Constructing a Curve with Movable Templates
Making a thin template in the shape r h a c and sliding it along to lay out a long curved line.
Leonardo sets out a method for tracing a long curve using a lettered master figure a c b d and a thin cut template. He proposes cutting a board (tavoletta) to the profile r h a c, then repositioning it step by step so that side r a comes to lie on h c, and continuing to swap templates until the whole curve is drawn. The upper and lower diagrams show curves with radiating construction lines and small semicircles, keyed to the letter labels in the text.
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A hundred-braccia master figure a c b d
Your master template is to be the figure a c b d, made a hundred braccia long, with a c equal to one finger's width. The two lines a b and c d are followed as far as r h, and a thin board is cut in the very shape r h a c.
Sliding and swapping the templates
The cut board is then shifted into position h c K n, placing side r a onto h c so that side h c comes to rest on K n. Better still, two like boards are used, set in contact and exchanged in turn to the end; such boards should be no less than two braccia long.
Equal angles and the departing curve b m
Angle b is made equal to angle d, and the upper angles at a and c equal to each other; side a b equals side c d and is set perpendicular on line b n. As angle d touches that line, it lifts away from line b m, giving the rule for the curved line b m that has parted from the straight b n.
