标题： 对连续分数的评论，该分数展示了杰出的拉格朗日如何表示二项式幂 显示英文标题

标题： Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit

摘要： 欧拉给出了(1 + x)n的连分数表示，涉及1,3,5,7,...和n^2-1,n^2-4,n^3-9,...以及z的平方，其中x=2y且y=z/(1-z)。他在z=t sqrt(-1)时对这个连分数进行求值，对于“消失”的n以及无限大的n，并推导出log、arctan等的连分数。这篇文章是从欧拉的拉丁原文翻译成德语的。 显示英文摘要

摘要： Euler gives a continued fraction representation of (1 + x)n. involving 1,3,5,7,... and n^2-1,n^2-4,n^3-9,... and squares of z, for x=2y and y=z/(1-z). He evaluates this continued fraction at z=t sqrt(-1), for "vanishing" n, and for infinite n and deduces a continued fraction for log, arctan, etc. The paper is translated from Euler's Latin original into German.