50 Mifcellanea Curiofa. 



If one term of the ratio, whereof L is the 

 Logarithm, be given, the other term will be 

 eafily had by the fame Rule : For if L were 

 Nafeirh Logarithm of the ratio of a the lefler 

 to b the greater term, b would be the Produd 

 of a into i-j-L-j- h LL-HLLL &c. ==^+^t+i 

 eXAsV^dSJ &c. But if were given, a would 

 b^UL] \b\A,~\b\J &c. Whence, by the 

 help of the Chiliads, the Number appertaining 

 to any Logarithm will be exa&ly had to the 

 utmoft extent of the Tables. If you feek the 

 neareft nextLogarithm,whether greater or lef- 

 fer, and call its Number a if lefler, or b if 

 greater than the given L, and the difference 

 thereof from the laid neareft Logarithm you 

 call / it will follow, that the Number an- 

 fwering to the Logarithm L will be either a 



into r-H^i / M^ /// +A /4 + & c - or elfe * 

 into 1— i///'t-*J /+ — >U l < &c. wherein as 



/ is lefs, the Series will converge the fwifter. 

 And if the fir ft 20000 Logarithms be given to 

 fourteen Places, there is rarely occafion for 

 the three firft fteps of this Series to find the 

 Number to as many places. But for Vlactfs 

 great Canon of 100000 Logarithms, which is 

 made but to ten places, there is fcarce ever 

 need for more than the firft ftep a-\- a I or a-\< 

 malm one cafe, or elfe b—b I or b — m b I in 

 the other, to have the Number true to as ma- 

 ny Figures as thofe Logarithms confift of. 



If future Induftry ihall ever produce Loga- 

 rithmick Tables to many more places than 

 now we have them the aforefaid Theorems 

 will be of more ufe to reduce the correfpondent 

 Natural Numbers to all the places thereof. 

 In order to make the firft Chiliad ferve all 



Ufes, 



