Constructing the quadrangular balance
Four weights hung in equal pairs on a circle, with a compass rule for its size
The central diagram shows a circle inscribed in a frame of vertical lines, with four weights hanging below and the letter labels of a full construction. Flanking columns of text explain the device: the right column states that weights hung on the quadrangular balance, however unequal, settle in equal pairs equidistant from the pole. The left column gives a compass rule for sizing the circle, drawing arcs b f, d o and r b from centres a and d so that each cuts one of the vertical lines m p, v K and t h to fix where each weight is attached, the fourth remaining on line a d at point c.
On this page
Weights hang in equal pairs about the pole
The weights fixed to the quadrangular balance, though of various amounts, come to rest in equal pairs, and those pairs stand equally distant from the pole of the balance.
Setting four weights on line a d within the circle
The four given weights are placed upon the line a d, and the circle that sustains them is divided into four equal parts of itself, r o f d, matched to the weights 3 2 5 1.
Compass rule to size the circle (lines t h, v K, x q, m p; arcs b f, d o, r b)
First draw the four lines above the weights, t h, v K, x q and m p. With the compass at d draw arc b f, giving the attachment of the least weight where it meets m p. From a draw arc d o, cutting v K at the next attachment, then arc r b from a again, cutting t h at the third; the fourth weight remains on line a d at point c.