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 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 follows: 1. To reduce a figure, as ABCDE (fig. 10, n° 1.) into a less compass. About the middle of the figure, as z, 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 abcd similar to ABCDE.

If the figure abcd had been required to be enlarged, there needed nothing but to produce the lines from the point beyond the angles, as zD, zC, &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 (ibid. n° 2.) required to be diminished in the proportion of the line AB to ab, (ibid. n° 3.) draw the indefinite line GH, (ibid. n° 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.