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

Table of contents

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[91.] PROPOSITIO III.
Page: 200 (125)
[92.] PROPOSITIO IV.
Page: 201 (126)
[93.] PROPOSITIO V.
Page: 202 (127)
[94.] PROPOSITIO VI.
Page: 208 (130)
[95.] DEFINITIO XIV.
Page: 210 (132)
[96.] DEFINITIO XV.
Page: 210 (132)
[97.] PROPOSITIO VII.
Page: 210 (132)
[98.] PROPOSITIO VIII.
Page: 211 (133)
[99.] PROPOSITIO IX.
Page: 213 (135)
[100.] PROPOSITIO X.
Page: 214 (136)
[101.] PROPOSITIO XI.
Page: 218 (137)
[102.] PROPOSITIO XII.
Page: 218 (137)
[103.] PROPOSITIO XIII.
Page: 221 (140)
[104.] PROPOSITIO XIV.
Page: 223 (142)
[105.] PROPOSITIO XV.
Page: 228 (144)
[106.] PROPOSITIO XVI.
Page: 232 (148)
[107.] PROPOSITIO XVII.
Page: 233 (149)
[108.] PROPOSITIO XVIII.
Page: 234 (150)
[109.] PROPOSITIO XIX.
Page: 237 (153)
[110.] PROPOSITIO XX.
Page: 238 (154)
[111.] PROPOSITIO XXI.
Page: 238 (154)
[112.] Centrum oſcillationis Circuli.
Page: 247 (157)
[113.] Centrum oſcillationis Rectanguli.
Page: 247 (157)
[114.] Centrum oſcillationis Trianguli iſoſcelis.
Page: 248 (158)
[115.] Centrum oſcillationis Parabolæ.
Page: 248 (158)
[116.] Centrum oſcillationis Sectoris circuli.
Page: 248 (158)
[117.] Centrum oſcillationis Circuli, aliter quam ſupra.
Page: 250 (160)
[118.] Centrum oſcillationis Peripheriæ circuli.
Page: 250 (160)
[119.] Centrum oſcillationis Polygonorum ordinatorum.
Page: 254 (161)
[120.] Loci plani & ſolidi uſus in hac Theoria.
Page: 254 (161)
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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
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            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-
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            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>
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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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