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数学 / 欧拉代数学 / Article 13 · Plus and minus together

第 13 条 · 加减混合

It is also easy to determine the value of similar expressions, in which both the signs + plus and - minus are found.

遇到同时含有 + 和 - 的类似式子,也很容易求出它们的值。

For example, 12 - 3 - 5 + 2 - 1 is the same as 5.

例如,12 - 3 - 5 + 2 - 1 等于 5。

We have only to collect separately the sum of the numbers that have the sign + before them, and subtract from it the sum of those that have the sign -.

我们只需把带 + 号的数先合成一组,把带 - 号的数也合成一组,再用前一组的和减去后一组的和。

Thus, the sum of 12 and 2 is 14; and that of 3, 5, and 1, is 9; hence 9 being taken from 14, there remain 5.

于是,12 和 2 的和是 14;3、5、1 的和是 9;从 14 中减去 9,剩下 5。

12 - 3 - 5 + 2 - 1 = (12 + 2) - (3 + 5 + 1) = 5

欧拉在这里已经开始按符号分类项。

  1. 正的一组:12 + 2 = 14。

  2. 负的一组:3 + 5 + 1 = 9。

  3. 14 - 9 = 5。