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数学 / 庞加莱三卷科学哲学 / The Non-Euclidean Geometries

卷一 3 · 非欧几何

Non-Euclidean geometry makes geometry a choice of convenient structure rather than a single visual necessity.

非欧几何让几何成为方便结构的选择,而不是唯一视觉必然。

Geometry is not destroyed when Euclid's postulate changes; it becomes more self-aware.

欧氏公设被替换时,几何不是被摧毁,而是更清楚地意识到自己的前提。

The Non-Euclidean Geometries should be read as a question about how science stabilizes its objects.

卷一 3 · 非欧几何 要读成一个问题:科学怎样让自己的对象稳定下来。

Why should this chapter be read after Lobachevsky?

为什么这章要接在罗巴切夫斯基之后读?

The originals show the mathematics; Poincare explains the epistemology of choosing a geometry.

原作展示数学,庞加莱解释选择一种几何的认识论。