Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Table of handwritten notes

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            eſt in eruendis legibus motuum corporum elaſticorum ex percuſſione, nec
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            non in ſtabiliendo centro oſcillationis penduli compoſiti; </s>
            <s xml:id="echoid-s320" xml:space="preserve">protulit autem axio-
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            ma hoc ſuum talibus verbis: </s>
            <s xml:id="echoid-s321" xml:space="preserve">Si pondera quotlibet vi gravitatis ſuæ moveri incipiant
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            utcunque, ſmgulaque rurſ{us} ad quietem ſponte reducantur, centrum gravitatis ex ipſis
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            c
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            ompoſitæ ad priſtinam altitudinem rediturum eſſe, ubi per vocem utcunque intelligit,
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            ſive ſe percutiant inter deſcenſum, ſive premant, aliove modo in ſe invicem agant corpora.
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            </s>
            <s xml:id="echoid-s322" xml:space="preserve">Ex iſto axiomate ſtatim ſequitur principium conſervationis virium vivarum,
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            quod ipfe etiam Hugenius demonſtravit, & </s>
            <s xml:id="echoid-s323" xml:space="preserve">quo aſſumitur: </s>
            <s xml:id="echoid-s324" xml:space="preserve">Si pondera quotli-
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            bet vi gravitatis ſuæ moveri incipiant utcunque, ſingulorum velocitates ubique tales fore,
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            ut producta, ex earum quadratis in ſu{as} maſſ{as} collecta, ſint proportionalia altitudini
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            verticali, per quam centrum gravitatis ex corporib{us} compoſitæ deſcendit, multiplicatæ per
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            maſſas omnium. </s>
            <s xml:id="echoid-s325" xml:space="preserve">Mirum eſt, quantam habeat hæc hypotheſis in Philoſophia me-
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            chanica utilitatem, quod, ſi quis alius, ſane Pater meus recte animadvertit,
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            qui id ſparſim, imprimis autem in Diſſertatione Pariſiis edita de legib{us} motuum & </s>
            <s xml:id="echoid-s326" xml:space="preserve">
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            in Tom. </s>
            <s xml:id="echoid-s327" xml:space="preserve">2. </s>
            <s xml:id="echoid-s328" xml:space="preserve">Comment. </s>
            <s xml:id="echoid-s329" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s330" xml:space="preserve">Imp. </s>
            <s xml:id="echoid-s331" xml:space="preserve">Sc. </s>
            <s xml:id="echoid-s332" xml:space="preserve">Petrop. </s>
            <s xml:id="echoid-s333" xml:space="preserve">oſtendit , idemque eſt, quod pro in-
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            veſtigandis Legibus motuum, ex propria gravitate ortorum, in fluidis adhibui; </s>
            <s xml:id="echoid-s334" xml:space="preserve">
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            poſui enim velocitates particularum conſtanter tales eſſe, ut, ſingulis vertica-
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            liter ſurſum motis ad ſtatum quietis usque, centrum earum gravitatis com-
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            mune ad priſtinam altitudinem aſcendat: </s>
            <s xml:id="echoid-s335" xml:space="preserve">malui autem ob rationem ſupra di-
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            ctam hanc hypotheſin verbis Hugenianis quam Paternis accommodare, eam-
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            que nomine æqualitatis inter deſcenſum actualem aſcenſumque potentialem inſignire,
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            quam altero conſervationis virium vivarum, quod etiamnum aliqui, præſertim in
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            Anglia, neſcio quo fato, faſtidiunt. </s>
            <s xml:id="echoid-s336" xml:space="preserve">Mihi quidem in tota doctrina Leibni-
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            tiana de viribus vivis nihil eſſe videtur, de quo non omnes, ſuo tamen qui-
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            vis loquendi modo, conveniant, quod, ni fallor, clare oſtendi in Comm. </s>
            <s xml:id="echoid-s337" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s338" xml:space="preserve">
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            Sc. </s>
            <s xml:id="echoid-s339" xml:space="preserve">Imp. </s>
            <s xml:id="echoid-s340" xml:space="preserve">Petrop. </s>
            <s xml:id="echoid-s341" xml:space="preserve">Tom. </s>
            <s xml:id="echoid-s342" xml:space="preserve">I. </s>
            <s xml:id="echoid-s343" xml:space="preserve">p. </s>
            <s xml:id="echoid-s344" xml:space="preserve">131. </s>
            <s xml:id="echoid-s345" xml:space="preserve">& </s>
            <s xml:id="echoid-s346" xml:space="preserve">ſeq. </s>
            <s xml:id="echoid-s347" xml:space="preserve">quem locum hic allegare volui, ne qui@
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            Lectorum ſe verbis offendi patiatur, ſciatque nihil a me accipi, quod in Me-
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            chanica receptum non ſit ab omnibus, & </s>
            <s xml:id="echoid-s348" xml:space="preserve">quod non neceſſario nexu cohæreat
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            cum eo, quod jam Galilæus poſuit, cum ſtatueret, incrementa velocitatum
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            proportionem ſequi compoſitam ex preſſionibus & </s>
            <s xml:id="echoid-s349" xml:space="preserve">momentis temporum.</s>
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            <s xml:id="echoid-s351" xml:space="preserve">§@ 20. </s>
            <s xml:id="echoid-s352" xml:space="preserve">De cætero quamvis principium prædictum univerſale ſit, non
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            tamen eſt ſine circumſpectione adhibendum, quia ſæpe contingit, ut motus
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            tranſeat in materiam alienam. </s>
            <s xml:id="echoid-s353" xml:space="preserve">Ita verbi gratia poſitio illius valet pro regu-
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            lis motuum ex percuſſione eruendis, ſi modo corpora ſint perfecte elaſtica;</s>
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