Kepler's second law becomes a theorem about central deflection and equal triangular areas.
开普勒第二定律在牛顿这里变成关于中心偏折和相等三角形面积的定理。
Equal-time triangles around S model Kepler's second law before the polygon becomes a curve.
围绕 S 的等时三角形先表达开普勒第二定律，再由折线极限变成曲线轨道。
Kepler second law in Newton's geometry shows how motion can be read by areas, tangents and departures from tangents.
命题 1 展开 · 开普勒第二定律的几何证明 说明运动可以由面积、切线和切线偏离量来读。
Why does a central impulse preserve the area swept from the center?
为什么指向中心的冲量会保留从中心扫过的面积？
The impulse is radial, so it does not add sideways area; taking the equal-time polygon smaller gives the continuous law.
冲量沿径向，不额外制造横向面积；把等时折线不断细分，就得到连续轨道的面积定律。
Break the curved orbit into equal-time chords around the center S.
先把曲线轨道拆成围绕中心 S 的等时小弦。
Without central impulse, the body would continue along the tangent and sweep an equal triangle.
若没有中心冲量，物体会沿切线继续走，并扫出相等三角形。
The impulse is radial toward S, so it shifts the point along a line through S and preserves the swept area.
冲量沿 S 的方向，把点移到通过 S 的直线上，因此保留扫过的面积。
Let the equal-time chords become indefinitely small; the polygonal area law becomes Kepler's continuous law.
令等时小弦无限变小，折线面积定律就成为开普勒连续面积定律。
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。