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数学 / 欧拉代数学 / Article 15 · Letters with plus and minus

第 15 条 · 字母式也按符号计算

It will not be attended with any more difficulty if, in order to generalise these operations, we make use of letters instead of real numbers.

如果为了把这些运算一般化而用字母代替实际数字,也不会增加任何困难。

It is evident, for example, that a - b - c + d - e, signifies that we have numbers expressed by a and d, and that from these numbers, or from their sum, we must subtract the numbers expressed by the letters b, c, e, which have before them the sign -.

例如,a - b - c + d - e 显然表示:我们有 a 和 d 所代表的数;从这些数,或者说从它们的和中,必须减去由 b、c、e 表示的那些数,因为它们前面带着 - 号。

a - b - c + d - e = (a + d) - (b + c + e)

字母式和数字式一样,先按符号分组。

  1. 带 + 的项:a、d。

  2. 带 - 的项:b、c、e。

  3. 所以可看成 (a + d) 减去 (b + c + e)。