216 Proceedings of Philosophical Societies. [March*, 



with which they are related. The explanations given of them 

 are founded on sound theory, and prove that the author, although 

 he resides in a distant department, has yet constantly kept pace 

 with the progress of the sciences, and is very capable of deduc- 

 ing useful applications from them. No one can fail to conduce 

 to this progress if, with such a spirit of inquiry as appears to 

 animate M. Vicat, he endeavours to enlighten with his know- 

 ledge the art in which he is employed, and engineers who are 

 placed in simileir circumstances indifferent parts of the kingdom,, 

 are under obligations to him both for the results of the work he 

 offers to them, and the example he offers them." We think, 

 therefore, that this work does in every respect merit insertion in 

 the Recueil des Savans Etrangers. 



Euclid in Greek, Latin, and French ; by M. Peyrard. — Com- 

 mittee, IMessrs. de Laplace, Legendre, Prony ; and Delambre, 

 Secretary. 



This third and last volume contains the 11th, 12th, and 13th 

 books of the Elements, the book of the data ; and, lastly, the 

 two supplementary books on the regular solids which are not 

 really by Euclid, and are generally attributed to Hypsicles of 

 Alexandria. The editor has thought it right to apologize for 

 having republished these two books, which he does not appear 

 to esteem very highly ; he is in our opinion not only sufficiently 

 justified by the example of so many other editors, one of whom 

 even thought it right to add a new supplement to those of Hyp- 

 sicles ; but we may say that these books are a necessary conti- 

 nuation of the 13th book of Euclid, who had merely touched 

 ■upon the theory of regular solids. In fact, Euclid contented. 



"himself with settling the edges of these bodies without saying a 

 word about the mutual inclinations of their surfices, or the 

 distance of these surfiices from their poles, or from the centre of 

 the sphere, nor does he speak of the surfaces or of the bulks of 

 the five re2;u1ar solids. 



Hypsicles has not, however, entirely exhausted the subject, 

 he merely gives the surfaces of the dodecahedron and the icosa- 

 hedron, he determines their proportions, which is also that of 



. their bulk, since the surfaces of these two bodies are at equal 



' distances from the centre of the sphere — a remark which he 

 might have extended to the hexahedron and the octahedron, as 

 has been done by one of his continuators. 



The subject of the inclinations is treated of more fully. In 

 order to determine them, Hypsicles begins by explaining the 

 general construction of his celebrated master, Isidorus. The 

 matter appeared so evident to that geometrician that he thought 

 it unnecessary to add any demonstrations. At first sight, it 

 might be imagined that Hypsicles wished to render it obscure 

 while demonstrating it, but from every appearance Isidorus 

 had, when he invented his constructions, the figures in rehef of 



' all the regular solids. With this assistance, which M. Peyrard 



