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

Table of handwritten notes

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            ſuarum ab axe oſcillationis, & </s>
            <s xml:id="echoid-s2908" xml:space="preserve">ſumma producto-
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              <note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" 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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            rum dividatur per id quod fit ducendo ponderum
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            ſummam, in diſtantiam centri gravitatis commu-
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            nis omnium ab eodem axe oſcillationis; </s>
            <s xml:id="echoid-s2909" xml:space="preserve">orietur lon-
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            gitudo penduli ſimplicis compoſito iſochroni, ſive di-
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            ſtantia inter axem & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">centrum oſcillationis ipſius
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            penduli compoſiti.</s>
            <s xml:id="echoid-s2911" xml:space="preserve"/>
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            <s xml:id="echoid-s2912" xml:space="preserve">Sint pondera pendulum componentia, (quorum nec figura
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              <note position="left" xlink:label="note-0186-02" xlink:href="note-0186-02a" xml:space="preserve">TAB. XIX.
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              Fig. 1. 2.</note>
            nec magnitudo, ſed gravitas tantum conſideretur), A, B, C,
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            ſuſpenſa ab axe, qui per punctum D, ad planum quod conſpi-
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            citur, rectus intelligitur. </s>
            <s xml:id="echoid-s2913" xml:space="preserve">In quo plano ſit quoque eorum cen-
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            trum commune gravitatis E; </s>
            <s xml:id="echoid-s2914" xml:space="preserve">nam pondera in diverſis eſſe ni-
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            hil refert. </s>
            <s xml:id="echoid-s2915" xml:space="preserve">Diſtantia puncti E ab axe, nempe recta E D, vo-
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            cetur d. </s>
            <s xml:id="echoid-s2916" xml:space="preserve">Item ponderis A diſtantia A D, ſit e; </s>
            <s xml:id="echoid-s2917" xml:space="preserve">B D, f;
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            </s>
            <s xml:id="echoid-s2918" xml:space="preserve">C D, g. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">Ducendo itaque ſingula pondera in quadrata ſua-
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            rum diſtantiarum, erit productorum ſumma a e e + b f f
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            + c g g. </s>
            <s xml:id="echoid-s2920" xml:space="preserve">Et rurſus, ducendo ſummam ponderum in diſtan-
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            tiam centri gravitatis omnium, productum æquale erit a d
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            + b d + c d . </s>
            <s xml:id="echoid-s2921" xml:space="preserve">Unde, productum prius per hoc
              <note symbol="*" position="left" xlink:label="note-0186-03" xlink:href="note-0186-03a" xml:space="preserve">Prop. 1.
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              h@.</note>
            do, habebitur {a e e + b f f + c @ @/a d + b d + c a}. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">Cui longitudini ſi æqualis ſta-
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            tuatur longitudo penduli ſimplicis F G, quæ etiam x vo-
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            cabitur; </s>
            <s xml:id="echoid-s2923" xml:space="preserve">dico hoc illi compoſito iſochronum eſſe.</s>
            <s xml:id="echoid-s2924" xml:space="preserve"/>
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            <s xml:id="echoid-s2925" xml:space="preserve">Ponantur enim tum pendulum F G, tum linea centri
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            D E, æqualibus angulis à linea perpendiculi remota, illud
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            ab F H, hæc ab D K, atque inde dimiſſa librari, & </s>
            <s xml:id="echoid-s2926" xml:space="preserve">in
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            recta D E ſumatur D L æqualis F G. </s>
            <s xml:id="echoid-s2927" xml:space="preserve">Itaque pondus G
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            penduli F G, integra oſcillatione arcum G M percurret,
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            quem linea perpendiculi F H medium ſecabit. </s>
            <s xml:id="echoid-s2928" xml:space="preserve">punctum ve-
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            ro L arcum illi ſimilem & </s>
            <s xml:id="echoid-s2929" xml:space="preserve">æqualem L N, quem medium
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            dividet D K. </s>
            <s xml:id="echoid-s2930" xml:space="preserve">Itemque centrum gravitatis E, percurret ſi-
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            milem arcum E I. </s>
            <s xml:id="echoid-s2931" xml:space="preserve">Quod ſi in arcubus G M, N L, ſum-
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            ptis punctis quibuslibet, ſimiliter ipſos dividentibus, ut O
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            & </s>
            <s xml:id="echoid-s2932" xml:space="preserve">P, eadem celeritas eſſe oſtendatur ponderis G in O, & </s>
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            puncti L in P; </s>
            <s xml:id="echoid-s2934" xml:space="preserve">conſtabit inde æqualibus temporibus </s>
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