Balances, a Beam's Load, and the Proportions of a Head
Weight-distribution problems, two wheels, an image-in-air note, and a youth's head drawn within arcs
A working page dominated by problems of weight and support. A series of balances and loaded beams pose questions about how a hundred-pound ball's weight divides between pivot b and support a, how much of a three-hundred-pound beam e d is carried at c and d, and how a two-hundred-pound beam f g loads its supports h and m; a further sketch contrasts two wheels, S with a large axle and t with a small one. Alongside the mechanics are a multiplication (28 × 3 = 84) and a note that every body fills the surrounding air with its own image along infinite radiant lines. Near the right margin, a fine profile of a youth is constructed within circular arcs centred on the ear and forehead.
On this page
Balance: how much do pivot b and support a bear?
A balance is blocked at a and pivots at b, with a hundred-pound weight f hung from the free end. If ball f weighs one hundred pounds, how much of it will pivot b feel, and how much will support a feel?
Beam e d weighing 300 pounds on supports c and d
A piece of wood e d rests on a support near its middle at c and at its end d. If it weighs three hundred pounds, how much does c support, and how much does d support?
Beam f g weighing 200 pounds on supports h and m
A piece of wood f g rests diagonally on two supports, h under end f and m under end g. If it weighs two hundred pounds, how much of its weight will h bear, and how much will m bear?
Two wheels: small axle S versus large axle t
Two wheels are drawn, the upper S with the larger axle and the lower t with the smaller. What difference is there between the effect of the wheel with the small axle and that of the wheel with the large axle?
Profile of a youth constructed within circular arcs
A profile of a young man is fitted into an arc of a circle centred on the midpoint of the ear, that midpoint linked to the underside of the nose by another arc of the same radius centred at the top of the forehead. The principal features touch the arcs at nearly regular, faintly marked intervals.
Every body fills the air with its image
Every body fills the surrounding air with its image, and this image is entire throughout and entire in each part. The air is filled with infinite straight, radiant lines that intersect and interweave without blocking one another, each representing the true form of its cause.