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1·The exact solution of the period is got by using the first kind of complete elliptic integral.

应用第一类完全椭圆积分求出了非线性振动周期的精确解。

2·This paper discusses Xia's achievements on the integral problem about quadratic curve, some of which were similar to modern elliptic integral and surpassed the level of Dai-wei-ji.

夏鸾翔是晚清较早研究微积分的中算家，据其《致曲术》、《万象一原》，可知他在二次曲线求积问题上得到了比较全面的成果，有的已超过《代微积拾级》，某些成果近似近代的椭圆积分。