Ideas from 'Elements of Geometry' by Euclid [290 BCE], by Theme Structure

[found in 'Euclid's Elements of Geometry (Gk/Eng)' by Euclid (ed/tr Fitzpatrick,Richard) [Lulu 2007,978-0-6151-7984-1]].

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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
Euclid needs a principle of continuity, saying some lines must intersect
Euclid's parallel postulate defines unique non-intersecting parallel lines
Modern geometries only accept various parts of the Euclid propositions
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