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

Table of Notes

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            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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