Refolution of Algebraical Equations. i o i 
whofe root is x, and which contains mn unknown quan- 
tities a, a , b , c, &c. b, a', , c\ &c. c, a , b', d', : for 
one, two or more of thefe unknown quantities may be 
affumed any quantities whatever, and thence may be de- 
duced equations of mn dimeniions, which may be re- 
duced to equations /+(a+ + / +fv / ^ J + 8zc.) 
x n 1 + &,c. — o of n dimenfions. 
In the fame manner maybe affumed equations, which 
involve Vf, ; v^, a/qJ, 
\/t, s/t z ,. vV, ,.•••> \/d~\ Sec; and from l'o reducing- 
them as to exterminate the irrational quantities, may of- 
ten be derived equations whofe refolutions or reductions 
are known. 
The method of transforming algebraical equations 
into others, whofe roots bear any affignable algebraical 
(but not exponential) relation to the roots 'of a given 
algebraical equation firft publiihed by me in the papers 
fent to the Royal Society, and afterward's in the year 
1760 ; and thirdly in my Mifcellanea Analytica ; and 
laftly in the Meditationes Algebraicee, and lince pub- 
lilhed by Mr. le grange in the Berlin ACts, is perhaps 
(as Mr. le grange, obferves) more general than Mr. 
hudde’s, or any transformation yet invented ; it is very 
■uftfal in. the refolution of numerous problems and. 
further. 
