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

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            <s xml:id="echoid-s1236" xml:space="preserve">
              <pb o="58" file="0090" n="94" rhead="CHRISTIANI HUGENII"/>
            hoc eſt celeritatem K F, quia K F æquatur ipſis H G, B D,
              <lb/>
              <note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            ſunt enim partes ſingulæ H K, F G, æquales ipſi A B,
              <lb/>
            ac proinde utraque ſimul ipſi B D, quam eſſe duplam
              <lb/>
            A B oſtendimus propoſitione 2. </s>
            <s xml:id="echoid-s1237" xml:space="preserve">Itaque celeritatem in fine
              <lb/>
            deſcenſus K acquiſitam ſurſum convertendo, ſi grave æqua-
              <lb/>
            bili motu ferretur, conficeret una temporis parte ſpatium
              <lb/>
            K F. </s>
            <s xml:id="echoid-s1238" xml:space="preserve">Atqui, gravitatis actione accedente, diminuetur
              <lb/>
            aſcenſus K F ſpatio F G ipſi A B æquali, ut patet ex di-
              <lb/>
            ctis ad hypotheſin initio ſumptam. </s>
            <s xml:id="echoid-s1239" xml:space="preserve">Ergo parte prima tempo-
              <lb/>
            ris aſcendet grave tantum per K G, quo eodem ſpatio parte
              <lb/>
            temporis noviſſima deſcenderat. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">Simul vero & </s>
            <s xml:id="echoid-s1241" xml:space="preserve">celeritati tan-
              <lb/>
            tum deceſſiſſe neceſſe eſt, quantum acquiritur temporis parte
              <lb/>
            una deorſum cadendo, hoc eſt celeritatem B D. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">Itaque gra-
              <lb/>
            ve, ubi ad G aſcenderit, habet celeritatem reliquam H G,
              <lb/>
            cum initio aſcenſus habuerit celeritatem H G una cum cele-
              <lb/>
            ritate B D. </s>
            <s xml:id="echoid-s1243" xml:space="preserve">Eſt autem ipſi H G æqualis G D; </s>
            <s xml:id="echoid-s1244" xml:space="preserve">quum æque-
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            tur ipſi F E una cum D B, hoc eſt una cum dupla A B,
              <lb/>
            hoc eſt una cum duabus F G & </s>
            <s xml:id="echoid-s1245" xml:space="preserve">E D; </s>
            <s xml:id="echoid-s1246" xml:space="preserve">Ergo ſi ex G, cum
              <lb/>
            celeritate æquabili, quantam illic habet, ſurſum pergeret,
              <lb/>
            conficeret una parte temporis ſpatium G D. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">Accedente au-
              <lb/>
            tem gravitatis actione, diminuetur aſcenſus iſte ſpatio D E,
              <lb/>
            ipſi A B æquali. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">Ergo, hac ſecunda parte temporis, aſcendet
              <lb/>
            per ſpatium G E, quod ſimili temporis parte etiam cadendo
              <lb/>
            tranſierat. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">Simul autem celeritati tantum deceſſiſſe denuo de-
              <lb/>
            bet quantum temporis parte una ex caſu acquiritur, nempe
              <lb/>
            celeritas B D. </s>
            <s xml:id="echoid-s1250" xml:space="preserve">Itaque ubi uſque ad E aſcenderit, habet dun-
              <lb/>
            taxat celeritatem F E, quæ nimirum relinquitur quum à
              <lb/>
            celeritate G D aufertur celeritas B D. </s>
            <s xml:id="echoid-s1251" xml:space="preserve">Nam B D, ut jam
              <lb/>
            diximus, æqualis eſt duabus D E, F G.</s>
            <s xml:id="echoid-s1252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1253" xml:space="preserve">Eſt autem ipſi F E æqualis E A, quum F E æquetur ipſi
              <lb/>
            B D bis ſumptæ, hoc eſt ipſi B D una cum dupla A B,
              <lb/>
            hoc eſt una cum duabus A B, D E. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">Ergo ſi ex E cum ce-
              <lb/>
            leritate æquabili, quantam illic habet, ſurſum pergeret, con-
              <lb/>
            fecturum eſſet una temporis parte ſpatium E A. </s>
            <s xml:id="echoid-s1255" xml:space="preserve">Sed acce-
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            dente actione gravitatis, diminuetur aſcenſus iſte ipſo ſpatio
              <lb/>
            A B. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">Proinde hac parte temporis per ſpatium E B </s>
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