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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              <pb o="59" file="0091" n="95" rhead="HOROLOG. OSCILLATOR."/>
            aſcendet, quod ſimili parte temporis deſcendendo quoque
              <lb/>
              <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            tranſierat. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">Hic vero rurſus celeritati tantum deceſſiſſe neceſſe
              <lb/>
            eſt quantum una temporis parte cadendo deorſum acquiritur,
              <lb/>
            hoc eſt celeritatem B D. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">Itaque grave, ubi uſque ad B a-
              <lb/>
            ſcenderit, habet celeritatem ipſam B D reliquam, cum in E
              <lb/>
            habuerit celeritatem F E ipſius B D duplam. </s>
            <s xml:id="echoid-s1259" xml:space="preserve">Si ergo ex B
              <lb/>
            cum celeritate æquabili, quantam illic habet, ſurſum per-
              <lb/>
            geret, confecturum eſſet parte una temporis ſpatium æquale
              <lb/>
            ipſi D B, hoc eſt duplum A B. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Sed accedente gravitatis
              <lb/>
            actione, diminuitur aſcenſus iſte ſpatio quod ipſi A B æqua-
              <lb/>
            le ſit. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Igitur hac parte temporis aſcendet tantummodo per
              <lb/>
            ſpatium B A, quod etiam primo deſcenſus tempore trans-
              <lb/>
            ierat. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Atque in fine quidem extremi temporis hujus neceſſa-
              <lb/>
            rio grave in A puncto reperietur. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Sed dicetur forſan altius
              <lb/>
            aſcendiſſe quam ad A, atque inde eo relapſum eſſe. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">At hoc
              <lb/>
            abſurdum eſſet, cum non poſſit, notu à gravitate profecto, al-
              <lb/>
            tius quam unde decidit aſcendere. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">Porro quum celeritati quam
              <lb/>
            in B habebat rurſus deceſſerit celeritas B D, patet jam gra-
              <lb/>
            vi in A conſtituto nullam celeritatem ſupereſſe, ac proinde
              <lb/>
            non altius excurſurum. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">Itaque oſtenſum eſt ad eandem unde
              <lb/>
            decidit altitudinem perveniſſe, & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">ſingula ſpatia, quæ æqua-
              <lb/>
            libus deſcenſus temporibus tranſmiſerat, eadem totidem a-
              <lb/>
            ſcenſus temporibus remenſum eſſe: </s>
            <s xml:id="echoid-s1268" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s1269" xml:space="preserve">æqualibus tempo-
              <lb/>
            ribus æqualia ipſi deceſſiſſe celeritatis momenta apparuit. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">Ergo
              <lb/>
            conſtat propoſitum.</s>
            <s xml:id="echoid-s1271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1272" xml:space="preserve">Quia vero in demonſtratione propoſitionis ſecundæ, ex
              <lb/>
            qua pendet præcedens, adſumptum fuit certam quandam eſ-
              <lb/>
            ſe proportionem ſpatiorum quæ continuis æqualibus tempo-
              <lb/>
            ribus à gravi cadente transeuntur, quæque eadem ſit, quæ-
              <lb/>
            cunque æqualia tempora accipiantur; </s>
            <s xml:id="echoid-s1273" xml:space="preserve">quod quidem & </s>
            <s xml:id="echoid-s1274" xml:space="preserve">ex
              <lb/>
            rei natura ita ſe habere neceſſe eſt, & </s>
            <s xml:id="echoid-s1275" xml:space="preserve">ſi negetur, fatendum
              <lb/>
            fruſtra proportionem iſtorum ſpatiorum inveſtigari. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Tamen,
              <lb/>
            quia propoſitum etiam absque hoc demonſtrari poteſt, Ga-
              <lb/>
            lilei methodum ſequendo, operæ pretium erit demonſtra-
              <lb/>
            tionem, ab illo minus perfecte traditam, hic accuratius
              <lb/>
            conſcribere. </s>
            <s xml:id="echoid-s1277" xml:space="preserve">itaque rurſum hic demonſtrabimus.</s>
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