新符号学

\frac{a}{b}}=d_{1}}以及{\dispystyle{\frac{c}{d}}-x=d_{2}}{\dispystyle{\frac{c}{d}}-x=d_{2}}

    如果有正整数m,k满足：{\dispystyle{\frac{kd}{mb}}={\frac{d_{1}}{d_{2}}}}{\dispystyle{\frac{kd}{mb}}={\frac{d_{1}}{d_{2}}}}

    那麽就有：{\dispystylex={\frac{ma kc}{mb kd}}}{\dispystylex={\frac{ma kc}{mb kd}}}

    证明如下：由条件可得

    {\dispystyle{\begin{aligned}bd_{1}&=bx-a\\dd_{2}&=c-dx\end{aligned}}}{\dispystyle{\begin{aligned}bd_{1}&=bx-a\\dd_{2}&=c-dx\end{aligned}}}

    而根据{\dispystyle{\frac{kd}{mb}}={\frac{d_{1}}{d_{2}}}}{\dispystyle{\frac{kd}{mb}}={\frac{d_{1}}{d_{2}}}}又有

    {\dispystylembd_{1}=kdd_{2}}

    代入上面的两个关系式可得：

    {\dispystylembx-a=kc-dx}

    2

    解关於x的一元一次方程就有结果：

    {\dispystylex={\frac{ma kc}{mb kd}}}

    应用编辑

    何承天调日法被同时代和後代数学家如赵爽，祖冲之，一行等运用。

    朔望月编辑

    何承天将{\dispystyle{\frac{9}{17}}=0.529412...\}{\dispystyle{\frac{9}{17}}=0.529412...\}作为朔望月零数部分的弱率，以{\dispystyle{\frac{26}{49}}=0.530612...\}{\dispystyle{\frac{26}{49}}=0.530612...\}作为朔望月零数部分的强率。运用调日法，最後得到{\dispystyle{\frac{399}{752}}\}{\dispystyle{\frac{399}{752}}\}，根据他的观测数值0.530585，首先计算d1,d2

    {\dispystyle{\begin{aligned}d_{1}&=0.530585-0.529412&=0.001173\\d_{2}&=0.530612-0.530585&=0.000027\end{aligned}}}{\dispystyle{\begin{aligned}d_{1}&=0.530585-0.529412&=0.001173\\d_{2}&=0.530612-0.530585&=0.000027\end{aligned}}}

    寻找满足以下关系的m,k值：

    {\dispystyle{\begin{aligned}{\frac{49k}{17m}}&={\frac{1173}{27}}\\{\frac{k}{m}}&