Triangular-Mouthed Bombard and Graded Thrown Weights
A rejected cannon design, balls of graded weight, and the declension of 'alter'
A mixed working page carrying a drawing of a bombard with a triangular mouth and, below, a cluster of balls of differing diameter, with smaller sketches at the right and lower margins. Leonardo rejects the triangular-mouthed design, noting that the coarse rush of fire in the wide part of the bore acts 'by the cube root.' A proportion problem follows on balls that must be of the same shape and material: dividing a ten-pound weight into pieces of one, two, three, and four pounds and firing them in equal time, he asks what proportion the distances of their first impacts will have, answering that the distances follow the proportion of the weights. The upper text is a Latin declension of the pronoun 'alter,' and a left-margin note records that Antonio de' Risi sits on the Council of Justice.
On this page
Why a triangular-mouthed bombard is rejected
Beside the drawing of a cannon labelled 'bombard with a triangular mouth,' Leonardo judges the design not good, because the coarse rush of the fire in the wide part of the bombard acts 'per radice cuba' (by the cube root). A heading 'Of the practice' follows.
Graded weights thrown in equal time
The balls must be of the same shape and equal material. If a power of 100 throws 10 pounds 100 braccia, then 11 pounds would go 99 braccia for excess weight and 9 pounds less than 100 for too much lightness. Dividing the 10 pounds into pieces of 1, 2, 3, and 4 pounds and throwing them in the same time, he asks what proportion the distances of their first impacts will have.
The distances follow the weights
Leonardo gives the answer to the graded-weight problem: the proportion of the three distances will be the same as the proportion of the three weights stated before.
Declension of 'alter' (the other of two)
Under the heading 'the other, understanding the one,' the pronoun is begun: nom. alter altera alterum, gen. alterius, dat. alter[i], with the accusative starting to be set down.