Two ways to dig a ditch: a labour-and-earth calculation
One man throwing earth back to the bank versus six men passing it across, worked out shovelful by shovelful
A long word-problem in earth-moving, illustrated by a plan of a ditch with six workmen (lettered c b a) and surrounded by dense columns of arithmetic. Leonardo compares two methods of excavating a shovel-wide trench across a ditch: a single man who works backward from the bank and repeatedly carries earth to it, and a team of six who divide the width into equal spaces and pass the earth from one to another. He reduces the first man's labour to spadefuls (each 1/6 of a braccio thick) and sums the outward and return carries to reach 5466 braccia done in 1822 units of time, that is one hour and 371/540, equal to 216 spadefuls or 36 barrows and roughly one and 4/5 cases. An inverted sketch of squares built on the sides of a 3-4-5 triangle sits at the foot of the sheet.
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Two excavation methods compared (workmen c b a)
A plan of the ditch shows workmen lettered c b a. The first labourer digs backward from a bank, throwing all his earth onto it until he is 6 braccia away, then carries earth forward across the remaining 30 braccia; the second method uses six men spaced equally across a 36-braccia width who pass the earth from one to another to the opposite bank.
Reducing the first man's labour to spadefuls and time
Taking each spadeful as 1/6 of a braccio, Leonardo counts 180 spadefuls over 30 braccia, takes the mean of 1 to 180 as 90, adds 1 to get 91, and computes 91 times 180 = 16380 sixths. Doubling for the return carries gives 32760 sixths, which divided by 6 yields 5460 braccia; with the first 6 braccia added the total is 5466, done in 1822 units of time, that is one hour and 371/540.
Columns of calculation and the carried loads
Several columns of figures work the division and multiplication behind the result, arriving at 216 spadefuls carried, which at 6 spadefuls per barrow make 36 barrows and, at 20 barrows per case, one and 4/5 cases. A top note frames the question of how much is carried per hour.
Squares on the sides of a 3-4-5 triangle
At the foot of the sheet, drawn upside down relative to the text, is a construction of squares built on the sides of a right triangle labelled 3 4 5. It illustrates the Pythagorean relation among the squares on the triangle's sides.