This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

Let a b (Fig. 369) be the chord, and c d the height of the segment. Secure two straight-edges, or rulers, in the position c e and c f, by nailing them together at c, and affixing a brace from c to f; put in pins at a and b; move the angular point c in the direction acb; keeping the edges of the triangle hard against the pins a and b; a pencil held at c will describe the arc acb.

Fig. 369.

A curve described by this process is accurately circular, and is not a mere approximation to a circular arc, as some may suppose. This method produces a circular curve, because all inscribed angles on one side of a chord-line are equal (Art. 356). To obtain the radius from a chord and its versed sine, see Art. 444.

If the angle formed by the rulers at c be a right angle, the segment described will be a semi-circle. This problem is useful in describing centres for brick arches, when they are required to be rather flat. Also, for the head hanging-stile of a window-frame, where a brick arch, instead of a stone lintel, is to be placed over it.

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