Circle and square: doubling, portions and proportion

The circle of the corners is double the circle of the sides

The circle that touches the four corners of a square is double the circle that touches its four sides; and dually, the square whose four sides touch a circle is double the square whose four corners touch that same circle.

232 portions of the greatest circle

Halving the greatest portion of the greatest circle and halving its 232 smallest portions leaves 116 as voids, the value of 116 minimal portions. The greatest circle is to have its circumference reduced by 6 portions together with the reduction of the 116.

Circle to circle as square to square

The proportion from circle to circle is as that from square to square, obtained by multiplying the diameter by itself. It reduces the ratio of the circles to the square of their diameters.

Two circles tangent to one square are double

Of two circles tangent to one square, the outer touching its four corners and the inner touching the middle of its four sides, the one is without doubt double the other.

Multiplications and doublings

Worked figures support the geometry: 12 times 7 makes 84, 15 times 6 makes 90, and 116 doubled makes 232. The columns tie the areas and portions to concrete numbers.

Rosette grids and interlace knots

Clusters of overlapping circles form hexagonal rosette (flower-of-life) grids at the top and lower centre, and small woven interlace knots are threaded among them.

In alto a destra, figura con:

Sotto la precedente, altra figura con:

Sotto la precedente, figura con:

A sinistra, dall'alto. Figura di cerchio con due cerchi minori e un bisangolo:

Più in basso:

Figura di cerchio con iscritto il lato di un esagono:

Figura di settore di cerchio colle lettere:

Figura di cerchio iscritto e circoscritto fra due quadrati:

Figura di quadrato iscritto e circoscritto tra due cerchi:

Tra le due figure precedenti:

Operazioni aritmetiche:

Upper right, a figure with:

Below the previous, another figure with:

Below the previous, a figure with:

On the left, from above. A figure of a circle with two smaller circles and a lens-shaped (two-angled) figure:

Further down:

A figure of a circle with the side of a hexagon inscribed:

A figure of a circular sector with the letters:

A figure of a circle inscribed and circumscribed between two squares:

A figure of a square inscribed and circumscribed between two circles:

Between the two preceding figures:

Arithmetical operations: