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

Table of figures

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            ti caſus ſui, vel potius, ſpatia, quæ percurrunt eodem tem-
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            pore, utut parvo; </s>
            <s xml:id="echoid-s5308" xml:space="preserve">hoc ſenſu ſumo 1
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            pro velocitate, quacum
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            omne corpus grave ſive magnum ſive parvum incipit deſcen-
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            dere ſuper planis æqualiter inclinatis; </s>
            <s xml:id="echoid-s5309" xml:space="preserve">nam, ut ſatis notum
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            eſt, illa velocitas eſt æqualis in omnibus corporibus.</s>
            <s xml:id="echoid-s5310" xml:space="preserve"/>
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            <s xml:id="echoid-s5311" xml:space="preserve">Concipio etiam, quantitatem motus corporis initio deſcen-
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            ſus ſui oriri ex maſſâ multiplicatâ per illam primam velocitatem;
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            </s>
            <s xml:id="echoid-s5312" xml:space="preserve">His ſuppoſitis, conſtat, quod corpus A conetur deſcendere
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            cum eâdem celeritate, quâ corpus B; </s>
            <s xml:id="echoid-s5313" xml:space="preserve">quod cum non poſ-
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            ſit, quoniam virgæ junctum eſt in puncto A, cujus veloci-
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            tas tantum eſt 4ta pars velocitatis B, debet accelerare mo-
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            tum corporis B in pendulo compoſito. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">Tota ergo difficultas
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            conſiſtit in rite determinandâ motûs augmentatione; </s>
            <s xml:id="echoid-s5315" xml:space="preserve">quod
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            hoc pacto facio.</s>
            <s xml:id="echoid-s5316" xml:space="preserve"/>
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            <s xml:id="echoid-s5317" xml:space="preserve">Sit x quantitas motus corporis A in pendulo compoſito,
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            reſiduus exceſſus quantitatis ejus motus erit ergo A - x, vis
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            hæc applicata in A exerit actionem in punctum fixum D & </s>
            <s xml:id="echoid-s5318" xml:space="preserve">
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            corpus B, quod conſiderari debet ut immobile ipſius reſpe-
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            ctu (quoniam clarum eſt, corpus B debere cenſeri immobile
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            reſpectu illius exceſſus) & </s>
            <s xml:id="echoid-s5319" xml:space="preserve">conſequenter virga B D debet
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            conſiderari ut vectis cujus extremitates ſuſtinentur in B & </s>
            <s xml:id="echoid-s5320" xml:space="preserve">D.
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            </s>
            <s xml:id="echoid-s5321" xml:space="preserve">habebimus ergo B D, 4. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">ad A D, 1. </s>
            <s xml:id="echoid-s5323" xml:space="preserve">ut A - x ad {1/4} A -{1/4} x portio-
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            nem exceſſus quantitatis motus corporis A, quæ communi-
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            catur corpori B; </s>
            <s xml:id="echoid-s5324" xml:space="preserve">ita ut quantitas motus corporis B in pen-
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            dulo compoſito ſit B + {1/4} A - {1/4} x id eſt {5/4} A - {1/4} x; </s>
            <s xml:id="echoid-s5325" xml:space="preserve">Jam vero
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            propter virgam inflexilem D B velocitas corporis B in pen-
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            dulo compoſito debet neceſſario eſſe quadrupla velocita-
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            tis corporis A, & </s>
            <s xml:id="echoid-s5326" xml:space="preserve">conſequenter etiam quantitas ejus motus,
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            quoniam corpora ſunt æqualia; </s>
            <s xml:id="echoid-s5327" xml:space="preserve">unde ſequitur æqualia eſſe
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            4 x & </s>
            <s xml:id="echoid-s5328" xml:space="preserve">{5/4} A - {1/4} x unde deducitur valor ipſius x, {5/17} A, qui ex-
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            primit quantitatem motus corporis A in pendulo compoſito; </s>
            <s xml:id="echoid-s5329" xml:space="preserve">
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            Jam ſi fiat, ut {5/17}, velocitas corporis A in pendulo compoſi-
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            to, eſt ad 1, velocitatem, omnium corporum gravium in
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            extremitate pendulorum ſimplicium, ita D A, 1; </s>
            <s xml:id="echoid-s5330" xml:space="preserve">eſt ad
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            D G, {17/5
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            }, erit hæc longitudo penduli ſimplicis iſochroni; </s>
            <s xml:id="echoid-s5331" xml:space="preserve">ſi
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            enim ſpatia ſunt inter ſe ut velocitates, tempora æqualia
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            ſunt.</s>
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