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

Table of Notes

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            aëris ααββ = D; </s>
            <s xml:id="echoid-s6501" xml:space="preserve">denſitas aëris ββγγ = D - d D, erit (per §.</s>
            <s xml:id="echoid-s6502" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6503" xml:space="preserve">α, β)
              <lb/>
            ſinus anguli contactus in b diviſus per ſinum totum, ſeu ipſe angulus conta-
              <lb/>
            ctus proportionalis differentiæ denſitatum d D multiplicatæ per rationem ſi-
              <lb/>
            nuum angulorum incidentiæ & </s>
            <s xml:id="echoid-s6504" xml:space="preserve">refractionis, id eſt, multiplicatæ per {be/eo}. </s>
            <s xml:id="echoid-s6505" xml:space="preserve">Si
              <lb/>
            vero ducatur B D perpendicularis ad FA productam, perſpicuum eſt, vix
              <lb/>
            differre {be/eo} & </s>
            <s xml:id="echoid-s6506" xml:space="preserve">{BD/Do}, ideo quod radius fere ſit rectus ſicque poſſit trian-
              <lb/>
            gulum B D o pro rectilineo haberi & </s>
            <s xml:id="echoid-s6507" xml:space="preserve">ſimili cum triangulo beo. </s>
            <s xml:id="echoid-s6508" xml:space="preserve">Igitur erit
              <lb/>
            angulus quæſitus F A H proportionalis ſ{BD/Do} X dD.</s>
            <s xml:id="echoid-s6509" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6510" xml:space="preserve">(δ) Hiſce veſtigiis inſiſtendo ponendoque eſſe ubiquel
              <unsure/>
            denſitatem
              <lb/>
            D = {22000/22000 + x}G, ubix exprimit lineam na numero pedum Pariſinorum
              <lb/>
            & </s>
            <s xml:id="echoid-s6511" xml:space="preserve">G denotat denſitatem aëris in loco obſervationis, inveni quod ſequitur.
              <lb/>
            </s>
            <s xml:id="echoid-s6512" xml:space="preserve">Sit ſinus altitudinis aſtri apparentis = f, coſinus = F, radius terræ = r
              <lb/>
            numero pedum Pariſinorum exprimendus: </s>
            <s xml:id="echoid-s6513" xml:space="preserve">indicetur numerus 22000 per a: </s>
            <s xml:id="echoid-s6514" xml:space="preserve">
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            ponatur porro ſinus totus = 1, angulus refractionis differentialis pro radio ex
              <lb/>
            aëre naturali in vacuum ſub angulo ſemirecto incidentis = g: </s>
            <s xml:id="echoid-s6515" xml:space="preserve">Denique bre-
              <lb/>
            vitatis ergo fiat 2r - 2a = α; </s>
            <s xml:id="echoid-s6516" xml:space="preserve">- FFrr + 2ar - aa = β: </s>
            <s xml:id="echoid-s6517" xml:space="preserve">& </s>
            <s xml:id="echoid-s6518" xml:space="preserve">erit β aut nu-
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            merus affirmativus aut negativus; </s>
            <s xml:id="echoid-s6519" xml:space="preserve">affirmativus erit, ſi altitudo apparens ſide-
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            ris parva fuerit & </s>
            <s xml:id="echoid-s6520" xml:space="preserve">quidem infra 2
              <emph style="super">0</emph>
            , 44
              <emph style="super">1</emph>
            : </s>
            <s xml:id="echoid-s6521" xml:space="preserve">ſecus erit negativus: </s>
            <s xml:id="echoid-s6522" xml:space="preserve">In priori ca-
              <lb/>
            ſu obtinebitur angulus quæſitus F A H hunc in modum: </s>
            <s xml:id="echoid-s6523" xml:space="preserve">Fiat nempe ſemicir-
              <lb/>
            culus M L F (Fig. </s>
            <s xml:id="echoid-s6524" xml:space="preserve">61.) </s>
            <s xml:id="echoid-s6525" xml:space="preserve">cujus radius A M = 1: </s>
            <s xml:id="echoid-s6526" xml:space="preserve">ſumatur A C = {α/2fr}; </s>
            <s xml:id="echoid-s6527" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">Fig. 61.</note>
            AB = {2β - αa/2afr}, ducanturque C D, B T ad M C perpendiculares & </s>
            <s xml:id="echoid-s6528" xml:space="preserve">erit an-
              <lb/>
            gulus F A H = {- fFrr/2β}g + {far/β}g + {farα x DT/2β√β}g.
              <lb/>
            </s>
            <s xml:id="echoid-s6529" xml:space="preserve">In caſu, quo β eſt negativus, erit idem angulus
              <lb/>
            F A H = {-far/β}g + {fFrr/β}g + {farα/2β√β}g x log. </s>
            <s xml:id="echoid-s6530" xml:space="preserve">{(α - 2√β) x (Fr - a + √β)/(α + 2√β) x (Fr - a - √β)}.</s>
            <s xml:id="echoid-s6531" xml:space="preserve"/>
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            <s xml:id="echoid-s6532" xml:space="preserve">(ε) Secundum iſtas hypotheſes ponendo pro radio terræ 19600000.
              <lb/>
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            <s xml:id="echoid-s6533" xml:space="preserve">poterit pro omni altitudine ſideris apparentis ejus determinari refractio aſtro-
              <lb/>
            nomica, ſi bene experimento inventus fuerit valor anguli g: </s>
            <s xml:id="echoid-s6534" xml:space="preserve">quia vero difficile
              <lb/>
            admodum eſt hunc valorem cum ſufficiente accuratione definire, </s>
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