3 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 14280 | The probability of two events is the first probability times the second probability assuming the first [Bayes] |
| Full Idea: The probability that two events will both happen is the probability of the first [multiplied by] the probability of the second on the supposition that the first happens. | |
| From: Thomas Bayes (Essay on a Problem in the Doctrine of Chances [1763]), quoted by Dorothy Edgington - Conditionals (Stanf) 3.1 |
| 3015 | The virtue of man is thoughtful foresight of future events [Chilo, by Diog. Laertius] |
| Full Idea: A foresight of future events, such as could be arrived at by consideration, is the virtue of man. | |
| From: report of Chilo (poems (frags) [c.490 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.4.1 |