Every segment bounded by a parabola and a chord is equal to four-thirds of the triangle which has the same base and equal height.
任意由抛物线和弦围成的弓形，面积等于同底同高三角形的四分之三。
当前 figure schema 只画点、直线、圆和角；这里用弦 Qq、顶点 P、直径 PV、切线 QT 和内接三角形骨架表示抛物线弓形。
Start from the base Qq and the diameter or tangent construction attached to the segment.
从底弦 Qq 以及与弓形配套的直径或切线构造开始。
Divide the base into equal parts and draw the corresponding diameters, chords and comparison triangles.
把底边等分，并作相应的直径、弦和比较三角形。
Use the previous conic and lever propositions to trap the segment between inner and outer sums.
用前面的圆锥曲线比例和杠杆命题，把弓形夹在内侧和外侧面积和之间。
If the segment were greater or less than 4/3 of the first triangle, the remaining small segments could be made smaller than the supposed excess, giving a contradiction.
若弓形大于或小于初始三角形的四分之三，就能把余下小弓形做到小于假设差额，从而推出矛盾。
In modern terms the area is the integral of a quadratic profile and equals 4/3 of the vertex triangle.
用现代话说，这是对二次曲线轮廓求积分，结果等于顶点三角形的 4/3；但阿基米德只用有限多边形和反证完成。
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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。