Fraction Arithmetic and Methods of Moving Earth
Division computations and an ounces-to-pound example beside notes on excavating a ditch
Most of the sheet is filled with fraction arithmetic: a worked multiplication of 2/3 by 4/5, an ounces-to-pound proportion, and repeated long-division columns (the same computation appearing at the top and again on the right). The left margin turns to earthworks, praising continuous circular movements of workers who never stop while carrying soil on their shoulders, in barrows or by cart, and comparing the time each method wastes. A small diagram of a ditch, lettered a, b and n, shows how earth thrown along one line would pile up in a heap.
On this page
Multiplying fractions and the ounces-and-pound example
The centre works 2/3 times 4/5 as 8/15 and poses proportion questions such as what results if 1/12 were treated as 1/6. Leonardo illustrates with weight: over twelve ounces, if one ounce were two, six would make one pound, before beginning a further case with one and 1/6.
Long-division computations
A block of division work handles large numerators and denominators such as 1922/4877 and 288/2231, with the intermediate figures 6693, 8781, 2198 and 6951. The same computation is repeated at the top of the sheet.
Continuous earth-moving: shoulders, barrows and carts
The circular motions of moving earth are very useful because the men never stop, and are done in several ways: carrying soil on the shoulders, with barrows, or with carts. The shoulder-carrier first fills his tray on the ground and loses time hoisting it, whereas the man with the barrow loses no time.
Throwing earth from a ditch (a, b, n)
A sketch marks the positions of workers digging a ditch. The line n a could throw the earth along the line n b, but it would remain all in a single heap at b.