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

Table of handwritten notes

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        <div xml:id="echoid-div184" type="section" level="1" n="143">
          <pb o="167" file="0181" n="181" rhead="SECTIO NONA."/>
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        <div xml:id="echoid-div186" type="section" level="1" n="144">
          <head xml:id="echoid-head191" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s4847" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4848" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">Non deſunt qui putent machinam excogitari poſſe, cujus ope
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            minimo labore maxima aquæ quantitas ad quamcunque altitudinem elevari
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            poſſit, animumque excrucient, in anquirendis rotis, vectibus, ponderibus
              <lb/>
            appendendis: </s>
            <s xml:id="echoid-s4850" xml:space="preserve">ſed operam perdunt, neque audiendi ſunt hujuſmodi promiſſo-
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            res, cum magni quid ſibi videntur inveniſſe: </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Optima machina eſt, ſi ſolum
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            ejus effectum reſpiciamus, quæ minimas patitur frictiones, nullosque gene-
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            rat motus inutiles, de quo utroque evitando præcepta trademus infrà,</s>
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        <div xml:id="echoid-div187" type="section" level="1" n="145">
          <head xml:id="echoid-head192" xml:space="preserve">Regula 3.</head>
          <p>
            <s xml:id="echoid-s4852" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4853" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4854" xml:space="preserve">In antliis, quales Figuris 45. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">& </s>
            <s xml:id="echoid-s4856" xml:space="preserve">47. </s>
            <s xml:id="echoid-s4857" xml:space="preserve">repræſentantur, in quibus ſu-
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            perficies aquæ interna A B in eadem propemodum altitudine eſt cum foramine
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            F, ſunt potentiæ abſolutæ pro iiſdem temporibus in triplicata ratione velocita-
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            tum aquarum exilientium.</s>
            <s xml:id="echoid-s4858" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div188" type="section" level="1" n="146">
          <head xml:id="echoid-head193" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4859" xml:space="preserve">Sunt enim potentiæ moventes in duplicata ratione velocitatum, quibus
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            aquæ per foramen F erumpunt & </s>
            <s xml:id="echoid-s4860" xml:space="preserve">velocitates potentiarum moventium ſequuntur
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            ipſam rationem velocitatum aquarum exilientium: </s>
            <s xml:id="echoid-s4861" xml:space="preserve">Sed pro iiſdem temporibus
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            ſunt potentiæ abſolutæ ut potentiæ moventes multiplicatæ per ſuas velocitates,
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            ergo patet propoſitio.</s>
            <s xml:id="echoid-s4862" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div189" type="section" level="1" n="147">
          <head xml:id="echoid-head194" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s4863" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4864" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4865" xml:space="preserve">Sequitur ex iſta regula, ſi animus ſit aquam per foramen F ad
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            altitudinem F G elevare, magnam potentiæ abſolutæ partem ſine fructu perdi,
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            cum aquæ majori impetu erumpunt, quam quæ altitudini F G reſpondeat;
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            </s>
            <s xml:id="echoid-s4866" xml:space="preserve">fac enim aquas dupla velocitate expelli, requiretur potentia abſoluta octupla,
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            neque tamen ratione finis propoſiti effectus plus quam duplus eſt cenſendus,
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            quia nempe eodem tempore dupla aquarum quantitas elevatur: </s>
            <s xml:id="echoid-s4867" xml:space="preserve">potuiſſetque
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            iſte effectus obtineri potentia abſoluta ſubquadrupla exprimendo aquas ſimplici
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            velocitate per foramen duplum; </s>
            <s xml:id="echoid-s4868" xml:space="preserve">Hoc igitur nomine tres quartæ partes iſtius
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            potentiæ inutiliter impenſæ dicendæ ſunt. </s>
            <s xml:id="echoid-s4869" xml:space="preserve">Originem hujus detrimenti indicavi
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            §. </s>
            <s xml:id="echoid-s4870" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4871" xml:space="preserve">eaque conſiſtit in motu qui generatur ad propoſitum finem inutili: </s>
            <s xml:id="echoid-s4872" xml:space="preserve"/>
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