Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of contents

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[121.] PROPOSITIO XXII.
Page: 261 (165)
[122.] Centrum oſcillationis in Pyramide.
Page: 262 (166)
[123.] Centrum oſcillationis Coni.
Page: 266 (167)
[124.] Centrum oſcillationis Sphæræ.
Page: 266 (167)
[125.] Centrum oſcillationis Cylindri.
Page: 267 (168)
[126.] Centrum oſcillationis Conoidis Parabolici.
Page: 267 (168)
[127.] Centrum oſcillationis Conoidis Hyperbolici.
Page: 268 (169)
[128.] Centrum oſcillationis dimidii Coni.
Page: 268 (169)
[129.] PROPOSITIO XXIII.
Page: 274 (172)
[130.] PROPOSITIO XXIV.
Page: 279 (177)
[131.] PROPOSITIO XXV.
Page: 280 (178)
[132.] PROPOSITIO XXVI.
Page: 284 (182)
[133.] HOROLOGII OSCILLATORII PARS QUINTA.
Page: 287 (185)
[134.] Horologii ſecundi conſtructio.
Page: 288 (186)
[135.] DE VI CENTRIFUGA ex motu circulari, Theoremata. I.
Page: 290 (188)
[136.] II.
Page: 290 (188)
[137.] III.
Page: 290 (188)
[138.] IV.
Page: 294 (189)
[139.] V.
Page: 294 (189)
[140.] VI.
Page: 294 (189)
[141.] VII.
Page: 295 (190)
[142.] VIII.
Page: 295 (190)
[143.] IX.
Page: 295 (190)
[144.] X.
Page: 296 (191)
[145.] XI.
Page: 296 (191)
[146.] XII.
Page: 296 (191)
[147.] XIII.
Page: 297 (192)
[148.] FINIS.
Page: 297 (192)
[149.] BREVIS INSTITUTIO DE USU HOROLOGIORUM AD INVENIENDAS LONGITUDINES.
Page: 298
[150.] Adr. Metius in Geographicis Inſtitutionibus Cap. 4.
Page: 299
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            P ſuperat triangulum A H L, erit igitur neceſſario figura
              <lb/>
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                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
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            circumſcripta minor plano P. </s>
            <s xml:id="echoid-s1322" xml:space="preserve">Conſtat jam, prima temporis
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            parte A C, minus ſpatium à mobili transmitti quam ſit B C,
              <lb/>
            quia hoc percurreretur eodem tempore A C cum celeritate
              <lb/>
            æquabili C K, quam demum in fine temporis A C mobile
              <lb/>
            adeptum eſt. </s>
            <s xml:id="echoid-s1323" xml:space="preserve">Similiter ſecunda parte temporis C E, minus
              <lb/>
            ſpatium motu accelerato transmittetur quam ſit D E, quia
              <lb/>
            hoc percurreretur eodem tempore C E, cum celeritate æ-
              <lb/>
            quabili E O, quam demum in fine temporis C E mobile aſ-
              <lb/>
            ſequitur. </s>
            <s xml:id="echoid-s1324" xml:space="preserve">Atque ita deinceps, ſingulis partibus temporis
              <lb/>
            A H, minora ſpatia à mobili trajicientur quam ſunt rectan-
              <lb/>
            gula figuræ circumſcriptæ, ipſis partibus adjacentia. </s>
            <s xml:id="echoid-s1325" xml:space="preserve">Quare
              <lb/>
            totum ſpatium motu accelerato peractum, minus erit ipſa fi-
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            gura circumſcripta. </s>
            <s xml:id="echoid-s1326" xml:space="preserve">Spatium vero illud æquale poſitum fuit
              <lb/>
            plano P; </s>
            <s xml:id="echoid-s1327" xml:space="preserve">ergo planum P minus quoque erit figura circum-
              <lb/>
            ſcripta. </s>
            <s xml:id="echoid-s1328" xml:space="preserve">quod eſt abſurdum, cum figura hæc plano P minor
              <lb/>
            oſtenſa fuerit. </s>
            <s xml:id="echoid-s1329" xml:space="preserve">Ergo planum P non majus eſt triangulo A H L,
              <lb/>
            ſed nec minus eſſe jam oſtenſum fuit. </s>
            <s xml:id="echoid-s1330" xml:space="preserve">Ergo æquale ſit neceſ-
              <lb/>
            ſe eſt; </s>
            <s xml:id="echoid-s1331" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1332" xml:space="preserve"/>
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            <s xml:id="echoid-s1333" xml:space="preserve">Et hæc quidem omnia quæ hactenus demonſtrata ſunt,
              <lb/>
            gravibus per plana inclinata deſcendentibus atque aſcenden-
              <lb/>
            tibus æque ac perpendiculariter motis convenire ſciendum
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s1334" xml:space="preserve">cum, quæ de effectu gravitatis poſita fuerunt, eadem
              <lb/>
            ratione utrobique ſint admittenda.</s>
            <s xml:id="echoid-s1335" xml:space="preserve"/>
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            <s xml:id="echoid-s1336" xml:space="preserve">Hinc vero non difficile jam erit demonſtrare propoſitionem
              <lb/>
            ſequentem quam concedi ſibi, ut quodammodo per ſe ma-
              <lb/>
            nifeſtam, Galileus poſtulavit. </s>
            <s xml:id="echoid-s1337" xml:space="preserve">nam demonſtratio illa quam
              <lb/>
            poſtea adferre conatus eſt, quæque in poſteriori operum
              <lb/>
            ejus editione extat, parum firma meo quidem judicio vide-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1338" xml:space="preserve">Eſt autem propoſitio hujusmodi.</s>
            <s xml:id="echoid-s1339" xml:space="preserve"/>
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          <head xml:id="echoid-head51" xml:space="preserve">PROPOSITIO VI.</head>
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            <s xml:id="echoid-s1340" xml:space="preserve">CEleritates gravium, ſuper diverſis planorum
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            inclinationibus deſcendendo acquiſitæ, æquales
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            ſunt, ſi planorum elevationes fuerint æquales.</s>
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