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

Table of contents

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[81.] VIII.
Page: 192 (120)
[82.] IX.
Page: 192 (120)
[83.] X.
Page: 192 (120)
[84.] XI.
Page: 192 (120)
[85.] XII.
Page: 193 (121)
[86.] XIII.
Page: 193 (121)
[87.] HYPOTHESES. I.
Page: 193 (121)
[88.] II.
Page: 198 (123)
[89.] PROPOSITIO I.
Page: 198 (123)
[90.] PROPOSITIO II.
Page: 200 (125)
[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)
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            ſpatium B D percurreretur. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">Feretur vero motu compoſito
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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">GRAVIUM</emph>
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            ex æquabili quo percurſurum eſſet ſpatium B D, & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">ex mo-
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            tu gravium cadentium, quo deprimi neceſſe eſt per ſpatium
              <lb/>
            ipſi A B æquale. </s>
            <s xml:id="echoid-s1128" xml:space="preserve">Quare ad B D addita D E, æquali A B,
              <lb/>
            ſcimus tempore ſecundo grave perventurum ad E.</s>
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          <p>
            <s xml:id="echoid-s1130" xml:space="preserve">Quod ſi vero inquiramus quam velocitatem habeat in E,
              <lb/>
            in fine ſecundi temporis, eam inveniemus duplam eſſe debe-
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            re velocitatis quam habebat in B fine temporis primi. </s>
            <s xml:id="echoid-s1131" xml:space="preserve">Dixi-
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            mus enim moveri compoſito motu ex æquabili cum celerita-
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            te acquiſita in B, & </s>
            <s xml:id="echoid-s1132" xml:space="preserve">ex motu à gravitate producto, qui
              <lb/>
            cum tempore ſecundo idem plane ſit ac primo, ideo decur-
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            ſu temporis ſecundi æqualem celeritatem gravi contuliſſe
              <lb/>
            debet atque in fine primi. </s>
            <s xml:id="echoid-s1133" xml:space="preserve">Quare cum acquiſitam in fine pri-
              <lb/>
            mi temporis celeritatem conſervaverit integram, apparet in
              <lb/>
            fine ſecundi temporis bis eam celeritatem ineſſe quam acqui-
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            ſiverat in fine temporis primi, ſive duplam.</s>
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            <s xml:id="echoid-s1135" xml:space="preserve">Quod ſi jam, poſtquam pervenit in E, pergeret deinceps
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            tantum moveri celeritate æquabili, quantam illic acquiſivit,
              <lb/>
            apparet tempore tertio, prioribus æquali, percurſurum ſpa-
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            tium E F, quod duplum futurum ſit ſpatii B D; </s>
            <s xml:id="echoid-s1136" xml:space="preserve">quia hoc
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            percurri diximus dimidia hujus celeritatis, motu æquabili,
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            & </s>
            <s xml:id="echoid-s1137" xml:space="preserve">temporis parte æquali. </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Accedente autem rurſus gravitatis
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            actione, percurret tempore tertio, præter ſpatium E F,
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            etiam ſpatium F G, ipſi A B vel D E æquale. </s>
            <s xml:id="echoid-s1139" xml:space="preserve">Itaque in
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            fine tertii temporis grave invenietur in G. </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Velocitatem vero
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            hîc habebit triplam jam ejus quam habebat in B, in fine pri-
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            mi temporis: </s>
            <s xml:id="echoid-s1141" xml:space="preserve">quia præter celeritatem acquiſitam in E, quam
              <lb/>
            diximus duplam eſſe acquiſitæ in B, vis gravitatis, tempo-
              <lb/>
            ris tertii decurſu, æqualem rurſus atque in fine primi cele-
              <lb/>
            ritatem contulit. </s>
            <s xml:id="echoid-s1142" xml:space="preserve">Quamobrem utraque celeritas, in fine tem-
              <lb/>
            poris tertii, triplam celeritatem conſtituet ejus quæ fuerat
              <lb/>
            in fine temporis primi.</s>
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            <s xml:id="echoid-s1144" xml:space="preserve">Eodem modo oſtendetur tempore quarto peragi debere & </s>
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            ſpatium G H triplum ſpatii B D, & </s>
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            æquale: </s>
            <s xml:id="echoid-s1147" xml:space="preserve">velocitatemque in K, in fine quarti temporis, fo-
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            re quadruplam ejus quæ fuerat in B, in fine temporis primi.</s>
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