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• Redemption, in law, a faculty or ricjht of re-entering uponlands, Sec. that have been sold and assigned, upon reimbursing thepurchase-money, with legal costs.

R EDENS, REDANS, or REDANT, ill fortification, a kindof Indented work in form of the teeth of a saw, with salient and reentering angles ; to the end that one part may Hank or defend an-other. See Fortification .

REDFORD, or RETFORD, East, a borough of England,in Nottinghamshire, 2,6 miles N. of Nottingham , and 144 N.NAY.of London .

REDHEAD, a promontory of Scotland , in Angus-shire, threeJililes S. of Montrose.

REDON, a town of France , and capital of a district, in the de-partment of file and Vilaine, and late province of Bretagne , 20tniles E. of Vannes, and 225 E. by S, of Paris .

REDONDA, a town of Portugal , in Beira, 17 miles S. NV. ofCoimbra . Lon. 8. 34. W. Eat. 40. 4. N.

REDONDELA, REDONDELLA, or REDONDILLO, arich town of Spain, in Galicia , with a strong castle; 8 miles S. ofPonte Vedra, and 32 \Y. S. NY. of Orense . Lon. 8. 15. \V. Lat.42. 18. N.

REDOUBT is a small square fort, without any defence but infront; used in trenches, lines of circnmvallation, contrava’lation,and approach; as also for the lodgings of corps de gard, and to.defend passages.

REDRUTH, a town of Cornwall , seated among extensive tin-works; 8 miles-VV. of Truro , 12 N. N. E. of Ilelstone, and 262W. S. W. of London , I .on. 5. 13. W. Lat. 50. 13. N.

• REDUCE, in chemistry, the same with reduct. See Reduct.

REDUCT, or REDUIT, a military term signifying an advan-tageous piece of ground, entrenched, and separated from the restof the place, camp, &c. for an army, garrison, &c. to retire to incase of a surprize.

Reduct, in building, a quirk or little place taken out of a largerto make it more uniform and regular; or for some other conveni-ence, as for a little cabinet a side of a chimney, for alcoves, &c.

Reduct, or Redux, among chemists, a powder by which cal-xined metals and minerals are again reduced to their regulus, orpure substance.

- REDUCTION, in arithmetic. See Arithmetic.

Reduction, in metallurgy, is the bringing back metalline sub-stances, which have been changed into scoria; or ashes, or other-wise divested of their metallic form, into their natural and original.state of metals again. See Metallurgy .

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

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

Reduction of Equations, in algebra, is the clearing themfrom all superfluous quantities, bringing them to their lowest terms,and separating the known from the unknown, till at length onlythe unknown quantity is found on one side, and known ones onthe other. The reduction of an equation is the last part of the re-solution of the problem. See Algebra .

Reduction of a Figure, Design, or Draught, is the mak-ing a copy of it either larger or smaller than the original, still pre-serving the form and proportion. The great use of the propor-tional compasses is the reduction of figures, &c. whence they arecalled compasses of reduction. There are various methods of re-ducing figures, &c. The most easy is by means of the penta-graph or parallelogram ; hut this has its defects. See Pf.nta-graph. The best and most usual methods of reduction are asfollows; l.To reduce a figure, as ABUDE, (Plate CLVI1. fig. 6,)into a less compass. About the middle of the figure, as z, pitchon a point, and from this point draw lines to its several angles A,B, C, Sec. then drawing the line ab parallel to AB, be parallel to BC,&c. you will have the figure flficrfesimilar to 4BCDE. If the figure^abede had been required to be enlarged, there needed nothing but toproduce the lines from the point beyond the angles, as zD, zC, Szc.and to draw lines, viz. DC, CB, &c. parallel to the sides de, cb,Si c. 2. To reduce a figure by the angle of proportion, supposethe figure ABCDE, (tig. 7,) required to he diminished in the pro-portion of the line AB to ab, (fig. 8.) Draw the indefinite line

