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

Table of Notes

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              <pb o="65" file="0099" n="104" rhead="HOROLOG. OSCILLATOR."/>
            per A B deſcendens eandem acquirit velocitatem in termi-
              <lb/>
              <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            no B, atque deſcendens per G B ; </s>
            <s xml:id="echoid-s1376" xml:space="preserve">manifeſtum eſt,
              <note symbol="*" position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            flexus ad B nihil obſtare motui ponatur, tantam velocitatem
              <lb/>
            bahiturum ubi in C pervenerit, quantam ſi per G C planum
              <lb/>
            deſcendiſſet; </s>
            <s xml:id="echoid-s1377" xml:space="preserve">hoc eſt, quantam haberet ex deſcenſu per E C.
              <lb/>
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            <s xml:id="echoid-s1378" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s1379" xml:space="preserve">reliquum planum C D eodem modo tranſibit ac ſi
              <lb/>
            per E C adveniſſet, ac proinde in D denique parem veloci-
              <lb/>
            tatem habebit, ac ſi deſcendiſſet per planum E D, hoc eſt,
              <lb/>
            eandem quam ex caſu perpendiculari per E F. </s>
            <s xml:id="echoid-s1380" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s1381" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s1382" xml:space="preserve">Hinc liquet etiam per circuli circumferentiam, vel per cur-
              <lb/>
            vam quamlibet lineam deſcendente mobili (nam curvas tan-
              <lb/>
            quam ex infinitis rectis compoſitæ eſſent hic conſiderare li-
              <lb/>
            cet) ſemper eandem illi velocitatem acquiri ſi ab æquali al-
              <lb/>
            titudine deſcenderit: </s>
            <s xml:id="echoid-s1383" xml:space="preserve">tantamque eam eſſe velocitatem, quan-
              <lb/>
            tam caſu perpendiculari ex eadem altitudine adipiſceretur.</s>
            <s xml:id="echoid-s1384" xml:space="preserve"/>
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          <head xml:id="echoid-head54" xml:space="preserve">PROPOSITIO IX.</head>
          <p style="it">
            <s xml:id="echoid-s1385" xml:space="preserve">SI grave, à deſcenſu, ſurſum convertat motum
              <lb/>
            ſuum, aſcendet ad eandem unde venit altitudi-
              <lb/>
            nem, per quascunque planas ſuperſicies contiguas,
              <lb/>
            & </s>
            <s xml:id="echoid-s1386" xml:space="preserve">quomodocunque inclinatas, inceſſerit.</s>
            <s xml:id="echoid-s1387" xml:space="preserve"/>
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            <s xml:id="echoid-s1388" xml:space="preserve">Cadat grave ex altitudine A B, & </s>
            <s xml:id="echoid-s1389" xml:space="preserve">ex puncto B inclinata
              <lb/>
              <note position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">TAB. VI.
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              Fig. 2.</note>
            ſint ſurſum plana B C, C D, D E, quorum extremitas E
              <lb/>
            ſit eadem altitudine cum puncto A. </s>
            <s xml:id="echoid-s1390" xml:space="preserve">Dico ſi mobile, poſt ca-
              <lb/>
            ſum per A B, convertat motum ut pergat moveri per dicta
              <lb/>
            plana inclinata, perventutum uſque in E.</s>
            <s xml:id="echoid-s1391" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1392" xml:space="preserve">Dicatur enim, ſi fieri poteſt, tantum ad G perventurum.
              <lb/>
            </s>
            <s xml:id="echoid-s1393" xml:space="preserve">Producantur B C & </s>
            <s xml:id="echoid-s1394" xml:space="preserve">C D, donec occurrant horizontali G F
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            in F & </s>
            <s xml:id="echoid-s1395" xml:space="preserve">H. </s>
            <s xml:id="echoid-s1396" xml:space="preserve">Cum igitur mobile, ſuperatis planis B C, C D,
              <lb/>
            habeat tantum eam velocitatem quâ poſſit aſcendere per
              <lb/>
            D G, vel per D H; </s>
            <s xml:id="echoid-s1397" xml:space="preserve">nam ad hæc utraque eadem velocitate
              <lb/>
            opus eſſe conſtat ex propoſitione 6; </s>
            <s xml:id="echoid-s1398" xml:space="preserve">Ergo, ſuperato plano
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            B C, eam duntaxat habebat qua potuiſſet aſcendere per C </s>
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