Page:Cyclopaedia, Chambers - Volume 1.djvu/163

 APP

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APP

copular Conjunction between them. See Substantive, Conjunction, Copulative, ££>c.

Thus, Flanders, bloody Theatre, horrible Scene of War,

APPRAISE, to rate, value, or fet a Price on Goods, by a Perfon who is a competent Judge, and is authorized thereto.

The Word is derived from the French apprecier, which

fignifies the fame thing Hence we. alfo fay an Apprai-

fer, a fworn Appraifcr, an Appraifement, &c.

A P PRENDRE, in our antient Law-Books, a Fee or Profit ro be taken or receiv'd. See Fee.

APPREHENSION, in Logick, thefirftldea which the Mind forms of any thing, abstractly of its particular Qua- lities- See Idea.

Aj>prehenf\on coincides with what we otherwife call 'Per- ception. See Perception.

The Word literally denotes the Action of the Hand, where- by it takes hold of, and grafps any thing $ being form'd of the Latin ad, to, and prehendo, 1 hold. See Compre- hension.

Apprehension, in Law, Signifies the feiz,ing a Criminal, in order to bring him to Juftice.

APPRENTICE, one who is bound by Covenant to ferve a Tradefman, or Artificer a certain Time ; ufually feven Years ; upon Condition of the Maibjr's instructing him in his Art or Myftery. See Trade, Commerce, Art, ££c. Sir Thomas Smithes, thar Apprentices are a kind of Bondmen, or Slaves, differing only in this that they are Servants by Covenant, and for a time. deRep. Anglor. Lib. 3. See Servant, Slave, ^3c

Antiently, Benchers in the Inns of Court were called Apprentices of the L.aiv, in Latin Apprenticii Juris No- biliores ; as appears by Mr, Seidell's Notes on Fortefcu : and fo the learned Plo-ivden itiles himfelf.

Sic Henry Finch in his Komotechnia writes himfelf Ap- prentice de Ley : Sir Edward Coke in his Inftit. fays, Ap- prcntiai Lcgis in pleading are called Homilies confiliarii, & in Legeperiti h and in another place, A pprentices and other Counfellors of Law.

APPROACHES, in Fortification, the feveral Works made by the Befiegers for advancing or getting nearer to a For- trefs, or Place befieged. See Work, Fortification.

Such are Frenches, Mines, Sapps, Lodgments, Batteries, \^c. See Trench, Mine, Sapp, Battery, c^c

Approaches, or Lines o/ApppvOach, are particularly ufed for Trenches dug in the Ground, and their Earth thrown up on the Side towards the Place befieged ; under Shelter or Defence whereof the Befiegers may approach, without Lofs, to the Parapet of the cover'd Way 5 and plant Guns, £5?c. wherewith to canonnade the Place. See Trench.

The Lines of Approach are to be connected by Lines of Communication. See Communication.

The Befieged frequently make Counter- Approaches, to interrupt and defeat the Enemies Approaches.

APPROPRIATE, Appropriated, in Philofophy, is iindcritood of fomething which is indeed common to feve- ral ■ yet, in fome refpects, is peculiarly attributed to one. See Proper and Common.

Thus, Creation is common to the Father, Son, and Holy Ghoft ; and yet is appropriated to the Father.

Appropriate, in Law, is undeitrood of a Church or Benefice, the Patronage whereof is annex'd to fome Church- £)ignity; fo that the Parfon receives the Tithes. See Church, Benefice, Patron ace, Parson, and Tithe. There are computed in England 5S45 Churches Appro- priate and Impropriate. See Appropriation, Impro- priation, &c> i

Appropriare ad Honor -em \ in Law, fignifics to bring a Manor within the Extent and Liberty of fuch an Honour. See Honour, Manor, £5c.

Appropriare Commune, in .Law, fignifies to difcom- mon, i- e. to feparate, and inclofe any Parcel of Land, which before was open Common. See Common.

