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Ideas of Euclid, by Text
[Greek, 330  270 BCE, Born in Alexandria. Studied at the Academy in Athens. Died in Alexandria.]
290BCE

Elements of Geometry


p.1

9603

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


p.2

8623

Proof reveals the interdependence of truths, as well as showing their certainty [Frege]


p.21

22278

Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter]


p.24

8673

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


p.55

6297

Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Resnik]


p.87

8738

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


p.106

13907

If you pick an arbitrary triangle, things proved of it are true of all triangles [Lemmon]


p.183

10250

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


p.259

10302

Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Bernays]


p.404

14157

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

7 Def 1

p.194

9894

A unit is that according to which each existing thing is said to be one

72a17

p.149

1600

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