Ald "Dre WARING On the) i 
the one generally finds too many, the other too few. 18. In 
the Medit. 1770, from the number of impoffible roots in a 
given equation («" — pe + &c. =0) is found the number of im- 
poffible roots in an equation, whofe roots (v) have any afi igna- 
ble relation to the roots of a given equation; and examples 
are given in the relation (nxt — n= 1px’ + &e. =U) 3 amd 
in an equation, whofe roots are the fquares of the dif- 
ferences of the roots of the given equation. 19. It is obferved 
in the Medit. 1770, that in two or more equations, having 
two or more unknown quantities, the fame irrationality will be 
contained in the correfpondent values of each of the unknown 
quantities, unlefs two or more values of one of them are 
equal, &c. The fame obfervation is alfo applied to the co- 
efficients of an equation deduced from a given equation. 20. 
In the Mifcell. was publifhed a new method of exterminating, 
from a given equation, irrational quantities, by finding the 
the multipliers, which, multiplied into it, give a rational pro- 
duct. 21. In the Medit. 1770, are given the different refolu- 
tions of a certain quantity (2° + rd*)*"t" and (a* +7ré°)*"+ into 
quantities of the fame kind. 22. Mr. pe La GRANGE has very 
elegantly demonftrated Mr. Wixson’s celebrated property of 
prime numbers contained in my book. In the laft edition of the 
Medit. the fame property is demonftrated, and fome fimilar 
ones added. 23. In the Mifcell. is given a method of finding 
all the integral correfpondent values of the unknown quantities 
of a given fimple equation, having two or more unknown 
quantities ; and, in the Medit. 1770, are given methods of re- 
ducing fimple and other algebraical equations into one, fo that 
fome unknown quantities may be exterminated; and if the 
unknown quantities of the refulting equations be integral or 
a rational, 