APPROPRIATION, the Aft of Appropriating, orap- plying a Church-Benefice, which of its own Nature is juris divinu and no Perfon's Patrimony, to the proper and perpe- tual Ufe of fome Religious Community. See Appro-

Appropriatien y is where the Advowfon of aParfonage is given or belongs to any Bifhoprick, religious Houfe, College, tic and to their Succeffors 5 fo that the Houfe or Body, is both Patron and Parfon, and fome one of the Mem- bers officiates as Vicar. See Parson, Advowson, ££?c. ^

It is called Appropriation, becaufe the Profits of the Li- ving are appropriated to the ufe of the Patrons ; fo that Parfons, tho' they are not ordinarily accounted 'Domini Ufit- fruHuarii, having no rightof Fee-fimple ; yet, by rcafon of the Perpetuity of. their Succcuion, are reputed Owners of the Fee-fimple, and are therefore called 'ProprietariU $ec Patrol and Patronage-

To make an Appropriation^ after Licence obtained of the King in Chancery, the Confent of the Diocefan, Pa- tron, and Incumbent, is neceffary, if the Church be full ; if it be void, the Diocefan and the Patron, upon the King's Licence, may conclude it, ...

To dijfolve an Appropriation, it is" enough to prefent a Clerk to the Bifhop, and he to inftitute and induct him % for that once done, the Benefice returns to its former Na- ture.

APPROVEMENTUM, Approveamentum, or Ap- provement, isfometimes ufed in antient Writers for Im- provement. See Improvement.

Thus, to Approve, Approbarc, is to make the beft be- nefit of a thing by increafing the Rent, &c.

In fome antient Statutes, Bailiffs of Lords in their Fran- chifesarecall'd their Approvers. See Bailiff.

Cam omnibus Approviamentis £j aliis pert'mentih fut$ t &c. Mon. Angl.

Approvement, is more particularly ufed where a Man hath common in the Lord's Wattes, and the Lord inclofeth part of his Wa lie for himfelf; leaving furficient Common s with Egrefs and Regrefs, for the Commoner.

APPROVER, one who confeffing Felony in himfelf, ap- pealeth or impcacheth another or more of his Accomplices,, See Appeal.

He is fo call'd becaufe he rauft prove what he hath al- ledg'd in his Appeal — —This Proof Ihould either be by

Battel, or by the Country,

See Proof, Battel, Pais,

Approvers ofthcKi

£S?i

the choice of the Appellee.

ire thofe who have the letting of the King's Demefnes in fmall Manors, &c. See De- mesne.

APPROXIMATION, in Arithmetkk, a continual ap- proach nearer flill and nearer to a Root or Quantity fought, without a poffibility of ever arriving at it exactly. See Root.

We have divers methods of Approximation delivered by Wallis, Raphfon, Hailey, Howard, &c. all of 'em being no other than Series's infinitely converging, or approaching {till nearer to the Quantity requir'd, according to the Na- ture of the Series. See Converging and Series.

'Tis evident, that if a number propos'd be not a true Square, it is in vain to hope for a juft quadratick Root thereof, explicable by rational Numbers, integers or frac- ted ; whence, in fuch Cafes, we mnft content ourfelves with Approximations, fomewhat near the Truth, without pretending to Accuracy : and fo for the Cubick Root, of what is not a perfect Cube ; and the like for fuperior Pow- ers. See Square, Cube, Power,Q_uAdrature, Ex- traction, £Jjc.

This the Antients were aware of, and accordingly had their Methods of Approx'rmation ; which, tho' fcarce ap- plied by them beyond the quadratick or perhaps the cu- bick Root, are yet equally practicable, by due Adjustments, to the fuperior Powers alfo: as is fhewn in the Philofoph. Iranfatl. N Q 215.

If there be a Non-quadratick or Non-cubick Number 5 the former being expreffed by aa-\~b, and the latter by aaa-\-b, where aa and aaa are the greateft Square and Cube in the propofed Numbers 3 then ^ aa ~\-b = a +

2 aa -J- 4 b

5 and ^>_^ = ^-f.

%aaa + b

= * a-\->

\/'i ',.' 4L-— will be eafy and expeditious Approximation

to the Square and Cube Root.

To extratl the Root of an Equation by Approximation.

i°. For a quadradic Equation fuppofe the Equation

x* — 5* — -31 = — 5 let the Root be 8 -f- y, fo that y may denote the Fraction, whereby the affumed Number either exceeds or comes fliort of the Root : Then

x' = 64. -f- i6y-\-y*

— 5#— — 40— 5 3

— si =—31

— 7 -f- n.y + jy 1 =0

Since the Powers of Fractions are continually decreafing s

and we only here want a Root nearly true ; y~ is cafl: away i Upon which,

— 7 4- * * 3 = °

y = jI = y# nearly =: o. 6

Wherefore x = 8 --. 6 = 8 . 6 Suppofe #= 8.tf-|-r. Then

. 3 i + V^-J =

WcR' 1.