REDUCTION

REDUCTION of a figure, design, or draught, is the making a copy thereof, either larger or smaller than the original; still preserving the form and proportion. The great use of the proportional compasses is the reduction

of figures, &c. whence they are called compasses of reduction. See the article COMPASS.

There are various methods of reducing figures, &c. the most easy is by means of the pentagraph, or parallelogram; but this hath its defects. See the article PENTAGRAPH.

The best and most usual methods of reduction are as follow: 1. To reduce a figure, as ABCDE (fig. 1.), into a less compass. About the middle of the figure, as $\backslash infty$, pitch on a point, and from this point draw lines to its several angles A, B, C, &c. then drawing the line $ab$ parallel to AB, $bc$ parallel to BC, &c. you will have the figure $abcde$ similar to ABCDE.

If the figure $abcde$ had been required to be enlarged, there needed nothing but to produce the lines from the point beyond the angles, as $\backslash infty\; D$, $\backslash infty\; C$, &c. and to draw lines, viz. DC, CB, &c. parallel to the sides $dc$, $cb$, &c.

2. To reduce a figure by the angle of proportion, suppose the figure ABCDE (fig. 2.) required to be diminished in the proportion of the line AB to $ab$ (fig. 3.) draw the indefinite line GH (fig. 4.), and from G to H set off the line AB. On G describe the arch HI. Set off the line $ab$ as a chord on HI, and draw GI. Then with the angle IGH you have all the measures of the figure to be drawn. Thus to lay down the point $c$, take the interval BC, and upon the point G describe the arch KL. Also on the point G describe MN; and upon A, with the distance MN, describe an arch cutting the preceding one in $c$, which will determine the side $bc$. And after the same manner are the other sides and angles to be described. The same process will also serve to enlarge the figure.

3. To reduce a figure by a scale. Measure all the sides of the figure, as ABCDE (fig. 2.) by a scale, and lay down the same measures respectively from a smaller scale in the proportion required.

4. To reduce a map, design, or figure, by squares. Divide the original into little squares, and divide a fresh paper of the dimensions required into the same number of squares, which are to be larger or less than the former, as the map is to be enlarged or diminished. This done in every square of the second figure, draw what you find in its correspondent one in the first.