Weights and Levers; Perspective through a Pane of Glass
De ponderibus: a lever and cord, a nail-and-board balance, blows and impacts, and rules for depicting relief
Under the repeated heading De ponderibus ("On weights"), Leonardo sets out several mechanics problems. A lever a b pulled by a cord is shown to impose the same force at c as if it were tied at d; a nail a d driven into a board is balanced so its pivot falls at c; and further notes compare the swift or short motion of wheels and classify motion as natural, violent, or mixed. Between these he inserts two picture-making rules: how to portray a relief at night by placing a sheet of paper between object and light, and how perspective is simply sight through a transparent pane of glass on which the pyramids of vision are marked. A final note states that equal blows from equal heights do equal violence, penetrating more the smaller the striking part.
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Lever a b and cord: equal force at b or d
A wheel with a lever on its axle is drawn, a cord tied at b meeting the rim at c. If you pull on lever a b from point c, with the cord tied at b, you impose exactly as much force as if the lever were tied at d.
Nail a d in board c d balanced at pivot c
A long nail a is driven so only its tip enters the end d of a board resting on a box at c. If a b weighs as much as b c d, the nail and board remain in equilibrium, with the pivot at point c.
Motion of wheels; kinds of motion
A wheel thin in the middle and thick at the rim moves swiftly; one thick in the middle and thin at the rim has a short movement. Every motion is natural, violent, or mixed (natural-violent), as seen in the descending balance.
Portraying a relief at night
To draw a relief by artificial light, place a sheet of paper that is not too glossy between the relief and the light. This screening yields good portraying.
Perspective as sight through a pane of glass
Perspective is nothing but viewing a site behind a quite transparent sheet of glass, on whose surface all the things beyond are marked. These are carried by pyramids to the point of the eye, and the pyramids intersect the glass.
Equal blows do equal violence
Blows falling from equal heights and caused by equal weights necessarily do equal violence to their objects. The smaller the part of the weight that strikes, the more it penetrates.