46 Miscellanea Curiofa. 



And this is the Refult of the Doctrine of 

 Mercator, as improved by the Learned Dr. 

 Wallis. But by the fecond Theorem, Hhz*. 



2f^2^L-l-HL & c . The fame Logarithms 

 z. 1 3*. 5 1 52,5 



are obtained by fewer fteps. To wit, 



45 273375 922640625 1 2515(585171875 

 &c. and 



£j 2 _2 2 



f?} 31 I I45725035 ' 3546351843241 °' 



which was invented and demonftrated in the 

 Hyperbolick Spaces Analogous to the Loga- 

 rithms, by the Excellent Mr. James Gregory, 

 in his Exercitatioties Geometric^, and fince fur- 

 ther profecuted by the aforefaid Mr. Sfeidall, 

 in a late Treatife, in Englijh, by him publilhed 

 on this Subject. But the Demonftration as 

 I conceive, was never till now perfected with- 

 out the confideration of the Hyperbola, which 

 in a matter purely Arithmetical as this is, can- 

 not be fo properly applied. But what follows 

 I think 1 may more juftly claim as my own, vii. 

 That the Logarithm of the ratio of the Geo- 

 metrical Mean to the Arithmetical between 

 22 and 24, or of V 528 to 23 will be found to 

 be either. 



1058 ^1 1 19364 88821 5334^" 626487882248 

 &c. or 



1057 ^ 354^79^579 ^ 65967655848528 5 &C * 



All 



