21 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] |
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] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |