JVlifcellanea Curiofa. ij 



Tangents are the true differences of Lon- 

 gitude. And this compared with our fecond 

 Corollary may fuffice for the ufe of the Tables 

 already computed. 



But if a Table of Logarithm Tangents be 

 made by extraction of the root of the Infiniteth 

 power, whofe Index is the length of the arch 

 you put for Unity, ( as for minutes the ,000 

 29o888ith,&c. power J which we will call a * 

 fuch a Scale of Tangents lhall be the true Me- 

 ridian Line, or fum of all the Secants taken, 

 infinitely many. Here the Reader is defired 

 to have recourfe to my little Treatife of 

 Logarithms, in the enfuing Difcourfe that I 

 may not need to repeat it. By what is there 

 delivered,it will follow, that putting t for the 

 excefs or defect of any Tangent above or under 

 the Radius or Tangent of 45 ; the Logarithm 

 pf the ratio of Radius to fuch Tangent wiltlje 

 f a into t— \tt lp ptt— \tttt -\-^t 5,&c« 



when the arch is greater than 45 gr > or 



m into* + \tt A- f; 3 if 4 * t'* > &c. 

 when it is lefs than 45.gr. And by the fame do- 

 arine putting T for the Tangent of any arch^ 

 and t for the difference thereof from the Tan- 

 gent of another arch, the Logarithm of their 

 ratio will be 



I . t tt »3 . t* » 



m into T T 277+ Jfi 1 4? ♦ 5* » 

 when T is the greater Term, or 



-into y - irr T "ps 1 -49 ~ l * c 



when T is the letter Term : _ 

 And if m be fuppofed ,0002908882, &c.— 