Gli, (fig. 9,) and from G to II set off the line AB. On G describethe arch III. Set ofl’the line ab as a chord on III, and draw CEThen with the angle 1CII you have all the measures of the figureto he drawn. Thus, to lay down the point r, take the intervalBC, and upon the point G describe the arch KL. Also on thepoint G describe MM ; and upon A, with the distance MN, de-scribe an arch cutting the preceding one in c, which will deter-mine the side be. And after the same manner are the frther sidesand angles to he described. The same process will also serve toenlarge the figure. 3. To reduce a figure by a scale. Measureall the sides of the figure, as ABCD E, (fig. 7,) by a scale, and laydown the same measures respectively from a smaller scale in theproportion required. 4. To reduce a map, design, or figure, bysquares. Divide the original into little squares; and divide afresh paper of the dimensions required into the same number ofsquares, which are to he larger or less than the former, as the mapis to he enlarged or diminished. This done, in every square ofthe second Figure draw what you find in its correspondent one inthe first.

R EDUNDANCY, or REDUNDANCE, a fault in discourse,consisting in the use of a superfluity of words. NY ords perfectlysynonymous are redundant, and ought to he retrenched.

Redundant, in music. \V hat tiie French call une accord su-perfine, which we have translated a redundant chord in the articleMusic (from D’Alembert ), has by others been rendered a chordextremely sharp, as in the translation of Rameau ’s Principles ofComposition. See Music.

Redundant Hyperbola, is a curve of the higher kind, thuscalled because it exceeds the conic section of that name, in thenumber of its hyperbolical legs ; being a triple hyperbola with sixhyperbolical legs. See Hyperbola, Curve , and Conic.

REDUPLICATION, in rhetoric, a figure whereby a verse be-gins with the same word as the preceding one ends with. SeeAnadiplosis.

Reduplication, in logic, a kind of condition expressed in aproposition indicating or assigning the manner wherein the predi-cate is attributed to the subject. Hence reduplicative proposi-tions are such wherein the subject is repeated with some circum-stance or condition. Thus, nu n, as men, are rational: kings,as kings, are subject to none hut Cod.

REED, in botany. See Arundo, and Bamboo .

REEF , a term in navigation. NVhen there is a great gale ofwind, they commonly roll up part of the sail below, that by Ibismeans it may become the narrower, and not draw so much wind ;which contracting or taking up the sail they call a reef, or reelingthe sail; so also when a topmast is sprung, as they call it, that is,when it is cracked, or almost broken in the cap, they cut off thelower piece that was nearly broken off, and setting the other part, nowmuch shorter, in the step again, they call it a reefed topmast.

Reef-band, apiece of canvass sewed on to strengthen the sailwhere the reefs are formed.

Ref.f-lines, small cords, used about the reef of a sa?f7

REEL, in the manufactories. There are various kinds of reels,some very simple, others very complex. Of the former kindsthose most in use are: 1. A little reel held in the hand, consistingof three pieces of wood, the biggest and longest whereof (whichdoes not exceed a foot and a half in length, and a quarter of aninch diameter) is traversed by two other pieces disposed in differ-,ent ways. 2. The common reel, or windlass, which turns upon apivot and four flights traversed by long pins or sticks, whereonthe skain to he reeled is put, and which are drawn closer, or openedwider, according to the skain. A representation of the commonreel is given in Plate CLVII. fig. 10, where A is the bench orseat of the reel, B the two uprights; C the arms of the reel, itsarbor turning, and hitching its little lantern ol four notches in theteeth of the wheel; D two wheels, the upper one of which movesthe lower by means of a pinion ; E a hammer, the handle whereofis lowered by a peg at the bottom of the lower wheel ; F a chordwhich is rolled round the axle of the lower wheels, and supports aweight w hich stops after a certain number of turns, to regulate thework-woman.

REELING, in the manufactories, the winding of silk, cotton,or the like, into a skain or upon a button, to prevent its entang-ling, It is also used for the charging or discharging of bobbins, orquills, to use them in the manufacture of different stuffs, as thread,

7 silk.