in the schools, a manner of bringing a term or proposition, which was before opposite to some other, to be equivalent to it.

in Arithmetic, that rule whereby numbers of different denominations are brought into one denomination. See ARITHMETIC.

REDUCTION of Equations, in Algebra, is the clearing them from all superfluous quantities, bringing them to their lowest terms, and separating the known from the unknown, till at length only the unknown quantity is found on one side, and known ones on the other. The reduction of an equation is the last part of the resolution of the problem. See ALGEBRA.

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 PENTAGRAM.

The best and most usual methods of reduction are as follow:

1. To reduce a figure, as ABCDE (fig. 1.), Plate into a less compass. About the middle of the figure, 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 D, C, &c., and to draw lines, viz. DC, CB, &c. parallel to the sides de, 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 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.

in Metallurgy, is the bringing back metallic substances which have been changed into scoriae or ashes, or otherwise divested of their metallic form, into their natural and original state of metals again. See ORES, reduction of.

in Surgery, denotes an operation whereby a dislocated, luxated, or fractured bone, is restored to its former state or place.