Notebook on Mechanics and Natural Philosophy

The perpendiculars perpendiculars original: "perpendicoli"; here referring to plumb lines or weights hanging vertically. that hang from the cord k m at the ends k m, even though they are equal in weight and in length from the cord, will not create an equal descent original: "andata"; referring to the downward motion or path of the cord. of that cord k m toward the earth, because the cord k m is not equal Leonardo likely means the cord is not perfectly horizontal or uniform in its distribution..

The equal movement of the weights f m n depends on the cord f n because it is equal meaning horizontal or uniform..

How much more will weight m weigh than weight h, their arms being equal, as much as arm h b is longer than arm m b of the balance m h, which is imagined to be fixed at b. Leonardo is describing the basic principle of the lever: the force exerted depends on the distance from the pivot point (b).

The weights original: "biltre"; a non-standard term likely referring to the masses or components in the diagram. m d n b are equally distant from the center of their pendulums, namely m and n, because said pendulums are equal to each other; and said pendulums are equidistant to the pole o, whereby that pole is at equal distances from those weights.

Ⓐ Weight m shall be maintained by the perpendicular b c, which is equally distant from the center of its motion, namely from the pole o; therefore, such a pendulum will not move weight m either further up or further down.

Ⓑ Weight m shall be maintained by the pendulum m b, which m b is at the same distance from the pole o as is the pendulum m a; therefore, weight m shall not be pulled further up by one pendulum than by the other, because they give equal help to weight m to keep it aloft; thus, weight m will remain fixed in that position.

Ⓢ Weight m shall be maintained by the pendulums m n and m a, which are of equal length, keeping the cord r m at r m. If weight m were pulled by pendulum m a further up by 1, whereas it is not pulled by pendulum m n (which pulls by 1/2), pendulum m a is pulled more by 1/2; therefore, weight m remains supported 1/2 more by pendulum m a than by pendulum m n.

A horizontal balance beam with points labeled k, i, m. Weights f, m, n hang from the beam. At the ends k and m, there are small angle or crank mechanisms.

A horizontal beam with two circular pulleys at points f and n. A cord passes over the pulleys, supporting three weights f, m, and n.

A geometric diagram showing a quadrant with a central point o. A horizontal line o-b and a radial line o-f. A diagonal arm labeled m-h is shown. Small '+' signs mark points along the lines, likely indicating centers of gravity or force vectors.

A complex geometric quadrant diagram showing various arcs and intersecting lines labeled o, n, d, b, h, m, f. It illustrates the geometry of a swinging arm or pendulum.

A quadrant diagram with a vertical axis and an arc, showing a weight m hanging from two cords m-a and m-r. Labels o, b, a, m, r, s define the geometry.

How much will weight m be?
Weight m shall be one pound original: "libra"; a standard Renaissance unit of weight..
How much will be the tension original: "tiramento"; the force of pull. of the cord m a, and how much will be the tension of the cord m r?