内容 向心力定律 · 13
Motte 1729 · reading base
Equal-area motion is Newton's geometric signature of a force directed to a center.
等面积运动是牛顿用来识别“力指向中心”的几何签名。
命题
Proposition 1 · law of areas shows how motion can be read by areas, tangents and departures from tangents.
命题 1 · 面积定律 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
Draw equal-time chords around a fixed point and compare the triangles they sweep.
围绕固定点画等时弦，比较相邻三角形扫过的面积。
解
If the inward impulses only change direction and not the radial area balance, equal areas follow.
若向内冲量只改变方向，不破坏径向面积平衡，等面积便随之成立。
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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