinde major quoque
              <lb/>
            probatur quam {a d y + b d y + c d y/x}. </s>
            <s xml:id="echoid-s2957" xml:space="preserve">Nam quia poſita eſt longitudo
              <lb/>
            x æqualis {a e e + b f f + g g/a d + b d + c d}; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">erit a d x + b d x + c d x æquale
              <lb/>
            a e e + b f f + c g g. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">Et ductis omnibus in y, & </s>
            <s xml:id="echoid-s2960" xml:space="preserve">dividen-
              <lb/>
            do per x x, erit {a d y + b d y + c d y/x} æquale {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Unde
              <lb/>
            quod dictum eſt conſequitur. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">Eſt autem ſumma iſta produ-
              <lb/>
            ctorum æqualis ei, quod fit ducendo altitudinem, ad quam
              <lb/>
            aſcendit centrum gravitatis commune ponderum A, B, C, in
              <lb/>
            ſummam ipſorum ponderum, a + b + c; </s>
            <s xml:id="echoid-s2963" xml:space="preserve">ſi nempe ſingu-
              <lb/>
            la, uti dictum, ſeorſim quousque poſſunt moveantur. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">Quan-
              <lb/>
            titas vero {a d y + b d y + c d y/x} producitur ex deſcenſu centri gravi-
              <lb/>
            tatis eorundem ponderum, (qui deſcenſus eſt R Q, ſive {d y/x},
              <lb/>
            ut ſupra inventum fuit,) in eandem quoque ponderum ſum-
              <lb/>
            mam a + b + c. </s>
            <s xml:id="echoid-s2965" xml:space="preserve">Ergo quum prius productum altero hoc
              <lb/>
            majus oſtenſum fuerit, ſequitur aſcenſum centri gravitatis
              <lb/>
            ponderum A, B, C, ſi, relicto pendulo ubi pervenere in
              <lb/>
            T, V, X, ſingula celeritates acquiſitas ſurſum convertant,
              <lb/>
            majorem fore ejusdem centri gravitatis deſcenſu, dum ex
              <lb/>
            A, B, C, moventur in T, V, X. </s>
            <s xml:id="echoid-s2966" xml:space="preserve">quod eſt abſurdum, cum
              <lb/>
            dictus aſcenſus deſcenſui æqualis eſſe debeat, per anteceden-
              <lb/>
            tem.</s>
            <s xml:id="echoid-s2967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">Eodem modo, ſi dicatur celeritatem puncti L, ubi per-
              <lb/>
            venerit in P, minorem eſſe celeritate ponderis G quum in O
              <lb/>
            pervenerit; </s>
            <s xml:id="echoid-s2969" xml:space="preserve">oſtendemus aſcenſum poſſibilem centri gravitatis
              <lb/>
            ponderum A, B, C, minorem eſſe quam deſcenſum, quod
              <lb/>
            eidem propoſitioni antecedenti repugnat. </s>
            <s xml:id="echoid-s2970" xml:space="preserve">Quare relinquitur
              <lb/>
            ut eadem ſit celeritas puncti L, ad P tranſlati, quæ ponde-
              <lb/>
            ris G in O. </s>
            <s xml:id="echoid-s2971" xml:space="preserve">Unde, ut ſuperius dictum, ſequitur pendulum
              <lb/>
            ſimplex F G compoſito ex A, B, C, iſochronum eſſe.</s>
            <s xml:id="echoid-s2972" xml:space="preserve"/>
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        <div xml:id="echoid-div250" type="section" level="1" n="94">
          <head xml:id="echoid-head120" xml:space="preserve">PROPOSITIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s2973" xml:space="preserve">DAto pendulo ex quotcunque ponderibus æqua-
              <lb/>
            libus compoſito; </s>
            <s xml:id="echoid-s2974" xml:space="preserve">ſi ſumma quadratorum </s>
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