内容 抛物线求积 · 05
Heath 1897 · preface paraphrase
Archimedes tells Dositheus that he first found the theorem by mechanics and then demonstrated it by geometry.
阿基米德告诉多西修斯：这个定理最初由力学方法发现，随后再用几何方法证明。
The theorem says that every segment bounded by a chord and a parabola is four-thirds of the triangle with the same base and equal height.
定理说：每个由一条弦和抛物线围成的弓形，都等于同底同高三角形的四分之三。
阅读顺序 context
Propositions 1-5 fix the conic geometry, 6-13 supply lever inequalities, 14-17 prove a first quadrature through tangents, and 18-24 give the cleaner inscribed-triangle exhaustion.
命题 1-5 固定圆锥曲线几何，6-13 给出杠杆不等式，14-17 先用切线三角形求积，18-24 再给出更干净的内接三角形穷竭证明。
The final proof is short only because the earlier machinery has already paid for every comparison.
最后证明看起来短，是因为前面的机器已经替每一次比较付过账了。
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