2o6 



SCIENCE PROGRESS 



Newton says " Dary is very SolicitOUS <>f mat licinal ies," 



and this seems to he confirmed by 8 letter of Dary to Newton 

 in which he says, " Although I sent you three papers yester- 

 day, I cannol forbear sending you tins." 



i)r. Walli b, than whom there could be no greater testimony, 

 called Dary a knowing man in algebra, and John Collins, 

 writing t<» Sir John Frederick, says, " 'Tis well known to very 



many thai Mr. Dary has furnished others with knowledge 

 therein, who, publishing the same, have concealed his name; 



i l<>i instance Dr. John Newton loth lately published a hook 



oi Arithmetic, another ol (lan^in^; all thai is novel in both 

 lie had from Mr. Dary "; and again, in writing to fames 

 fnej'oiv, says " One Mi. Dary asserts s connection between 

 the quadrature ol the hyperbola and that oi a segmenl oi 8 



< a « le ; 1 1 go, I hen a I a hie ol areas ol segments, I h«' he .1 ol which 



li by Sybranl riant/., will he ol areata use than is imagined." 

 We have reason to believe thai we have here the hrsl 

 introduction ol the hyperbolic functions usually attributed 

 to Lambcrl in iy f »^; thai is, exactly one hundred years 



llftei Dary had noticed the i el.it ion. hi|>. II. •.eein. .il.o 



to have considered th<' question ol ruled surfaces, and when 

 considering th< - forms ol tuns, or vessels, he introduces the 

 term cylindroid. He also appears to have introduced b method 

 oi quadratures l>y the .ml <>i finite differences, ' for 

 which," he says, " I have ii.nl abundance "i contemplative 



solace and satisfaction." Il is also to be noticed th.it he 



uses the term " congruent set ol intervals," and 11 would be 

 interesting to know d this is no1 th< - flrsl time the expression 

 i . used, 



Dary's (greatest claim to Immortality, and the one which 

 most intimately concerns us in the. paper, is the solution oi 

 iilgchriih equations l>\ the process ol iteration, 



i he. in modern notation may be written the hnnt </>"(\) 



when /; increases without hnnt i. a solution ol $(%) I 



it illustrates how important theorems are forgotten, thai 

 when some years .\\\^ the LCditor ol tins Journal showed me a 

 papei he had written, on the solution oi the general equation, I 

 immediately observed thai the method he had used was essen 

 tially thai oi D.n\ (a man oi whom the authoi oi the papei 

 had nevei heard )• This was only parth the fact, because Sir 

 Ronald Ross in his solution had gone furthei into the conditions 



