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The present article investigates a passage of the Timaeus in which Plato describes the construction of the pyramid. Scholars traditionally interpreted it as involving that the solid angle at the vertex of the pyramid is equal, or nearly so, to 180°, a value which they took to be that of the most obtuse of plane angles. I argue that this interpretation is not warranted, because it conflicts with both the geometrical principles which Plato in all probability knew and the context of the Timaeus. As well as recalling the definitions and properties of plane angles and solid angles in Euclid’s Elements, I offer an alternative interpretation, which in my opinion improves the comprehension of the passage, and makes it consistent with both the immediate and wider context of the Timaeus. I suggest that the passage marks a transition from plane geometry to solid geometry within Plato’s account of the universe.

Viewing the World from Different Angles: Plato’s Timaeus 54E-55A