In the Timaeus, Plato uses an apparently redundant number of two right-angled elementary triangles - six scalene triangles and four isosceles triangles - to construct, respectively, the equilateral triangle and the square, the two faces that bound the solids underpinning the four genera of the world. I argue that these constructions involve a circle circumscribed about each face, and that the notion of "circularity", as well as the forms of uniformity and self-similarity may have inspired them. With Euclid's Elements in mind, I propose that analysis of the two faces as a function of the parameters of the circles circumscribing them and of the two elementary triangles answers questions that have long puzzled commentators of the Timaeus.
It's a World Made of Triangles: Plato's Timaeus 53B-55C
Paparazzo E
2015
Abstract
In the Timaeus, Plato uses an apparently redundant number of two right-angled elementary triangles - six scalene triangles and four isosceles triangles - to construct, respectively, the equilateral triangle and the square, the two faces that bound the solids underpinning the four genera of the world. I argue that these constructions involve a circle circumscribed about each face, and that the notion of "circularity", as well as the forms of uniformity and self-similarity may have inspired them. With Euclid's Elements in mind, I propose that analysis of the two faces as a function of the parameters of the circles circumscribing them and of the two elementary triangles answers questions that have long puzzled commentators of the Timaeus.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.