本帖最后由 也和话 于 2011-8-2 22:49 编辑
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““如何证明三角形任意两边和大于第三边”
最佳答案
两点之间直线最短(这个是公理),所以两边和大于第三边啊
http://zhidao.baidu.com/question/22641635.html
所以先有两点之间直线最短这条公理,从而可推导出三角形任意两边和大于第三边。而不是用三角形任意两边和大于第三边来证明两点之间直线最短。”
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欧几里得的《几何原本》的五个公设:
1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
他当作大家都知道“直线”是什么,根本就没有给直线下定义。
他的“三角形任意两边和大于第三边”证明在 Book I, postulate 20. |