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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            <emph style="sc">De de-</emph>
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            <emph style="sc">SOENSU</emph>
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            <emph style="sc">GRAVIUM</emph>
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          <head xml:id="echoid-head50" xml:space="preserve">PROPOSITIO V. </head>
          <p style="it">
            <s xml:id="echoid-s1279" xml:space="preserve">SPatium peractum certo tempore, à gravi è quie-
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            te caſum inchoante, dimidium eſſe ejus ſpatii
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            quod pari tempore transiret motu æquabili, cum
              <lb/>
            celeritate quam acquiſivit ultimo caſus momento.</s>
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          <p>
            <s xml:id="echoid-s1281" xml:space="preserve">Sit tempus deſcenſus totius A H, quo tempore mobile
              <lb/>
              <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 3.</note>
            peregerit ſpatium quoddam cujus quantitas deſignetur plano P.
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            </s>
            <s xml:id="echoid-s1282" xml:space="preserve">ductaque H L perpendiculari ad A H, longitudinis cujus-
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            libet, referat illa celeritatem in fine caſus acquiſitam. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Dein-
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            de completo rectangulo A H L M, intelligatur eo notari
              <lb/>
            quantitas ſpatii quod percurreretur tempore A H, cum ce-
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            leritate H L. </s>
            <s xml:id="echoid-s1284" xml:space="preserve">Oſtendendum eſt igitur planum P dimidium
              <lb/>
            eſſe rectanguli M H, hoc eſt, ducta diagonali A L, æqua-
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            le triangulo A H L.</s>
            <s xml:id="echoid-s1285" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1286" xml:space="preserve">Si planum P non eſt æquale triangulo A H L, ergo aut
              <lb/>
            minus eo erit, aut majus. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">Sit primo, ſi fieri poteſt, pla-
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            num P minus triangulo A H L. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">dividatur autem A H in tot
              <lb/>
            partes æquales A C, C E, E G &</s>
            <s xml:id="echoid-s1289" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1290" xml:space="preserve">ut, circumſcriptâ tri-
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            angulo A H L figurâ è rectangulis quorum altitudo ſingulis
              <lb/>
            diviſionum ipſius A H partibus æquetur, ut ſunt rectangula
              <lb/>
            B C, D E, F G, alterâque eidem triangulo inſcriptâ, ex
              <lb/>
            rectangulis ejusdem altitudinis, ut ſunt K E, O G &</s>
            <s xml:id="echoid-s1291" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1292" xml:space="preserve">ut,
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            inquam, exceſſus illius figuræ ſupra hanc, minor ſit exceſ-
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            ſu trianguli A H L ſupra planum P. </s>
            <s xml:id="echoid-s1293" xml:space="preserve">hoc enim fieri poſſe
              <lb/>
            perſpicuum eſt, cum totus exceſſus figuræ circumſcriptæ ſu-
              <lb/>
            per inſcriptam æquetur rectangulo infimo, baſin habenti H L.
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            </s>
            <s xml:id="echoid-s1294" xml:space="preserve">Erit itaque omnino exceſſus ipſius trianguli A H L ſupra
              <lb/>
            figuram inſcriptam minor quam ſupra planum P, ac proin-
              <lb/>
            de figura triangulo inſcripta major plano P. </s>
            <s xml:id="echoid-s1295" xml:space="preserve">Porro autem,
              <lb/>
            quum recta A H tempus totius deſcenſus referat, ejus par-
              <lb/>
            tes æquales A C, C E, E G, æquales temporis illius par-
              <lb/>
            tes referent. </s>
            <s xml:id="echoid-s1296" xml:space="preserve">Cumque celeritates mobilis cadentis creſcant
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0092-03" xlink:href="note-0092-03a" xml:space="preserve">Prop. I.
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              huj.</note>
            eadem proportione qua tempora deſcenſus ; </s>
            <s xml:id="echoid-s1297" xml:space="preserve">ſitque </s>
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