IND 



indented line, in such a manner as to 

 leave half the word on one part, and half 

 on the other; and this custom is still pre- 

 served in making out the indentures of a 

 fine. But at last, indenting only hath 

 come into use, without cutting through 

 any letters at all, and it seems at present 

 to serve for little other purpose than to 

 give name to the species of the deed. 



INDEPENDENTS, or COXGREGATIOKT- 

 ALISTS, in church history, a sect of Pro- 

 testant Dissenters, which first made its 

 appearance in Holland in the year 1616. 

 Mr. John Robinson appears to have been 

 the founder of this sect. The appella- 

 r tion of Independents was applied to, and 

 adopted by, this denomination of Chris- 

 tians, from their maintaining that all 

 Christian congregations are so many in- 

 dependent religious societies, having a 

 right to be governed by their own laws, 

 without being subject to any further or fo- 

 reign jurisdiction. This term was pub- 

 licly acknowledged in the year 1644, by 

 those English Dissenters, who held simi- 

 lar sentiments respecting church govern- 

 ment to the Independents in Holland; 

 but on account of the ill use that many 

 made of the term, by a perversion of its 

 original meaning and religious designa- 

 tion, the English Independents renounced 

 it, and adopted that of Congregationalists, 

 or Congregational brethren. The term 

 Independent is still, however, applied to 

 various sects of Protestant Dissenters, 

 and seems justly applicable to almost 

 every sect of nonconformists in this coun- 

 try. 



The doctrines of the Independents are 

 the same as those of the BROWN ISTS. It 

 is said, that the only difference between 

 these sects was, that the Brownists were 

 illiberal in their views concerning other 

 denominations, while the Independents 

 entertained enlarged conceptions of 

 church communion, and allowed that 

 other churches, though different from 

 them in points of discipline, might pro- 

 perly be called Christian churches. It is, 

 however, to be feared that the Indepen- 

 dents, properly so called, being Calvin- 

 ists as to points of faith, do not cherish 

 very liberal sentiments concerning the 

 salvation of those who differ from them 

 in most ot their articles of belief. A spi- 

 rit which seems to be a natural effect of 

 the creed of the Geneva Reformer. See 

 BUOWNISTS and PRESBYTERIANS. 



INDETERMINATE, in general, an ap- 

 pellation given to whatever is not certain, 

 fixed, and limited; in which sense it is 

 the same with indefinite. 



INDETERMINATE problem, is that which 



IND 



admits of many different solutions and an- 

 swers, called also an unlimited problem. 

 In questions of this kind, the number of 

 unknown quantities concerned is greater 

 than the number of the conditions and 

 equations by which they are to be found; 

 from which it happens, that generally 

 some other conditions or quantities are 

 assumed, to supply the defect, which, be- 

 ing taken at pleasure, give the same num- 

 ber of answers as varieties in those as- 

 sumptions. If, for instance, it were re- 

 quired to find the value of two square 

 numbers, whose difference is equal to a, 

 a given quantity. Here if x 2 and y 1 de- 

 note the squares, then x 2 y*-=*a t which 

 is only one equation for finding two quan- 

 tities. Now, by assuming some other un- 

 known quantity, as 2, so that zx-\-y=. 



the sum of the roots; then is x= . 



And by the same mode y= 



which 



are the two roots having the difference 

 of their squares equal to a given quantity 

 a, and are expressed by means of an as- 

 sumed quantity z; so that there will be 

 as many answers to the question, as there 

 can be taken values of the indeterminate 

 quantity z. 



Mr. Leslie, in the transactions of the 

 Royal Society of Edinburgh, has given a 

 paper on this subject, the object of which 

 is to resolve the complicated expressions 

 which we obtain in the solution of inde- 

 terminate problems into simple equa- 

 tions, and this is done by means of a 

 principle, which, though extremely sim- 

 ple, admits of a very extensive applica- 

 tion. Let A\B be any compound quan- 

 tity equal to another, CxD, and let m be 

 any rational number assumed at pleasure; 

 it is manifest that, taking equimultiples, 

 AXW B=CXw D. Tf, therefore, we sup- 

 pose that A = m D, it must follow that 



7nB = C, or B = . Thus two equations 

 m 



of a lower dimension are obtained. If 

 these be capable of further decomposi- 

 tion, we may assume the multiples n and 

 p, and form four equations still more sim- 

 ple. By the repeated application of this 

 principle, an higher equation, admitting of 

 divisors, will be resolved into those of the 

 first order, the number of which will be 

 one greater than that of the multiples as- 



