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| 16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
| Full Idea: In mathematics it is useful for the understanding of the property of the equality of the interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and the plane. | |
| From: Aristotle (De Anima [c.329 BCE], 402b18) | |
| A reaction: Although Aristotle was cautious about this, he clearly endorses here the idea that essences play an explanatory role in geometry. The caution is in the word 'useful', rather than 'vital'. How else can we arrive at this result, though? |