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

Table of Notes

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            non conſiderantur neque magnitudo neque figura, quaſi ſin-
              <lb/>
            gula in unicum punctum reducta forent; </s>
            <s xml:id="echoid-s4767" xml:space="preserve">ſi ſeparatim ſuſ-
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            penſa ex eodem puncto D, & </s>
            <s xml:id="echoid-s4768" xml:space="preserve">elevata ad idem planum Ho-
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            rizontale D A B, dimittantur usque ad F & </s>
            <s xml:id="echoid-s4769" xml:space="preserve">G, gravitates
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            eorum, ex ratione Mechanica, quæ cum experimentis, & </s>
            <s xml:id="echoid-s4770" xml:space="preserve">prin-
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            cipiis Phyſices congruit, augebuntur in tali ratione, vel quod
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            idem eſt, acquirent velocitates tales, ut harum quadrata ſint
              <lb/>
            inter ſe ut altitudines A H & </s>
            <s xml:id="echoid-s4771" xml:space="preserve">B I. </s>
            <s xml:id="echoid-s4772" xml:space="preserve">unde illa pondera per-
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            pendiculariter deſcendunt ad Horizontem.</s>
            <s xml:id="echoid-s4773" xml:space="preserve"/>
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            <s xml:id="echoid-s4774" xml:space="preserve">Quod ſi dein pondera hæc duo, lineâ aut virgâ inflexi-
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            li A B, quam pondere expertem ponimus, conjungamus,
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            & </s>
            <s xml:id="echoid-s4775" xml:space="preserve">ex eodem puncto D, ad memoratas diſtantias D A & </s>
            <s xml:id="echoid-s4776" xml:space="preserve">D B,
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            ſuſpenſa, dimittamus ad F & </s>
            <s xml:id="echoid-s4777" xml:space="preserve">G ab eâdem, quâ ante, alti-
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            tudine. </s>
            <s xml:id="echoid-s4778" xml:space="preserve">Pendulum ex illis compoſitum, acquiret tantum
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            velocitatis quantum ſumma duorum Pendulorum ſimplicium,
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            quoniam commune gravitatis centrum E idem, quod antea,
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            manebit, & </s>
            <s xml:id="echoid-s4779" xml:space="preserve">ponderum non mutatur ſitus reſpectu centri Telluris;
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            </s>
            <s xml:id="echoid-s4780" xml:space="preserve">ſed partes, in quas tota illa velocitas ſe diſtribuet ponderibus
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            A & </s>
            <s xml:id="echoid-s4781" xml:space="preserve">B, erunt inter ſe ut arcus A F, B G, vel ut radii D F, D G; </s>
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            quoniam in hoc caſu ratio inter motus ponderum pendebit
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            ab eorum ſitu reſpectu puncti ſuſpenſionis D, quod eſt mo-
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            tuum centrum. </s>
            <s xml:id="echoid-s4783" xml:space="preserve">Triangula autem H A F & </s>
            <s xml:id="echoid-s4784" xml:space="preserve">I B G, ut & </s>
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            triangula A F D, B G D cum ſint ſimilia, latera eorum
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            A H & </s>
            <s xml:id="echoid-s4786" xml:space="preserve">B I, A F & </s>
            <s xml:id="echoid-s4787" xml:space="preserve">B G, D F & </s>
            <s xml:id="echoid-s4788" xml:space="preserve">D G ſunt proportio-
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            nalia, id eſt datur eadem ratio inter altitudines, unde pon-
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            dera A & </s>
            <s xml:id="echoid-s4789" xml:space="preserve">B deſcendunt, & </s>
            <s xml:id="echoid-s4790" xml:space="preserve">inter velocitates quas acquirunt
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            deſcendendo; </s>
            <s xml:id="echoid-s4791" xml:space="preserve">ſed altitudines ſunt eædem ac in priori ſup-
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            poſitione; </s>
            <s xml:id="echoid-s4792" xml:space="preserve">ergo velocitates ſunt diverſæ, quoniam illæ altitu-
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            dines, quæ ſunt proportionales velocitatibus ponderum ſimul
              <lb/>
            appenſorum, non ſunt proportionales niſi quadratis veloci-
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            tatum, quando ſunt ſeparata.</s>
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            <s xml:id="echoid-s4794" xml:space="preserve">Porro ponamus pendulum compoſitum in vibratione ſuâ
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            occurrere plano duro D F G, quo rumpatur, ita ut a ſe in-
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            vicem pondera ſolvantur, erunt hæc reflexa juxta tangentes ar-
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            cuum F A & </s>
            <s xml:id="echoid-s4795" xml:space="preserve">G B ad altitudines, quæ inter ſe erunt ut quadrata
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            velocitatum, quas cadendo acquiſivere, id eſt, ut </s>
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