
Augustus De Morgan (1806-1871), British mathematician and logician, might have written later:
"The moving power of mathematical invention is both reasoning and imagination."
Here's a description of the Three Points design, perhaps a reflection of "sanitas cyclometricus" (2013 coinage to complement De Morgan's "morbus cyclometricus")
and an example of the power of reasoning and imagination:

Inscribe a square within a circle so that two opposite sides are horizontal. Draw a straight line connecting the lower right corner with the upper left corner. Imagine the clockwise rotation* of the leftmost right triangle, keeping the left side length constant, the right side at 135 degrees and the horizontal side at 180 degrees.

The length of the horizontal side always defines the side of a square. And when a certain scalene triangle is created, this side defines the side of the square of the circle, visually proving that only 3 points on a circle are required to draw its square.
* The triangle does not actually "rotate": the angle of the left side changes from 90 degrees to 45 degrees (close to 72.597 when the scalene triangle is created).
To evaluate the scalene triangle, let the circle's diameter = 2000000 units; length of left side = square root of 2 x 1000000 and length of horizontal side
= square root of Pi x 1000000 (proof that transcendental Pi can be represented by a geometric object

).
Rod