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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            quadratum A B ad quadratum C D. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">quare neceſſe eſt ut
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                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
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                <emph style="sc">@RAVIUM</emph>
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            eandem habeat. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">Porro cum celeritates in fine temporum A B,
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            C D acquiſitæ ſint inter ſe ſicut ipſamet tempora; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">apparet
              <lb/>
            rationem ſpatiorum E ad F eandem quoque eſſe quæ qua-
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            dratorum temporum A B, C D, quibus transmiſſa ſunt.
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            </s>
            <s xml:id="echoid-s1220" xml:space="preserve">Itaque conſtat propoſitum.</s>
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          <head xml:id="echoid-head49" xml:space="preserve">PROPOSITIO IV.</head>
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            <s xml:id="echoid-s1222" xml:space="preserve">SI grave celeritate ea quam in fine deſcenſus ac-
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            quiſivit ſurſum tendere cœperit, fiet ut paribus
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            temporis partibus, ſpatia quæ prius ſurſum, ea-
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            dem deorſum transeat, adeoque ad eandem unde
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            deſcenderat altitudinem aſcendat. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Item ut æquali-
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            bus temporis partibus æqualia amittat celeritatis
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            momenta.</s>
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          <note position="right" xml:space="preserve">TAB. V.
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          Fig. 1.</note>
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            <s xml:id="echoid-s1225" xml:space="preserve">Sunto enim ut in propoſitione 2, ſpatia quotlibet, æqua-
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            libus temporis partibus cadendo è quiete peracta, quorum
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            primum A B; </s>
            <s xml:id="echoid-s1226" xml:space="preserve">ſecundum compoſitum ex B D, quod celeri-
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            tate æquabili acquiſita per A B tranſeundum erat, & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">ex D E
              <lb/>
            ipſi A B æquali; </s>
            <s xml:id="echoid-s1228" xml:space="preserve">tertium compoſitum, ex E F, duplo
              <lb/>
            ipſius B D, & </s>
            <s xml:id="echoid-s1229" xml:space="preserve">ex F G, eidem A B æquali; </s>
            <s xml:id="echoid-s1230" xml:space="preserve">quartum com-
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            poſitum ex G H, triplo ipſius B D, & </s>
            <s xml:id="echoid-s1231" xml:space="preserve">ex H K ipſi itidem
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            A B æquali, atque eadem ratione porro creſcentia, ſi plu-
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            ra fuerint. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Dico totidem æqualibus temporibus eadem ſpatia
              <lb/>
            K G, G E, E B, B A, ſingula ſingulis peragenda eſſe à
              <lb/>
            gravi ſurſum tendente, atque incipiente cum celeritate in
              <lb/>
            fine deſcenſus K acquiſita.</s>
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          </p>
          <p>
            <s xml:id="echoid-s1234" xml:space="preserve">Brevitatis autem gratia celeritas quæque deſignetur de-
              <lb/>
            inceps longitudine ſpatii quod grave motu æquabili, cum
              <lb/>
            celeritate illa, atque temporis parte una, quales in deſcen-
              <lb/>
            ſu conſideravimus, tranſmiſſurum eſſet.</s>
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            <s xml:id="echoid-s1236" xml:space="preserve">Itaque ex oſtenſis dicta propoſitione, cum in K grave
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            pervenerit, habet celeritatem G H auctam celeritate B </s>
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