### 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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###### 2. Reason / E. Argument / 6. Conclusive Proof
 8623 Proof reveals the interdependence of truths, as well as showing their certainty [Frege]
###### 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
 13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Lemmon]
###### 6. Mathematics / A. Nature of Mathematics / 2. Geometry
 6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Resnik]
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of 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. Nature of 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 / 5. The Infinite / a. The Infinite
 8738 Postulate 2 says a line can be extended continuously [Shapiro]
###### 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
 10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Bernays]
 8673 Euclid's parallel postulate defines unique non-intersecting 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 / 5. 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 [Roochnik]