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In order to this, divide the leaft by To many of 1 its Denominations as are contained in the next greater : Thus 24.720 Pence, divided by 12, and the Quotient by 20, give 103 Pounds. See Division.
If there remain any thing in each Divifion, 'tis refpectively either odd Pence, or Shillings : Thus 671 3 Pence reduced, gives 27/. 19 s. 5 d. cut off the laft, the reft is the Pounds required.
To expedite the Practice, feveral compendious Ways of Re- duBion have been invented. See Practice.
Thus Ells are turn'd into Yards, by adding a fourth to the Number of Yards; and into Ells Flemifli by adding a fifth.— Ells Flemijb are reduced into Yards, by fubftrafting a Quarter.— Ells Flemijb reduced to Ells Englifli by multiplying by fix, and cutting off the right hand Figure. See Ell, &c.
Great Pounds of Silk of 24 Ounces, are reduced to Pounds of i(S Ounces, by adding one Half. Pounds of 16 Ounces into Pounds of 24, by fubltracting three Quarters.
Reduction of Fractions. See Fraction.
Reduction of Equations, in Algebra, is the clearing them from all fuperfluous Quantities, bringing down the Quantities to their loweft Terms, and feparating the known Quantities from the unknown,- 'till, at length, only the unknown Quantity is found on one Side, and unknown ones on the other. See Equation.
The ReduBjon of an Equation is the laft Part of the Refbluti- on of the Problem. See Resolution.
The end of all Algebraical Operations, is to have the unknown Letter alone in one Member of the Equation; and in the other, ail the known Letters, without any mixture of unknown ; for, in this Cafe, 'tis evident the Value of the unknown Quantity is found.
This ReduBion is effected by adding the Quantities fubflract- ed, fubftracting thofe added; multiplying thofe divided, and di- viding thofe multiplied; extracting the Roots out of Powers, and ratling Roots to Powers; fo as ilill to preferve an Equality. See Equality.
This fuffices for the ReduBion of fimple Equations ; but for higher Equations, the Proccfs is Ids obvious.
From the manner wherein Powers are form'd, 'tis evident, that as the unknown Letter is rais'd to a higher Power, it will be found, in its lower Powers, mix'd and combined fo many more times with known Quantities, and of confequence will be fo much the more difficult to be difengaged therefrom. And the difficulty is the fame, where there are feveral unknown Letters multiplied fingly one againft another, and again multiplied by known Letters. See Problem.
The Reduction of the Equation being made ; from the laft; Quantity thus gain'd, the Geometrical Conftruction is to be dedu- ced. See Construction.
Reduction of a Figure, a Defign, or Draught, is the making a Copy thereof either larger or fmaller than the Original; ftiil preferring the Form and Proportion. See Figure.
The grand ufe of the proportional Compafles is in the ReduBi- on of Figures, ef c. whence they are alfo called Compajfes of Re- duction. See Compasses.
There are various Methods of reducing Figures, ef r. The moft eafy is by means of the Pentagraph or Parallelogram ; but this has its Defects. See Pentagraph.
The belt and moft ufual Methods of ReduBion, are as fol- low.
To reduce a Figure : As ABCDE, Tab. Geometry, Fig, 64. in- to a lefs Compals : about the middle of the Figure, as z. ; pitch on a Point ; and from this Point draw Lines to its fe- veral Angles A, B, C, &c. Then drawing the Line ab Parallel to AB, be Parallel to BC, e£ c. you will have the Figure abede ii- milar to ABCDE.
If the Figure abede 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, DB, &c. Parallel to the Sides ac, ab, &c.
To reduce a Figure by the Angle of Proportion.
Suppofe the Figure ABCDE (Fig. t>f .) required to be dimi- nifhed in the Proportion of the Line AB, to ab (Fig. 66.) draw the indefinite Line GH, (Fig. 6-j.) and from G to H fet off the Line AB : On G defcribe 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 Meafures of the Figure to be drawn.
Thus, to lay down the Point c, take the Interval BC, and up- on the Point G defcribe the Arch KL; alfo, on the Point G defcribe MN; and upon A with the Diftance MN defcribe an Arch cutting the preceeding one in c, which will determine the Side be. And after the fame manner are all the other Sides and Angles to be defcribed — .The fame Procefs will ferveto enlarge the Figure.
To reduce a Figure by a Scale. Meafure all the Sides of the Figure, e. gr. ABCDE, by a Scale ; and lay down the fame Meafures, refpectively, from a fmaller Scale in the Proportion required. See Scale.
To reduce a Ma}, Defign, or Figure, by Square;. Divide the Original into little Squares, and divide a frefh Paper
of the Dimenfions requited, into the fam: Number of Squares; which will be larger, or lei} than the former, as the Map is to be inlarged ordimimfhed.
This done in every Square of the fecond Figure, draw what you find in its Correfpondent one in the firft. See Map, &c.
