236 . PHILOSOPHICAL TRANSACTIONS. [aNNO 1668. 



For it has been demonstrated that J- of any term in the last column, is less 

 than the term next after it ; and therefore that -a- of the last term, at which you 

 stop, is less than the remaining terms ; and that the total of these is less than 

 •I- of a third proportional to the two last. 



And therefore ABCyE being = 0,75 0,75 



and E d C y ::> 0,05685279 and < 0,05685290 



And ABCdE is<: 0,69314720 and :> 0,69314709 



But when A E : B C : : 5 ♦ 4, or as E A to K H, then will the space A B C E, 

 or now the space A H K E (A H = ^ A B) be found as follows : 

 8 X 9 X 10) 1. (0,0013888888 0,0013888888 



16X 17 X 18) 1. (0,0002042484-) 0003504472 0,0003504472 



18X19X20) 1. (0,0001461988/^ ^' 3)0,0000878204(0,0000292735 



32X33X34) 1. (0,0000278520) 0018271564 



34X35X36) 1: (0,0000233426 f +o'o000292735 



36X37X38) 1. (0,0000197566r^^^^"^^7^^"^ ^-^ P^ 



38X39X40) 1. (0,0000168691) 0,0018564299 <:Eab 



But 0,0003504472 t 



0,0000878204 [-H- 

 0,000022007 37 J 



Therefore 0,0018271564 

 4-0,0000220074 

 -j- 0,000007 33 5 8 



0,0018564996 >Eab 



Therefore E M b (fig. 4) being = 0,025 



Eab>- 0,0018564299 and 



0,025 



: 0,001 8564996 



EMba (%.4) orEKM (%. l) > 0,02685643 and <:o,02685650 

 A HKM<: 0,22314356 and >0,223 14349 



Therefore 3A B C d E = 2,079441 54 

 and A H K E = 0,2231435 



ABCdE(whenAE:BC:: 10:1) = 2,3025850 



Therefore the logar. of 10 

 is to the log. of 2 



as 2,302585 

 to 0,693147, 



