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

通常，随着除数变小，结果就会变大。

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

利用一些机智机械技巧 莱布尼茨乘法器也够乘数和除数。

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“residue”有点夸张，其实就余数，而“mod”除数。

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)远格点数量这个问题涉及将这个简单函数在N所有除数上求和。 现在，记我们为什么要这样做。