466 Notices respecting New Books, 



E (fig. 73.) opposite toe undergo no decrement ; the other, 

 ^hat the ridges opposite to B remain in a similar manner 

 unaltered. 



[To be continued.] 



LXIX. Notices respecting New Books. 



M, 



.R. T. Leybourn, of the Royal Military College, has 

 just published the ninth number of his periodical work, 

 entitled The Mrahematical Repository : it contains, be- 

 sides various articles, solutions of inathemalical questions 

 proposed in the seventh number, and a series of new ques- 

 tions, to which he solicits answers from his correspond- 

 ents, with a view to their being inserted in the eleventh 

 number. In publishing this work the editor has in view 

 to promote the study of the various branches of the ma- 

 thematics, by affording to the student an opportunity of 

 cultivating his powers of invention in resolving problems 

 which depend on its different theories ; and also to collect 

 together and preserve the fruits of the studies of his in- 

 genious correspondents, among whom he includes some of 

 the most skilful mathematicians in this country. The 

 number here announced completes the second volume of 

 the work ; and as some account of the contents of both 

 volumes may not be unacceptable to such of our readers as 

 cultivate the science of which they treat, we shall briefly 

 enumerate them. 



Vol. 1. part 1st, consists of one hundred and twenty 

 questions, both in pure and mixt mathematics, almost all 

 of which are entirely new, and, in general, each is accom- 

 panied with several solutions by different mathematicians. 

 Part 2d, consisting of original essays, comprehends 

 the following articles: — 1. Demonstrations of some pro- 

 positions relating to such portions of the surface and so- 

 lidity of a sphere as may be exactly squared and cubed, by 

 Mr. Ivory. — 2. Demonstration of a theorem, respecting 

 prime numbers, by Mr. Ivory. — 3. Tagnani's theorem re- 

 fipecting elliptic arches, rendered more general, by Mr. 

 Ivory. — 4. A geometrical porism, with two examples of 

 its application to the solu-tion of problems, by Scoticus. — 

 5. Geometrical propositions, by Mr. Ivory. — 6. Solution 

 of a dynamical question, by Mr. Ivory. — 7- Of thee qni- 

 librium of a very long and slender cylinder floating in a 

 fluid, by Jac. Rube. — 8. Of the length of an arc of a 

 circle in terms of the tangent, by Mr. JBcnjaraiaGompertz. 



— 9. Geo- 



