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

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              <pb o="55" file="0087" n="91" rhead="HOROLOG. OSCILLATOR."/>
            B D. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">Sicut igitur D B ad B A ita erit quadrupla D B ad
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            E A: </s>
            <s xml:id="echoid-s1169" xml:space="preserve">unde E A quadrupla erit ipſius B A: </s>
            <s xml:id="echoid-s1170" xml:space="preserve">eadem vero E A
              <lb/>
            æquatur, uti diximus, & </s>
            <s xml:id="echoid-s1171" xml:space="preserve">duplæ A B & </s>
            <s xml:id="echoid-s1172" xml:space="preserve">ſimplici B D. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">er-
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            go B D duplæ A B æqualis erit; </s>
            <s xml:id="echoid-s1174" xml:space="preserve">quod erat demonſtran-
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            dum.</s>
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          <head xml:id="echoid-head48" xml:space="preserve">PROPOSITIO III.</head>
          <p style="it">
            <s xml:id="echoid-s1176" xml:space="preserve">SPatia duo, à gravi cadente quibuslibet tempo-
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            ribus transmiſſa, quorum utrumque ab initio
              <lb/>
            deſcenſus accipiatur, ſunt inter ſe in ratione du-
              <lb/>
            plicata eorundem temporum, ſive ut temporum qua-
              <lb/>
            drata, ſive etiam ut quadrata celeritatum in fine
              <lb/>
            cujusque temporis acquiſitarum.</s>
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          </p>
          <p>
            <s xml:id="echoid-s1178" xml:space="preserve">Quum enim oſtenſum ſit propoſitione antecedenti ſpa-
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 1.</note>
            tia A B, B E, E G, G K, quotcunque fuerint, æqualibus
              <lb/>
            temporibus à cadente, peracta, creſcere æquali exceſſu, qui
              <lb/>
            exceſſus ſit ipſi B D æqualis: </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Patet nunc, quoniam B D eſt
              <lb/>
            dupla A B, ſpatium B E fore triplum A B; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">E G quintu-
              <lb/>
            plum ejuſdem A B; </s>
            <s xml:id="echoid-s1181" xml:space="preserve">G K ſeptuplum; </s>
            <s xml:id="echoid-s1182" xml:space="preserve">aliaque deinceps au-
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            ctum iri ſecundum progreſſionem numerorum imparium ab
              <lb/>
            unitate, 1, 3, 5, 7, 9, &</s>
            <s xml:id="echoid-s1183" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">cumque quotlibet horum nu-
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            merorum, ſeſe conſequentium, ſumma faciat quadratum,
              <lb/>
            cujus latus eſt ipſa adſumptorum numerorum multitudo (ve-
              <lb/>
            lut ſi tres primi addantur, facient novem, ſi quatuor ſexde-
              <lb/>
            cim) ſequitur hinc ſpatia, à gravi cadente tranſmiſſa, quo-
              <lb/>
            rum utrumque à principio caſus inchoetur, eſſe inter ſe in
              <lb/>
            ratione duplicata temporum quibus caſus duravit, ſi nempe
              <lb/>
            tempora commenſurabilia ſumantur.</s>
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            <s xml:id="echoid-s1186" xml:space="preserve">Facile autem & </s>
            <s xml:id="echoid-s1187" xml:space="preserve">ad tempora incommenſurabilia demonſtra-
              <lb/>
              <note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 2.</note>
            tio extendetur. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">Sint enim tempora hujuſmodi, quorum inter
              <lb/>
            ſe ratio ea quæ linearum A B, C D. </s>
            <s xml:id="echoid-s1189" xml:space="preserve">ſpatiaque temporibus
              <lb/>
            his tranſmiſſa ſint E, & </s>
            <s xml:id="echoid-s1190" xml:space="preserve">F, utraque nimirum ab initio de-
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            ſcenſus adſumpta. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Dico eſſe, ut quadratum A B ad quadra-
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            tum C D, ita ſpatium E ad F.</s>
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