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Axiom: 1.1: Straight Line Determined by Two Distinct Points

(Postulate 1 from Book 1 of Euclid’s “Elements”)

Let it have been postulated to draw a straight line from any point to any point.

Modern Formulation

Two distinct points $$A$$ and $$B$$ always completely determine a straight line $$a$$.

Instead of saying “is determined”, we also say that

• $$a$$ “goes through” $$A$$ and $$B$$,
• $$A$$ and $$B$$ “lie” on $$a$$.

| | | | | created: 2014-06-14 20:33:50 | modified: 2019-03-23 08:20:05 | by: bookofproofs | references: [626], [628], [6419]

1.Explanation: Why did Euclid postulate the axiom of straight line determined by two points?

CC BY-SA 4.0

[626] Callahan, Daniel: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014