Falling Water, Heavy Bodies, and the Balance
Descent toward the centre of the world, statics of the balance, and foreshortened letters
A densely worked opening on the science of weight. Folio 175v treats water falling from the crest of a wave and the general law that every heavy body moves only by descending toward the centre of the world by the shortest path, the heavier moving faster; a marginal spiral shows a weight circling the centre on a curved line. Folio 174r develops the statics of the balance under the heading "Mechanical elements," with lettered diagrams on equal and unequal weights, the angles at the balance-pole, and the obliquity of lines through the sphere of air. A closing note explains how to make foreshortened letters by cutting stencils and casting sunlight through them. Additional lettered and numbered diagrams on the sheet are noted but not transcribed.
On this page
Water falling from the crest of a wave
Water falls along any line from the summit of a wave to its base; its ruin has swifter impetus where the descent is less oblique and grows slower where more oblique. The rebounding foam breaks more where it meets a more resistant obstacle.
Every heavy body descends toward the centre of the world
No heavy body moves of itself unless it descends; the motion of every weight is toward the centre, and the greater weight is the faster. A weight descends most easily where it meets least resistance, by the shortest way, and since nothing is lower than the centre of the world, there it comes to rest. Nature brings forth its effects by the briefest means.
Mechanical elements of the balance
Under the heading "Mechanical elements," weights that resist one another equally in the balance have the fastenings of their cords equidistant from the centre of the world; therefore those fastenings are equidistant from that centre, and the angles made by the junction of the cords are equal.
Why weight b will not rest: it lies nearer the centre than a
In the lettered diagram the weight b is closer to the centre of the world than the weight a, so the balance will not stay still in the position drawn. Leonardo adds that the higher thing is the one more remote from the centre of the world.
Obliquity of lines drawn through the sphere of air
Imagine many straight lines with various obliquities drawn from a single point through the sphere of air to the opposite side: the more oblique line is the shorter, and the more oblique is the one more remote from the centre of the world. Since a heavy body stops only at the middle of such a line, its motion is briefest along the most oblique line.
Making foreshortened letters with projected sunlight
To make foreshortened letters, stretch the paper on a frame, draw and then cut out the letters, and let the sun's rays pass through those openings onto another stretched paper; then remake the missing angles.
