20 ideas
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| 10247 | We have no adequate logic at the moment, so mathematicians must create one [Veblen] |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| 7544 | Many people imagine that to experience is to understand [Goethe] |
| 7541 | Man never understands how anthropomorphic he is [Goethe] |
| 7543 | We gain self-knowledge through action, not thought - especially when doing our duty [Goethe] |
| 7540 | Beauty is a manifestation of secret natural laws [Goethe] |
| 7538 | The happiest people link the beginning and end of life [Goethe] |
| 7542 | The best form of government teaches us to govern ourselves [Goethe] |
| 7539 | To get duties from people without rights, you must pay them well [Goethe] |