Water rebound, a semicircle problem, and Salai's expenses
Leonardo on the rebound of colliding waters, beside geometry, arithmetic puzzles and a household expense list
The right leaf (f. 147r) argues that the rebound of water can never equal the incident motion and that, when two waters collide, the weaker makes the greater rebound, so the rebounds stand in inverse proportion to the colliding powers. The left leaf (f. 148v) mixes a geometry problem on dividing a semicircle between parallel lines, a run of arithmetic exercises on fractions and parts of numbers, and, at top left, a day's food expenses in another hand, probably Salai's. Both leaves carry figures with letters, a large red-chalk drawing with numbers, and a row of decorative pen flourishes at the foot of f. 147r; some of this further material is untranscribed.
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The rebound of water never equals its incident motion
Leonardo sets down for debate that when two simple motions oppose one another, the more powerful better fulfils its natural intent. He concludes that the motion of water's rebound (balzo) can never equal the incident motion, so that the marked b s cannot equal a s and falls short of its due by as much as the object yields.
Dividing a semicircle between two parallel lines
A problem asks for three-quarters of a semicircle taken between two parallel lines. As a general rule Leonardo extracts four 'pyramids' (triangles) from the circle, the remainder giving the quantity sought.
Finding parts and fractions of numbers
A sequence of fraction exercises: take a number of which 4 is a quarter, namely 16, then find the fifth of 20, the sixth of 24, and so on. Subtracting 4 from 8, 12 and 16 leaves the half, two-thirds and three-quarters respectively.
A day's food expenses (Tuesday)
In another hand, probably Salai's, a Tuesday's outlay is itemised for bread, meat, wine, fruit, soup and salad in soldi and denari, with the day's figure given as 32.