32 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] |
| 8143 | Self is the rider, intellect the charioteer, mind the reins, and body the chariot [Anon (Upan)] |
| 8147 | We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)] |
| 8155 | Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)] |
| 8142 | The wise prefer good to pleasure; the foolish are drawn to pleasure by desire [Anon (Upan)] |
| 8151 | Let your teacher be a god to you [Anon (Upan)] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 8153 | By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)] |
| 8154 | Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 8148 | Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)] |
| 8144 | Brahman is the Uncaused Cause [Anon (Upan)] |
| 8152 | Earth, food, fire, sun are all forms of Brahman [Anon (Upan)] |
| 8156 | The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)] |
| 8157 | A man with desires is continually reborn, until his desires are stilled [Anon (Upan)] |
| 8159 | Damayata - be self-controlled! Datta - be charitable! Dayadhwam - be compassionate! [Anon (Upan)] |
| 8145 | Those ignorant of Atman return as animals or plants, according to their merits [Anon (Upan)] |
| 8149 | Charity and ritual observance distract from the highest good of religion [Anon (Upan)] |
| 8158 | Do not seek to know Brahman by arguments, for arguments are idle and vain [Anon (Upan)] |
| 8146 | The immortal in us is the part that never sleeps, and shapes our dreams [Anon (Upan)] |
| 8150 | The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)] |