Raising weights by inclined plane, pulley, screw and capstan
Rules on rollers and oblique paths, and equating four weight-lifting instruments
This folio (176v) gathers rules on moving and raising weights with least force. A flat load set upon perfect balls resting on a perfect plane is drawn out most easily, and a weight raised by an oblique path reaches its height the more easily the longer the path along which it is pulled. Marginal diagrams (numbered 67, 68, 69) show a plank on three rollers, a plate with rollers and diagonal cords, and a drum from which ten cords labelled a b c d e f g h i K descend; a final rule equates the inclined plane, pulley-tackle, screw and capstan for lifting a weight with equal force.
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A load on rolling balls is easiest to move
No perfectly flat weight is drawn from its place more easily than one established upon perfect balls which are set upon a perfect plane. The rollers under the plank at the left illustrate the point.
The longer the oblique path, the easier the lift
A weight raised on high is the easier in its motion the longer its oblique path; and a weight raised by an oblique way reaches its height the more easily the longer the path by which it is pulled.
Which pair of cords makes the motion hardest
Beneath the drum diagram Leonardo asks which pair of cords will render the motion more difficult: a-K, or b-i, or c-h, or d-g, or e-f. The cords hang from a common drum in the sketch at the lower left.
Equating the four instruments for raising weights
To raise a weight with equal force by four instruments — the oblique path, the pulley-tackle, the screw and the wheel (that is, the capstan) — the cord of the tackle must equal the turns of the screw and the length of the oblique path.