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

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              <pb o="188" file="0202" n="202" rhead="HYDRODYNAMICÆ"/>
            qui ſi vocetur X, ejuſque coſinus x, ſit o, 60000X + o, 80000 (1 + x)
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            = or = 1, 83800: </s>
            <s xml:id="echoid-s5426" xml:space="preserve">pro iſta conditione invenitur arcus a g h M s proxime
              <lb/>
            175 {1/2} grad. </s>
            <s xml:id="echoid-s5427" xml:space="preserve">incidente puncto s in plagam a g M: </s>
            <s xml:id="echoid-s5428" xml:space="preserve">Et cum arcus a g fuerit 48
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            ,
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            35
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            , erit tandem arcus g h M s 126
              <emph style="super">0</emph>
            , 55
              <emph style="super">1</emph>
            , qui proinde erit ad circumfe-
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            rentiam circuli præterpropter ut 10 ad 29: </s>
            <s xml:id="echoid-s5429" xml:space="preserve">ſimiliſque ratio intercedit inter ar-
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            cum helicis o p q integramque helicem.</s>
            <s xml:id="echoid-s5430" xml:space="preserve"/>
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            <s xml:id="echoid-s5431" xml:space="preserve">Conſequens inde eſt, ſingulis revolutionibus cochlea à Vitruvio de-
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            ſcripta proxime ejici {10/29} illius quantitatis, quam helix integra & </s>
            <s xml:id="echoid-s5432" xml:space="preserve">plena con-
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            tinet, ſeu paullulum ultra trientem.</s>
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        <div xml:id="echoid-div224" type="section" level="1" n="177">
          <head xml:id="echoid-head225" xml:space="preserve">Scholium 3.</head>
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            <s xml:id="echoid-s5434" xml:space="preserve">(IX) Notandum tamen eſt, quæcunque ſit aquæ quantitas, quæ qua-
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            libet cochleæ revolutione canalem inferius ingreditur, ſuperiuſque ex eodem
              <lb/>
            eſſluit, nullum nec detrimentum nec lucrum propterea cadere in potentiam ab-
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            ſolutam ſi nulla habeatur frictionum ration, quia potentia movens cæteris paribus
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            illi quantitati proportionalis eſt. </s>
            <s xml:id="echoid-s5435" xml:space="preserve">At vero quia frictiones ſemper obſtant, eædem-
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            que fere ſunt ob pondus machinæ proprium, ſive major ſive minor quantitas
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            aquæ hauriatur, opera utique danda eſt, ut iſta quantitas cæteris paribus fiat
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            maxima: </s>
            <s xml:id="echoid-s5436" xml:space="preserve">Hâc de re nunc agam paullo diſertius.</s>
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        <div xml:id="echoid-div225" type="section" level="1" n="178">
          <head xml:id="echoid-head226" xml:space="preserve">Scholium 4.</head>
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            <s xml:id="echoid-s5438" xml:space="preserve">(X) Jam innui ſuprà, creſcere rationem arcus g h M s ad circumferen-
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            tiam circuli decreſcentibus angulis s a o & </s>
            <s xml:id="echoid-s5439" xml:space="preserve">N M G: </s>
            <s xml:id="echoid-s5440" xml:space="preserve">uterque igitur minimus eſſet
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            conſtruendus, niſi alia obſtarent incommoda, præſertim ratione anguli N M G.
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            </s>
            <s xml:id="echoid-s5441" xml:space="preserve">Quod ad angulum s a o attinet, poteſt is fere ad lubitum diminui, neque aliud
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            inde incommodum reſultat, niſi quod latera canalis circumflectendi nimis ad
              <lb/>
            ſe invicem accedere poſſunt: </s>
            <s xml:id="echoid-s5442" xml:space="preserve">E contrario à diminutione iſtius anguli aliud ob-
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            tinetur compendium, nempe quod tunc eo verticalius poſſit erigi machina ip-
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            ſaque aqua eo altius elevari, etenim angulus a M H ſemper major eſſe debet
              <lb/>
            angulo s a o: </s>
            <s xml:id="echoid-s5443" xml:space="preserve">à verticaliori autem cochleæ poſitione ſimul obtinetur, ut mino-
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            ri incommodo ſit machinæ proprium pondus eaque facilius ſuſtineatur.</s>
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            <s xml:id="echoid-s5445" xml:space="preserve">Hæc ita perpendens crediderim fere ſufficere poſſe angulum 5 graduum,
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            quem faciat canalis cum baſe nuclei. </s>
            <s xml:id="echoid-s5446" xml:space="preserve">Cardanus quoque minorem iſtum </s>
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