Inclined beams with counterweights, levers and calculations
Treating an inclined beam by its lever arm; 5 x 10 = 50 and 16 x 8 = 128
Several inclined and horizontal beams are drawn with counterweights, pulleys and a protractor-like arc, annotated with values such as 1½, 4½, 16 and 128. Leonardo treats an inclined beam as if it were as long as the line a n, notes that a beam without a lever will not straighten along its line, and works a lever example in which the cord at c acts as if attached at o, its arm n o going five times into n c, so a pole carrying 10 yields 5 x 10 = 50. A small multiplication, 16 x 8 = 128, accompanies the beam values.
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An inclined beam reckoned by its horizontal line a n
The inclined beam is treated as if it were as long as the line a n, letting its effective length be read from the horizontal projection. It is annotated 1½, n a, r and 4½.
Without a lever, the beam will not straighten
Of one inclined beam with a counterweight Leonardo notes that, because it has no lever, it will not straighten along the line.
Lever arm n o into n c gives a 1-against-5 advantage
The cord attached at c acts as if attached at o; measuring how many times the lever n o goes into n c gives 1 against 5. At the middle of the simple pole, which carries 10, five times ten makes 50.
The multiplication 16 x 8 = 128
A short arithmetical working gives 16 times 8 equal to 128, the same value that labels the horizontal beam above.