# Pantograph

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PANTOGRAPH is an instrument for making a reduced, an enlarged, or an exact copy of a plane figure. One of the simplest forms is represented in fig. 1. Four links of wood or metal are jointed together so as to form a parallelogram ABCS. On two sides BA and BC produced points P and P' are taken in a line with 5, so that the triangles PSA and SP'C are similar, as the sides of the fixed in a plane, and if P be made to describe any given figure, the point P' will describe another figure which is similar and similarly situated to the given one with S as centre of similitude, the ratio of similitude being PS SP'. Thus if the point S be fixed at S fig. 2, and if P be made to describe the figure ABCD, then P' will describe the similar figure A'B'C'D'. For the geometry of figures which are similar and similarly situated, compare " Similar Figures" under PROJECTION.

For practical working there is at P a steel tracer having a fine but not sharp point, and at P' a tracing pencil for drawing the copy, or sometimes- a sharp steel point for at once engraving the copy on a plate of metal. To obtain the smooth and steady motion of the instrument required for delicate work, a variety of different constructions are in use under various names, but all rest on the above principle that three points are kept in a line with their distances in a constant ratio. It will be noticed if any three points T, Q, Q' in a Hue be taken, as in fig. 1, these fulfil the conditions required, so that, for instance, T might be taken as the fixed point, and Q, Q' as the tracer and pencil.

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