The Simple Beam-Balance and a Furrow-Straightening Plough
Lever arms in ratio 8 to 1 balancing 64 pounds, and a sighted plough for straight furrows
The page opens with 'the nature of the simple beam and its lever', illustrated by a graduated steelyard whose short arm n m is eight times shorter than the long arm m o, from which a weight marked 63/64 hangs. Leonardo works the numbers: because n m is eight times stronger, a load of 8 pounds at o is balanced by 64 pounds, the opposite arm counting 8 pounds of its own weight reckoned at the middle. Below, a plough fitted with three sights (b and d on the beam, m on the yoke) is offered as a way to cut a straight furrow many miles long: when one ox lags, sight m twists out of the level line b to d, and the ploughman slows the faster ox to correct the line.
On this page
Steelyard: an 8-to-1 lever balancing 64 pounds
Because the arm n m is eight times shorter than the opposite arm m o, it can sustain eight times more weight. So if m o is loaded at o with 8 pounds, n m sustains exactly 64 pounds; the part of the rod on this side of the pole counts as 1 pound with 63 hung at the middle to make 64, while the opposite arm's own 8 pounds, reckoned at the middle, resists the opposing 64.
A plough sighted for a straight furrow of many miles
Sights b and d fixed on the plough-beam must line up with a third sight fixed low on the yoke at m. If one ox walks lower or faster than the other the furrow bends and sight m leaves the level line b to d; the ploughman, seeing the alignment fail, at once slackens the faster ox.
Keeping a long earth-line true by paired draught oxen
To drive a straight furrow many miles long the two oxen must walk exactly alike, since any difference in their pace or level throws the cut off the straight and out of the sighted level line, which the ploughman then corrects.