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

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          <pb o="56" file="0088" n="92" rhead="CHRISTIANI HUGENII"/>
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            <s xml:id="echoid-s1193" xml:space="preserve">Si enim negetur; </s>
            <s xml:id="echoid-s1194" xml:space="preserve">habeat primo, ſi poteſt, ſpatium E ad F
              <lb/>
              <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            majorem rationem quam quadratum A B ad quadratum
              <lb/>
            C D, nempe eam quam quadratum A B ad quadratum C
              <lb/>
            G, ſumta C G minore quam C D, & </s>
            <s xml:id="echoid-s1195" xml:space="preserve">à C D auferatur
              <lb/>
            pars D H, minor quam D G exceſſus C D ſupra C G,
              <lb/>
            atque ita ut reliqua H C commenſurabilis ſit ipſi A B;
              <lb/>
            </s>
            <s xml:id="echoid-s1196" xml:space="preserve">hoc enim fieri poſſe conſtat. </s>
            <s xml:id="echoid-s1197" xml:space="preserve">Erit ergo C H major quam
              <lb/>
            C G. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">Atqui ut quadratum temporis A B ad quadratum tem-
              <lb/>
            poris C H, ita ſpatium E, quod tempore A B peractum
              <lb/>
            eſt, ad ſpatium peractum tempore C H, per ſuperiùs oſten-
              <lb/>
            ſa. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">Hoc vero ſpatio majus eſt illud quod tempore C D per-
              <lb/>
            curritur, nempe ſpatium F. </s>
            <s xml:id="echoid-s1200" xml:space="preserve">ergo ſpatii E ad ſpatium F mi-
              <lb/>
            nor eſt ratio quam quadrati A B ad quadratum C H. </s>
            <s xml:id="echoid-s1201" xml:space="preserve">Sicut
              <lb/>
            autem ſpatium E ad F, ita ponebatur eſſe quadratum A B
              <lb/>
            ad quadratum C G; </s>
            <s xml:id="echoid-s1202" xml:space="preserve">ergo minor quoque erit ratio quadrati
              <lb/>
            A B ad quadratum C G, quam quadrati A B ad quadra-
              <lb/>
            tum C H, ac proinde quadratum C G majus quadrato C
              <lb/>
            H; </s>
            <s xml:id="echoid-s1203" xml:space="preserve">quod eſt abſurdum, quum C H major dicta ſit quam
              <lb/>
            C G. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">Non habet igitur ſpatium E ad F majorem rationem
              <lb/>
            quam quadratum A B ad quadratum C D.</s>
            <s xml:id="echoid-s1205" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1206" xml:space="preserve">Habeat jam, ſi poteſt, minorem; </s>
            <s xml:id="echoid-s1207" xml:space="preserve">ſitque ratio ſpatii E ad
              <lb/>
            F eadem quæ quadrati A B ad quadratum C L, ſumptâ C L
              <lb/>
            majore quam C D, & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">à C L auferatur L K minor ex-
              <lb/>
            ceſſu L D, quo C D ſuperatur à C L, atque ita
              <lb/>
            ut reliqua K C ſit commenſurabilis A B. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Quia ergo ut qua-
              <lb/>
            dratum temporis A B ad quadratum temporis C K, ita eſt
              <lb/>
            ſpatium E, peractum tempore A B, ad ſpatium peractum
              <lb/>
            tempore C K. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">Hoc vero ſpatio minus eſt ſpatium peractum
              <lb/>
            tempore C D, nempe ſpatium F. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">erit proinde ſpatii E ad
              <lb/>
            F major ratio quam quadrati A B ad quadratum C K. </s>
            <s xml:id="echoid-s1212" xml:space="preserve">Sic-
              <lb/>
            ut autem ſpatium E ad F, ita ponebatur eſſe quadratum
              <lb/>
            A B ad quadratum C L. </s>
            <s xml:id="echoid-s1213" xml:space="preserve">Ergo major erit ratio quadrati A B
              <lb/>
            ad quadratum C L quam ejuſdem quadrati A B ad quadra-
              <lb/>
            tum C K, ideoque quadratum C L minus erit quam qu. </s>
            <s xml:id="echoid-s1214" xml:space="preserve">C K.
              <lb/>
            </s>
            <s xml:id="echoid-s1215" xml:space="preserve">quod eſt abſurdum, quum C L major ſit quam C K. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">
              <lb/>
            Ergo neque minorem rationem habet ſpatium E ad F </s>
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