Twelve transformation problems for a solid board
Shorten, lengthen, thicken, thin, widen, narrow — how does each dimension respond?
This closely written page, in Leonardo's mirror script, sets out a systematic table of twelve problems on transforming a solid board without changing its volume. Each numbered case fixes one of the three dimensions - length, width, thickness - alters a second, and asks by how much the third responds. A closing rubric, 'Modo di proporre' (way of proposing), gives the standard wording of the exercise. The sheet belongs to the notebook's studies on the measurement of solids.
On this page
Twelve paired transformations of a solid board
A numbered list of twelve problems treats a wooden board (tavola) as a solid: each case fixes one dimension, alters a second, and asks how much a third changes - for example, shorten without changing the thickness and ask how much it widens. Because the transformations preserve the body's volume, the questions are exercises in the measurement of solids.
Modo di proporre: how to frame the problem
A closing rubric, 'Way of proposing,' gives the standard form of the exercise: if the given board shortens to a stated limit without change of width, how much will it thicken? It casts the transformations as proportional problems in a constant-volume board.