REDUCTION

, in general, is the bringing or changing some thing to a different form, state, or denomination.

Reduction, in Arithmetic

, is commonly understood of the changing of money, weights, or measures, to other denominations, of the same value; and it is of two kinds, Reduction Descending, which is the changing a number to its equivalent value in a lower denomination; as pounds into shillings or pence: and Reduction Ascending, which is the changing numbers to higher denominations; as pence to shillings or pounds.

Rule. To perform Reduction; consider how many of the less denomination make one of the greater, as how many pence make a shilling, or how many shillings make a pound; and multiply by that number when the Reduction is descending, but divide by it when it is ascending. So to reduce 23l. into pence; and conversely those pence into pounds; multiply or divide by 12 and 20, as here below.

23l.12 )5520d.
20
460sh.20 )460sh.
1223l.
5520d.

Reduction of Fractions. See Fraction, and DECIMAL.

Reduction of Equations, in Algebra. See EQUATION.

Reduction os Curves. See Curve.

Reduction of a Figure, Design, or Draught, is the making a copy of it, either larger or smaller than the original, but still preserving the form and proportion.

Figures and plans are reduced, and copied, in various ways; as by the Pentagraph, and Proportional compasses. See Pentagraph, and Proportional COMPASSES. The best of the other methods of reducing are as below.

To reduce a Simple Rectilinear Figure by Lines.

Pitch upon a point P any where about the given figure ABCDE, either within it, or without it, or in one side or angle; but near the middle is best. From that point P draw lines through all the angles; upon one | of which take Pa to PA in the proposed proportion of the scales, or linear dimensions; then draw ab parallel to AB, bc to BC, &c; so shall abcde be the reduced figure sought, either greater or smaller than the original.

To Reduce a Figure by a Scale.—Measure all the sides, and diagonals, of the figure, as ABCDE, by a scale; and lay down the same measures respectively, from another scale, in the proportion required.

To Reduce a Map, Design, or Figure, by Squares.— Divide the original into a number of little squares; and divide a fresh paper, of the dimensions required, into the same number of other squares, either greater or smaller as required. This done, in every square of the second figure, draw what is found in the corresponding square of the first or original figure.

The cross lines forming these squares, may be drawn with a pencil, and these rubbed out again after the work is finished. But a more ready and convenient way, especially when such Reductions are often wanted, would be to keep always at hand frames of squares ready made, of several sizes; for by only just laying them down upon the papers, the corresponding parts may be readily copied. These frames may be made of four stiff or inflexible bars, strung across with horse hairs, or fine catgut.

Reduction to the Ecliptic, in Astronomy, is the difference between the argument of latitude, as NP, and an arc of the ecliptic NR, intercepted between the place of a planet, and the node.—To find this Reduction, or difference; in the right-angled spherical triangle NPR, are given the angle of inclination, and the argument of latitude NP; to find NR; then the difference between NP and NR is the Reduction sought.

REDUNDANT Hyperbola, is a curve of the higher kind, so called because it exceeds the conical hyperbola in the number of legs; being a triple hyperbola, with 6 hyperbolic legs. See Newton's Enum. Lin. tertii Ordinis, nomina formarum, &c.

RE-ENTERING Angle, in Fortification, is an angle whose point is turned inwards, or towards the place.

REFLECTED Ray, or Vision, is that which is made by the reflection of light, or by light first re- ceived upon the surface of some body, and thence reflected again. See Ray, Vision, and REFLECTION.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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RECTILINEAL
RED
REDANS
REDINTEGRATION
REDOUBT
* REDUCTION
REFLECTING
REFLECTION
REFRACTION
REGEL
REGION