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

Table of contents

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[161.] Regula 8.
Page: 190 (176)
[162.] Scholium.
Page: 191 (177)
[163.] Regula 9.
Page: 191 (177)
[164.] Scholium.
Page: 191 (177)
[165.] Scholium Generale.
Page: 192 (178)
[166.] (B) De machinis hydraulicis aquas ſine not abili impetu ex loco humiliori in altiorem tranſportantibus. Regula 10.
Page: 192 (178)
[167.] Demonſtratio.
Page: 193 (179)
[168.] Corollarium.
Page: 193 (179)
[169.] Scholium 1.
Page: 193 (179)
[170.] Scholium 2.
Page: 194 (180)
[171.] Scholium Generale.
Page: 194 (180)
[172.] Commentationes ſpeciales de Cochlea Archimedis.
Page: 197 (183)
[173.] Problema.
Page: 200 (186)
[174.] Solutio.
Page: 200 (186)
[175.] Scholium 1.
Page: 200 (186)
[176.] Scholium 2.
Page: 201 (187)
[177.] Scholium 3.
Page: 202 (188)
[178.] Scholium 4.
Page: 202 (188)
[179.] Problema.
Page: 203 (189)
[180.] Solutio.
Page: 203 (189)
[181.] Scholium 1.
Page: 205 (191)
[182.] Scholium 2.
Page: 205 (191)
[183.] (C) De Machinis, quæ ab impetu fluidi, veluti vi venti moventur.
Page: 207 (193)
[184.] HYDRODYNAMICÆ SECTIO DECIMA. De affectionibus atque motibus fluidorum elaſti-corum, præcipue autem aëris. §. 1.
Page: 214 (200)
[185.] Digreſsio de refractione radiorum per atmoſphæ-ram transeuntium.
Page: 233 (219)
[186.] Problema.
Page: 238 (224)
[187.] Solutio.
Page: 238 (224)
[188.] Problema.
Page: 240 (226)
[189.] Solutio.
Page: 240 (226)
[190.] Corollarium 1.
Page: 241 (227)
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              <pb o="183" file="0197" n="197" rhead="SECTIO NONA."/>
            generalibus fieri poteſt, examinavimns, haud abs re erit exemplum aliquod
              <lb/>
            ſpeciale accuratius pertractare, & </s>
            <s xml:id="echoid-s5275" xml:space="preserve">quia cochlea Archimedis multis gaudet
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            egregiis proprietatibus, quas nemo ſatis, quantum ſcio, aperuit, ab ha
              <unsure/>
            c
              <lb/>
            exemplum deſumam idque eo libentius, quod multi ſint, qui contra no-
              <lb/>
            ſtras regulas putant ſingularem huic cochleæ virtutem ineſſe pro elevanda
              <lb/>
            magna aquæ quantitate brevi tempore parvaque vi: </s>
            <s xml:id="echoid-s5276" xml:space="preserve">falluntur autem qui ita
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            cogitant: </s>
            <s xml:id="echoid-s5277" xml:space="preserve">nam ſi obſtaculorum accidentalium nulla habeatur ratio, idem
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            præſtat eadem potentia abſoluta, quod reliquæ machinæ omnes.</s>
            <s xml:id="echoid-s5278" xml:space="preserve"/>
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        <div xml:id="echoid-div218" type="section" level="1" n="172">
          <head xml:id="echoid-head220" style="it" xml:space="preserve">Commentationes ſpeciales de Cochlea Archimedis.</head>
          <p>
            <s xml:id="echoid-s5279" xml:space="preserve">(I.) </s>
            <s xml:id="echoid-s5280" xml:space="preserve">Varii ſunt auctores, qui modum docuerunt conſtruendi hanc co-
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            chleam: </s>
            <s xml:id="echoid-s5281" xml:space="preserve">ſumma huc redit, ut canalis quidam aut plures ſuperficiei cylindricæ
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            circumflectantur, & </s>
            <s xml:id="echoid-s5282" xml:space="preserve">ita quidem ut canalis ubique eandem habeat inclinationem
              <lb/>
            ratione axis cylindri, quam Vitruvius præter neceſſitatem in omnibus cochleis
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            fieri jubet ad angulum ſemirectum. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">Requiritur ergo ante omnia, ut in ſuperfi-
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            cie cylindri linea ſpiralis ducatur ad cujus normam canalis ſit ponendus, id quod
              <lb/>
            facillime meo judicio in ſuperficie admodum polita fieri poterit (præſertim cum
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            helices non parum à ſe diſtare debent) circumvolvendo eidem aliquoties funi-
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            culum: </s>
            <s xml:id="echoid-s5284" xml:space="preserve">hic enim tenſus ſua ſponte deſideratam lineam faciet, neque enim ſpi-
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            ralis ſibi ſimilis ubique eſſe pote ſt, aut conſtantem habere ad axem cylindri in-
              <lb/>
            clinationem, quin arcus inter duo puncta interceptus ſit omnium arcuum eoſ-
              <lb/>
            dem terminos habentium minimus, quam indolem funiculo extenſo compe-
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            tere palam eſt: </s>
            <s xml:id="echoid-s5285" xml:space="preserve">ſi vero frictiones impedimento ſint, filum ad minora interval-
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            la extendi poterit. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Sed non eſt, cur in re per ſe pluribus modis facillima ſcru-
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            puloſi ſimus.</s>
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            <s xml:id="echoid-s5288" xml:space="preserve">Lex ſpiralis primaria eſt, ut ubique æqualiter ad axem cylindri incli-
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            net, cui legi ſequens innititur conſtructio, quam in gratiam infra dicendorum
              <lb/>
            apponam:</s>
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          <p>
            <s xml:id="echoid-s5290" xml:space="preserve">Finge cylindrum rectum M a f N (Fig. </s>
            <s xml:id="echoid-s5291" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5292" xml:space="preserve">(1)) cujus ſuperficiei ſit in-
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">Fig. 52.
                <lb/>
              (1.)</note>
            ſcribenda deſiderata ſpiralis a 1 b 2 c 3 d &</s>
            <s xml:id="echoid-s5293" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">eandemque ſuperficiem puta ex-
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            plicatam in planam figura præditam parallelogrammi rectanguli A a f F
              <lb/>
            (Fig. </s>
            <s xml:id="echoid-s5295" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5296" xml:space="preserve">(2)), ſumantur hic ab una parte A B, B C, C D, D E, & </s>
            <s xml:id="echoid-s5297" xml:space="preserve">E F, ab al-
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              <note position="right" xlink:label="note-0197-02" xlink:href="note-0197-02a" xml:space="preserve">Fig. 52.
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              (2.)</note>
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