Constructing the triangular balance
A compass procedure for the equilateral (curved-sided) triangle of a three-weight balance
At the top a curved-sided equilateral triangle is drawn with three weights hanging from its points, forming what Leonardo calls the triangular balance for three loads. The long instruction below is a compass-and-straightedge construction to find the true size of that triangle: starting from a base line p o carrying the given weights, it raises perpendiculars b p and c o, then swings arcs from points m, n and r until their intersection t falls exactly on the perpendicular b p. Corrective steps tell the reader how to lengthen or shorten line m n and reopen the compass when the intersection falls short of or beyond that line.
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The triangular balance for three weights
The construction is meant to fix the true length of the arms of a triangular balance carrying three given weights, shown suspended from the three corners of the drawn triangle. The base line p o is laid down first and the given weights set upon it.
Compass construction of the triangle (p, o, b, c, m, n, r, t)
On the ends of line p o raise the two perpendiculars b p and c o. Setting the compass foot at m, draw line n S touching both perpendiculars; then from n draw a line to r. If the intersection of the two lines falls short of b p, add the missing space above n and reopen the compass until the intersection t lands on b p; if t falls outside b p, subtract the excess below n and narrow the compass accordingly.