Reduction to the Ecliptic, in Aftronomy, is the difference between the Argument of Latitude, as NP, (Tab. AJlronomy, Fig. 2.6.) and an Arch of the Ecliptic NR, intercepted between the Plane of a Planet, and the Node N. See Ecliptic.
To find the Reduliion : The Angle of Inclination PNR, and the Argument of Latitude NP being given ; find, by the Doct- rine of Sphericks, the Arch NR: Subftract NR and NP from each other, the Remainder is the ReduBim.
Reduction into the frfl Matter, a Term which the Alchy- mifts ufe when they find their Subitances putrify, and grow black.
Or rather ReduBim is the converting of a dry Matter into a Liquid, particularly Water; which they hold the Principle of all things. See Water, Principle, &c.
The ReduBim of Metals into their firft Matter or Principles, they teach, can only be effected by Mercury ; nothing elfe be- ing able to loofen the fix'd Sulphur of metallic Bodies, which binds them together. See Metal and Mercury.
Reduction, in Chirurgery, is an Operation whereby a diflo- cated, luxated, or fract ured Bone, is reltored to its former Place. See Bone, Luxation, Dislocation, F"racture.
The ReduBion is always performed e're any Remedy be applied.
REDUNDANCE, or Redundancy, a rault in Difcourle, arifmg from a fuperiiuity of Words. See Pleonasm.
Words, perfectly fynonimous, are Redundant, and ought to be retrench'd. — Redundancy makes the Style weak and languid.
REDUNDANT Hyperbola, is a Curve of the higher Kind, thus called becaufe it exceeds the Conic Seflion of that Name in the Number of its Hyperbolical Legs ; being a Triple Hyper- bola, with fix Hyperbolical Legs, oee Curve and Hyper- bola.
REDUPLICATION, in Rhetoric, a Figure wherein a Verfe begins with the lime Word as the preceeding one ends. See Verse.
Reduplication, in Logick, is a Kind of Condition exprefs'd in a Propolition, indicating or alligning the Manner wherein the Predicate is attributed to the Subject.
The ulual Reduplicating Words are quatenus, as, fo far as, con* fider'd as, inafmuch as, &c. Hence,
REDUPLICATIVE Proportions, are fuch wherein the Sub- jea is repeated, with fome Circumftance or Condition : Thus, Men, as Men, are Rational : Kings, as Kings, are fubject to none but God.
REE, a Portuguese Coin. See Coin and Millree.'
REED, an antient Jeirifb Meafure. See Measure.
Anfwerable to this is the Carma or Cane of fome modern Na- tions. See Cane.
REEF, a Term in Navigation— When there is a great Gale of Wind, they commonly roll up Part of the Sail below, that by this means it may become the narrower, and not draw fo much Wind ,- which contracting or taking up of the Sail, they call a Reef, or Reefing the Sail. J
So alio when a Top-Malt is fprung, as they call it, that is, crack d, oralmoft broken in the Cap; they cut off the lower Piece that was near broken off, and letting the other Part, now much ihorter, in the Step again, call it a Reef'dlop-Ma).
REEL, in the Manufactures, a Machine Serving for the Of- fice of Reeling. See Reeling.
There are various Kinds of Reels; fome very fimple, others very complex; of the former Kind, thofe moft in ufe are,
l°. A little Reel held in the Hand, confining of three Pieces of Wood; the biggeftand longeft whereof (which does not ex- ceed a Foot and a half in length, and ± of an Inch in Diameter) is traverfed by two other Pieces difpofed different Ways.
2 P . The Common Reel, or Windlafs, which turns upon a Pivot, and has four Wings, travers'd by long Pins or Sticks, whereon the Skam to be reel'd is put, and which are drawn clofer, or o- pen'd wider, according 10 the Skain.
Other Reels ufed in particular Arts, are explain'd under their particular Articles; as the Reel ufed in the milling of Silk, under the Article Milling: And that in the Reeling or Winding of SUBS, under the Article Silk, Sc.
...p™ G ' in the Manufadories, the winding of Thread, Silk, Cotton, or the like, into a Skain, or upon a Bottom ■ to prevent its intangling. See Silk, &c.
'Tis alfo ufed lor the charging or difcharging of Bobins or Quills, to ufe them in the Manutafiure of different Stuffs, as Thread Silk, Cotton, &c.
Reeling is perform'd different Ways, and by different Fn. gmes. See Reel.
RE-ENTERING Angle, in Fortification. See Angle.
RE-ENTRY, in Law, the reluming or retaking that PolTeffi- on which we had lately fore-gone. See Entry.
As, if I make a Leafe of Land, or Tenement, I do therefore forego the PoOeffion; and if I do condition with the Leffee, That for Non-payment of the Rent at the Day, it |fhall be law- ful for me to Re-enter; this is as much as if I conditioned to take
