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.
Gist of Idea
To understand a triangle summing to two right angles, we need to know the essence of a line
Source
Aristotle (De Anima [c.329 BCE], 402b18)
Book Reference
Aristotle: 'The Basic Works of Aristotle', ed/tr. McKeon,Richard [Modern Library Classics 2001], p.536
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?