30 8 Mr. HELLiNs’s ‘Theorems 
and annuities, but alfo in the finding of fluents, and the 
fummation of infinite feries. 
Some of the greateft mathematicians that this king- 
dom ever. produced, as Sir isaac newton, Dr. halley, 
Mr. cotes, and Mr. simpson, have thought it not be- 
neath them to improve the conftruCtion of logarithms* 
which ftrongly argues the utility of thofe artificial num- 
bers, and may fuggeft to us that the conftruCtion of them 
cannot be much further improved. 
Now, although we fhould be very diffident in our ex- 
pectations of improvement in any part of the mathema- 
tics after it has been handled by fuch great men, yet, if 
the method of computing be in general long and te- 
dious, or if there ftill remain any particular difficulty, I 
believe, no good reafon can be given why every attempt 
to abridge the one, or remove the other, fhould be dis- 
couraged. The eafy method of computing the loga- 
rithms of large numbers given in page 49. of Mr. simp- 
son’s pamphlet on Trigonometry is a proof that thofe 
gentlemen, who were of opinion that nothing better was. 
to be hoped for, or expected, than what they publifhed 
on the fubjeCt in the beginning of this century, were 
miftaken. And the following theorems, inferior to 
none as to convergency, and ufeful in deducing the lo- 
garithms of great fractions from thofe of fmall ones, or 
the 
