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 2007,9780615179841]].
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6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
9603

An assumption that there is a largest prime leads to a contradiction [Brown,JR]

6. Mathematics / A. Nature of Mathematics / 3. Numbers / m. One
9894

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
8738

Postulate 2 says a line can be extended continuously [Shapiro]

6. Mathematics / B. Foundations for Mathematics / 2. Axioms for Geometry
8673

Euclid's parallel postulate defines unique nonintersecting parallel lines [Friend]

10250

Euclid needs a principle of continuity, saying some lines must intersect [Shapiro]

14157

Modern geometries only accept various parts of the Euclid propositions [Russell]

6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / b. Greek arithmetic
1600

Euclid's common notions or axioms are what we must have if we are to learn anything at all
