Normally, dividing by smaller and smaller numbers gives you bigger and bigger answers.

通常，随的变小，得到的结果就会变大。

With some clever mechanical tricks, the Step Reckoner was also able to multiply and divide numbers.

利用一些机智的机械技巧 莱布尼茨乘法器也够乘和。

The word " residue" here is sort of an overdramatic way of saying remainder and mod means something like where the thing you divide by is.

这里的“residue”有点夸张，其实就是指余，而“mod”指的是。

This question of counting the number of lattice points a distance sqrt(N) away from the origin involves adding up the value of this simple function over all divisors of N. Now, remember why we're doing all of this.

计算距离原点sqrt(N)远的格点量这个问题涉及将这个简单函在N的所有上求和。 现在，记得我们为什么要这样做。