The preceding trapezium inequality remains true in the right-angle limiting case.
前一梯形不等式在直角特例中仍然成立。
AOB 是以 O 为支点的水平杠杆;右侧三角形或梯形悬挂在 OB 上,左侧面积 P 与它平衡。
Place AOB as a lever supported at O and hang the given triangle or trapezium on the right side.
把 AOB 看作以 O 为支点的杠杆,并把给定三角形或梯形悬在右侧。
Replace the suspended figure by an equal weight acting through its center of gravity.
把悬挂图形等效为经过重心的一份重量;这一换位不改变平衡。
Compare the lever arms. The ratio of arms becomes the ratio between the suspended figure and the balancing area.
比较两侧力臂;力臂之比转化为悬挂图形与平衡面积之比。
The required equality or inequality follows from where the center line falls between the marked points.
重心竖线落在相应标记点之间,于是得到本命题需要的等式或不等式。
These mechanical propositions are not a modern force diagram for its own sake; they convert centers of gravity into area inequalities used later.
这些机械命题不是孤立的力学图,而是把重心和平衡换成后面需要的面积不等式。
不看完整证明,说明“命题 11 · 直角特例的梯形平衡”这一命题的已知、要证和关键比较对象。
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- 先把几何对象命名,再说它们之间要比较什么量。
- 穷竭法命题要特别留意“若大于”和“若小于”两边。