4.2 MtfceUanea Curiofa. 



But if the ratio of a to b be fuppofed divi- 

 ded into two parts, viz. into the ratio of * to 

 the Arithmetical Mean between the terms, 

 and the ratio of the faid Arithmetical Mean 

 to the other term b, then will the Sum of the 

 Logarithms of thofe two rat tones be the Loga- 

 rithm of the ratio of a to b - 7 and fubftituting 

 i z inftead of | a +i b the faid Arithmetical 

 Mean, the Logarithms of thofe rationes will be 

 by the foregoing Rule, 



1 . X XX . X? , X 4 X* X s ' ' j 



» K 2 H 3^ 4f< 5 1 6 ^ 



I . X XX X* X* X* X 6 



the Sum i . 2 * , . , 2x * 2x7 o .„ 

 me n — ^—^^—^ r^-Scc. will 



whereorw * 3t J 5r 7? T 



be the Logarithm of the ratio of a to whofe 

 difference is x and Sum And this Series 

 converges twice as fwift as the former, and 

 therefore is more proper for the Practice of 

 making Logarithms : Which it performs with 

 that expedition, that where x the difference 

 is but the hundredth part of the Sum, the 



2. x 



firft ftep fuffices to feven places of the 



z 



Logarithm, and the fecond ftep to twelve: 

 But if Briggs^s firft Twenty Chiliads of Loga- 

 rithms be fuppofed made, as he has very care- 

 fully computed them to fourteen places, the 

 firft ftep alone, is capable to give the Loga- 

 rithm of any intermediate Number true to all 

 the places of thofe Tables. 



After the fame manner may the difference 

 of the faid two Logarithms be very fitly ap- 

 plied 



