Dividing a Line, Rectangle and Square into Numbered Parts
Plane figures partitioned into cells that sum to 12, 48 and 144
On this leaf Leonardo studies the division of geometric figures into numbered parts. A straight segment is split into 4 and 8 (summing 12); a rectangle is partitioned into cells of 16 and 32 (total 48); and a square is quartered into cells of 32, 32, 64 and 16 (total 144). The exercise ties the plane figures to the arithmetic of their subdivided areas. The figures are drawn partly in pencil and gone over in pen.
On this page
A straight line divided 4 and 8, summing 12
A straight segment is divided into two parts marked 4 and 8, and their sum 12 is written beneath it. The figure treats the division of a line into numbered, proportional parts.
Rectangle partitioned into cells 16 and 32 (total 48)
A rectangle with sides 4 and 8 (and 12 along its length) is split into two cells bearing the products 16 and 32, whose sum 48 is noted at the side. Leonardo works out how the area subdivides arithmetically as the sides are partitioned.
Square partitioned into cells totalling 144
A square is quartered and its cells labelled 32, 32, 64 and 16, with the total 144 written below. The exercise carries the same numbered subdivision from the rectangle over to the square.