Summation of Series. Ali 
had heard, that a feries for that purpofe was contained in my 
book, but had not feen it. In the fame book is given a method 
of finding the aggregates of any algebraical functions of each of | 
the roots of given equations, which is fomewhat improved 
in the latter editions. 8. In the fame book are aflumed 
ge ond Set AE ees where % is any rational 
pe tage” ' 4c. pz gz 7 +&c. 
quantity whatever for + andy, the unknown quantities of a given 
equation of two or more dimenfions. g. In the Mifcell. Analyt. 
_a biquadratic (4°+2p=9x°+rx+s5, of which no term 
is deftroyed) is reduced to a quadratic (# + px t+nu= 
JP +antgxtVstn’ 3) and in the fecond edition of it, 
printed in the years 1767, 1768, 1769, and publifhed in the 
beginning of the year 1770, the values of # are found 
B+yd h) b) 
& 2s iad aide 
Z4 2, 2 


; and the fix values of Wy +2n+q 
es ge) ees 
refpeciively =——, — —— and their nega- 

ab—yd ay—Bo 
Pais ? 
tives; and the fix values of /s+n° refpectively —— ; 

oe and their negatives. 10. From a given biquadratic 
(+9 +ry+5=0) by affluming y°+ay+=v and @ and 4 
fuch quantities as to make the fecond and fourth terms of 
the refulting equations to vanifh, there refults an equation 
(v'+Av°+B=0) of the formula of a quadratic. Mr. pELA 
Grance has afcribed this refolution to Mr. T’scHIRNHAUSEN ; 
but in the Leipfic A&ts the refolution of a cubic is given by 
Mr. T'scHIRNHAUSEN, but not of a biquadratic: his general 
defign feems to be the extermination of all the terms. 
Hhhz2 anes Mir. 
