Circle theorems: chords, secants, tangents and Pythagoras
The internal-times-external segment rule, worked as 16 x 12 = 192, with figures of tangents and the Pythagorean theorem
The page states a rule for lines cutting a circle: for each line, its internal part multiplied by its external part yields the same product as the others, illustrated by four secants where 16 and 12 give 192. Below, a series of figures shows a circle with two tangents in three variants, a figure of the theorem of Pythagoras, and a circle with parallel tangents. One block is noted as drawn upside-down (capovolto).
On this page
Equal products of the internal and external parts of secants
For each line drawn across the circle, its internal part multiplied by its external part gives a product equal to that of the other lines. Four secants illustrate the equal-product rule.
The product 16 x 12 = 192
The numerals accompanying the four secants give 16 and 12 with the product 192. They confirm the equal-product rule numerically.
Tangent figures and the Pythagorean theorem
The lower half of the leaf carries three figures of a circle with two tangents, a figure of the theorem of Pythagoras, and a circle with parallel tangents.