内容 向心力定律 · 16
Motte 1729 · reading base
Force is read from how far the orbit falls away from the tangent in a small time.
力从轨道在极短时间内偏离切线的距离里读出来。
命题
Proposition 3 · measuring force geometrically shows how motion can be read by areas, tangents and departures from tangents.
命题 3 · 用几何量读力 说明运动可以由面积、切线和切线偏离量来读。
读法检查 worked example
题
Compare the tangent continuation with the actual curved path.
比较切线延长和真实曲线路径。
解
The departure is small, but its ratio to the squared time is the force clue.
偏离很小，但它和时间平方的比例给出力的线索。
互链 context
与阿基米德穷竭法 archimedes-selections/overview、极限思想史 math-meta/topic-limit-history、微积分发明史 math-meta/topic-calculus-invention、柯西严格化 cauchy-cours/overview 和牛顿代数面 newton-arithmetica/overview 对读。
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