内容 物体运动的引理 · 05
Motte 1729 · reading base
Curved areas are compared by rectilinear pieces whose errors can be made negligible.
曲边面积靠直边小片比较，关键是误差能被压到可忽略。
命题
Lemma 4 · curvilinear and rectilinear figures gives a geometric way to compare quantities at the edge of vanishing.
引理 4 · 曲边图形与直边近似 给出一种几何方法，用来比较即将消失的量。
读法检查 worked example
题
Replace a small curved sector by a triangle and track the difference.
把一个很小的曲边扇形换成三角形，并追踪差额。
解
The replacement is allowed only because the difference disappears faster than the controlled comparison.
替换成立，是因为差额比正在控制的比较更快消失。
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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