Decomposing the Square: Gnomon and Supplements
The diameter, the parallelograms about it, and their supplements
A column of small figures in the inner margin decomposes a parallelogram (here a square) step by step: the diagonal (diameter) that divides it, a parallel added to the base, and a parallel added to a side producing a gnomon whose inner corner meets the diagonal. Leonardo names the parts, calling the figures set about the diameter and 'transfixed' by it, and the 'third parallelograms' the supplements of those about the diameter. He also records the common notion that if from two equal things an equal thing is removed the remainders are equal, and adds an elongated parallelogram showing the same construction.
On this page
The diameter divides the square
Beside the second figure Leonardo notes that the diameter (the diagonal) divides the square into two equal parts.
Parallelograms about the diameter and their supplements
The parallelograms positioned about the diameter are said to be transfixed by it, while the 'third parallelograms' are called supplements — that is, the supplements of those placed about the diameter. A gnomon is formed whose inner corner meets the diagonal.
A common notion: equals removed from equals
Below the smaller view of the square, with one supplement removed, Leonardo writes the common notion that if from two equal things an equal thing is removed, the remainders too are equal.