REC 



REC 



a, recoveree, and a vouchee. The reco- 

 verer is the plaintiff or demandant, that 

 brings the writ of entry. The recoveree 

 is the defendant or tenant of the land, 

 against whom the writ is brought. The 

 vouchee, is he whom the defendant or te- 

 nant voucheth or calls to warranty of the 

 land in demand, cither to descend the 

 right, or to yield him other lands in 

 value, according to a supposed agree- 

 ment. And this being by consent and 

 permission of the parties, it is therefore 

 said that a recovery is suffered. 



A common recovery may be had of 

 such things, for the most part, as pass by 

 :i fine. An use may be raised upon a re- 

 covery, as well as upon a fine ; and the 

 same rules are generally to be observed 

 and followed for the guiding and direct- 

 5ng the uses of a recovery, as are observ- 

 ed for the guidance and direction of a 

 fine. That is to say, that when a fine is 

 levied, or a recovery is suffered, a deed 

 is made between the parties really inte- 

 rested, which declares the purposes of 

 the fine or recovery, and this deed is 

 called a deed to lead or to declare the 

 uses, according as it is made before or af- 

 ter the fine or recovery. To enter at 

 full into the learning of fines and recove- 

 ries, would be impossible in a general 

 dictionary. It is sufficient to say, that 

 both of them are in the nature of a sham 

 suit, while one of which is compromised, 

 nnd the other carried on to judgment by 

 default between the parties really inte- 

 rested, and the use of them is to enable a 

 married woman to make a good convey- 

 ance, and a tenant in tail to turn his es- 

 tate into an estate in fee, or as it is called, 

 to dock or bar the entail. See P'IXE and 

 ESTATE. 



RECTANGLE, in geometry, the same 

 with a right-angled parallelogram. In 

 arithmetic and algebra, a rectangle signi- 

 fies the same with factum or product. 



RECTANGLED, RECTANGULAR, or 

 RIGHT-ANGLED, appellations given to fi- 

 gures and solids which have one or more 

 right angles : thus a triangle with one 

 right angle, is termed a rectangled trian- 

 gle ; also parallelograms with right angles, 

 squares, cubes, &c. are rectangular. So- 

 lids, as cones, cylinders, &c. are also said 

 to be rectangular, with respect to their 

 situation, when their axes are perpendicu- 

 lar Ifo the plane of the horizon. The an- 

 cient geometricians always called the 

 parabola, the rectangular section of a 

 cone. 



RECTIFICATION, the art of setting 

 any thing to rights : and hence, to rectify 



the globes, is to lit them for performing 

 any pi-oblem. 



RECTIFICATION, in geometry, is the 

 finding a rig] it line, equal in length to a 

 curve. The rectification of curves is a 

 branch of the higher geometry, where the 

 use of the inverse method of fluctions is 

 very conspicuous, of which we shall give 

 an example. 



Case I. Let A C G, (Plate Miscel. XIII. 

 fig. 15.) be any kind of curve, whose or- 

 dinates are parallel to themselves, and 

 perpendicular to the axis A Q. Then if 

 the fluxion of the absciss A M be denoted 

 by M in, or by C n, (equal and parallel to 

 M M ) and n S, equal and parallel to C r, 

 be the representation of the correspond- 

 ing fluxion of the ordinute M C ; then 

 will the diagonal C S, touching the curve 

 in C, be the line which the generating 

 point p would describe, were its motion 

 to become uniform at C ; which line, 

 therefore, truly expresses the fluxion of 

 the space A C, gone over. Hence, put- 

 ing A M = x, C M = y, and A C = z ; we 



have ~ ( C S = ^ C n'- -j- S n 1 = 



^x 1 -j- y 3 " ; from which, and the equa- 

 tion of the curve, the value of z maybe 

 determined. Thus, let the curve pro- 

 posed be a parabola of any kind, the ge- 

 neral equation for which is x = ^_ i ; 



and hence x = -, and therefore 



a i 



( = = ,/Ff3')= Jy+V^ 



= y X 1 -H -4^1" > the fluentof which, 

 a ** 



universally expressed in an infinite series. 



i5 X 



Case II. Let all the ordinates of the 

 proposed curve A R M (fig. 16), be re- 

 ferred to a centre C : then putting the 

 tangent R P (intercepted by the perpen- 

 dicular C P) = t, the arch, B N, of a cir- 

 cle, described about the centre C, = x ; 

 and the radius C N (or C B) = a; we 

 have *-::: y (C! R) : f (R P) ; and, con- 

 sequently, z = ^- : from whence the 



value of r may be found, if the relation of 

 y and t is given. But, in other cases, it 

 will be better to work from the following 





