This drawing is a fairly accurate representation of Michael Maier's picture of The Philosopher's Stone on plate XXI of the Atalanta Fugiens (Circa 1617).

I have added a couple of additional features to show more of it's true Nature, namely:

A third Circle; A second Square; 4 lines; and 7 Symbols, these being of the 7 Planets/Metals of Alchemy. Also there are some measures indicating the relative values/sizes of each figure in the drawing.

The drawing is able to be created using only a compass and straightedge, no ruler is necessary.

The figure takes for it's basic value the radius used to draw the first small circle, for convenience this is taken to have the length of 1 unit.

This makes the constructed square 2 units in side length and width.

By drawing 2 lines from the 2 lower corners of the Square to where they meet at the middle of the top of the Square a Triangle is formed that has the same dimensions as the Square; 2 units high and 2 wide. Split the two vertical halves of the Triangle and move them apart so that they 'add' to the Square's sides and also copy the Triangle in the Square and move it on top of the Square and you then form a second Triangle that is 2 times the size of the first.

By taking the diameter of the Square as a new radius and placing the compass needle where the Circle and Square and Triangle meet at the top, a second Circle can be drawn which touches only 2 points of Maier's Triangle.

This Circle has a radius of 2 times Root 2 units, giving a diameter of 4 Root 2 or approximately 5.65685 units.

You may notice that the diameter of this large Circle passes along the uppermost part of the Square. This line 'divides' the Above, from the Below or the Spiritual realm from the Physical one.

You might also notice that there is a similar line just below it? This line passes through the actual centre of the large Triangle. By adjusting the width of the compass to the distance between the centre of the Triangle and any one point you can then draw a circle that completely en-compass-es the large Triangle. The centre of the Triangle is located 3 units up from the bottom of the Circle and Square and a single unit down from their tops: a 3 to 1 ratio.

What is unusual about this Circle is that it's diameter is exactly 5 units. We can then draw a second Square that exactly encompasses the Circle, being a 5 x 5 Square with an area of 25 units squared. I have elevated this Square by a single unit to place it where it lies in the drawing.

Why???

Well, it is now concentric with the large Circle and intersects that Circle with it's sides in 8 places.

Anyone care to guess what the area of that large Circle is?

The radius is 2 x Root 2 units long (approximately 2.82 units) making the area Pi times 2 Rot 2 squared or....

24.9832 units! The more mathematically inclined among you might also be able to see the true value is 8 Pi units squared (2 Root 2 squared = 8) which approximates to 25.1327 units squared. To get this value the sides of the Square would have to be extended by just 0.066 units at either end. This is 0.1325 of 1 per cent of the side length or 0.01325% longer than the original 5 square. This would be within the visual margin of error of a pencil line drawing.

In other words the large Circle is practically the same area (within an extremely small margin of error) as the 5 unit Square. We have squared the Circle!

It is also worth noting that the large Triangle and the small circle between them can show the Exact length of Phi units - 1.6180339887.... which can be used to complete the drawing with a perfect Pentagram/Pentagon.