296 Analyses of Books. [April, 



most impressive words : — " Next time I would recommend a little 

 more consideration." 1 am very respectfully, Sir, 



Your most obedient Servant, 



James Grikrson. 



James-Square, Edinburgh, 

 I2th Feb. 1814. 



Article XT. 

 Analyses of Books. 



Memoires de VAcademie Imperiale des Sciences de St. Peterslourq. 

 Tomes uiliiu St. Petersbourg. 1809, 1810, l&ll. 



{Continued fr^m p. 225.) 



Vol. II. 



1. Solution of a Problem, memorable on account of a singular 

 artifice in the calculus. By L. Euler. P. 1. The problem is as 

 follows : — To find a curve line, A M, 

 having the co-ordinates C P = t, P M 

 — y, the arch A M = // S, a nd the 

 straight line C M = V x"- + y^ = z-, 

 in which the integral a/v 1 may be a max- 

 imum or minimum, v being any func- 

 tion of z. 



2. A simpler Solution of the Diophantine Problem, respecting a 

 Triangle in which the straight Lines bisecting the opposite Sides 

 from the Angles may be expressed rationally. By L. Euler. P. 10. 



3. A simple Solution of the following Problem : To find a 

 sphere which will touch four spheres in what way soever they are 

 placed. By L. Euler. P. I7. 



4 Of innumerable Curves capable of being described round a 

 fixed Point fo that any Angle formed in that Point may cut off from 

 them equal arches. By Nicolaus Fuss. P. 29. 



5. Some Ol.servations concerning the Resolution of circular 

 Arches. By Nicolaus Fuss. P. 48. 



6. On the Reduction of Expressions of the form 1/ a dt b V c 

 to the binomial jn ± n V c. By C. F. Kausler. P. 64. 



7 Of the curvature of Lines described on the Surface of a 

 Sphere By Nicolaus Fuss. P. 73. 



8. Integration of the Formulas , < ■ ^ ... . /,■ ; — ptt 



and , f'i\'^ ^']' ^ . By St. Rumovski. P. 84. 



(1 - Z 2) ^ (i - 6 Z2 + 2")^ •'^ 



9. Reflections on those periodical continued Fractions which 



