222 Analijses of Books. [March, 



Article XII. 



Analyses of Books. 



Memoires cle I'Academie Imperiale des Sciences de St. Pefersloztrq. 

 To7?76'5 i. ii. iii. St. Petersboiirg. 1809, 1810, IS 11. 



The Imperial Academy of Peteisburgh have always made mathe- 

 matics the most prominent department of their memoirs. On that 

 account, the present volumes, though of a very considerable size, 

 and containing abundance of valuable papers, are not very suscep- 

 tible of abridgement. I shall satisfy myself with giving the titles 

 of the mathematical papers. This will apprize the mathematical 

 reader of the kind of i.rticles they contain, and the probability of 

 his finding any particular topic in them, of whicli he may be in 

 search. Of the other papers, as far as they come within the plan 

 of this work, 1 shall endeavour to give an abridged but tolerably 

 accurate view. 



Vol. I. 



1. On the Resolution of compound Fractions into simple ones. 

 By L. Elder. P. 3. 



2. Elucidations of the geometrical Problem respecting the Qua- 

 driscction of a Triangle, formerly treated of by James Bernoulli. 

 By L. Euler. P. 26. 



3. A complete Solution or the Problem of the Quadrisection of 

 a Triangle, by two straight lines cutting each other. By L. Euler. 

 P. 4.9. 



4. A Decade of geometrical Problems in the Inverse Method of 

 Tangents, relating to the Radius of Osculation. By Nicolaus 

 Fuss. p. 88. 



. 5. Integration of some Formulas of differential Angles. By 

 N. Fuss. P. 138. 



6. A Method of converting any given Series into continued 

 Fractions. By C. F\ Causler. P. 156. 



7- Attempt to demonstrate the Principles of Virtual Velocity. 

 By B. Viscovatotr. P. 178. 



8. Of the important Use of continued Fractions in the Integral 

 Calculus. By C. F. Causler. P. 181. 



9. A direct and ir>.versc Demonstration of the general Principle 

 of Equilibrium, in an elementary Manner, with the Application 

 of this Principle to Machines. By S. Gourieff". P. 195. 



10. Of thi. general Mothud of reducing all Kinds of Quantities 

 to continued Fractions. By B. Viscovatoff. P. 226. 



11. Hypothetical Law of the Inclination of the Needle in all 

 Parts of the Earth By W. L. Krattt. P. 218. This is a simplifi- 

 cation of ihe well known Theory of Biot, published in 1804. 



12. Solution oi" the following Diophantine Proplcm : To divide 

 a given ilTltmbcr intg any number of parts, so. that their sum (one. 



