Squaring of lunes continued, with a theorem on the square
More crescent-and-portion equivalences, a side-versus-diagonal proposition, and two memoranda
The verso of the same strip carries a further multitude of small lune and portion figures, again testing equivalences between crescents, portions and their complements, with several diagrams flatly marked 'false'. One column states a genuine proposition: similar segments built on the side and on the diagonal of the same square stand in the ratio two to one. Interspersed among the constructions are two brief memoranda, one a reminder to have someone draw where the shells are at Monte Mario, the other the phrase 'It blows with force'.
On this page
Similar segments on the side and diagonal of a square
Leonardo states that similar circular segments, one made on the side and the other on the diagonal of the same square, will be double one to the other; and repeats the rule that among similar segments those are double one another of which one stands on the side and one on the diagonal of a single square. It is a correct consequence of the diagonal being the side times root two.
Squaring construction transferring a into a square (a, o, n, m, f)
Take a to the o and restore its value with n m, and you will have o n m f as a square equal to a o f. The step exchanges a curved portion for an equal rectilinear one to complete the quadrature.
Squaring a crescent (a, b, c, o, r)
Place, or rather restore, a to b r in c o as its value, and you will have b c o r equal to b a r. Another instance of converting a crescent-bounded area into an equal rectilinear figure.
Reminder to have the shells at Monte Mario drawn
A memorandum among the diagrams: have someone draw for you where the shells (nicchi) are at Monte Mario. It is a note to himself set apart from the surrounding geometry.
