cardan’s Rule to the fecond Cafe , &?c. 
99 
fame numeral coefficients-, ff, — - 323 ’ 48 ° — , Sec 
9’ 6561’ 4,782,969’ 8, 13;, 830, 269’ OC '-" 
as they denoted in the two laft Articles, to wit, the co- 
zz z 6 2; 10 z 14 z 18 
efficients of -, — , — , — , See. or of the odd powers 
of — in the feries which is equal to 
ee 
And it is 
alfo ffiewn in Art. 6 and 1 2 of this paper, that this ex- 
preffion, computed to a given number of terms, gives 
the value of x fomewhat more exadtly than the former 
expreffion, \ //3 e x the infinite feries 2 +— -- 
1 7 gee 243c 4 6561c 6 
&c. if computed only to the fame number of terms. 
Art. 20, As to the fecond branch of the fecond cafe 
of the equation x 3 -qx=r , or that in which ^ is lefs than 
half — , or than--, I do not know any method of ex- 
27 54 - 
tending cardan’s rule to it. But I have been informed 
by my learned and ingenious friend Dr. charle's hut- 
ton, Profeflbr of Mathematicks in the Royal Academy 
at Woolwich, that he has difeovered fuch a method : 
and I hope he will foon communicate it to this learned 
Society. 
