Ideas of Euclid, by Theme

[Greek, 330 - 270 BCE, Born in Alexandria. Studied at the Academy in Athens. Died in Alexandria.]

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
An assumption that there is a largest prime leads to a contradiction
6. Mathematics / A. Nature of Mathematics / 3. Numbers / m. One
A unit is that according to which each existing thing is said to be one
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / a. The Infinite
Postulate 2 says a line can be extended continuously
6. Mathematics / B. Foundations for Mathematics / 2. Axioms for Geometry
Modern geometries only accept various parts of the Euclid propositions
Euclid's parallel postulate defines unique non-intersecting parallel lines
Euclid needs a principle of continuity, saying some lines must intersect
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / b. Greek arithmetic
Euclid's common notions or axioms are what we must have if we are to learn anything at all