’ 
Legendre’s Geometry. 301 
od is indicated i in Euclid B. XII. prop. 16th. It consists 
in assuming two concentric circumferences, and circum- 
scribing about the smaller a regular polygon which does 
not touch the greater; or inscribing a regular polygon in 
the greater, which does not touch the smaller. On these 
polygons, as bases, in case circumstances require it sregular 
polyedrons are supposed to be constructed, and it is de- 
monstrated, that the assigned measure of the solid or sur- 
face in question,cannot be that of one greater or less, with- 
out falling into the absurdity of cite Sete that a figure con- 
tained by another is the greater of the two, These de- 
monstrations are long, and on rantine of the frequent repe- 
tition of the same constructions, become somewhat tedious. 
But they have the merit of being plain, and satisfactory, 
although indirect; and we think, on the whole, that the 
method pursued by Legendre is the best. Lacroix’s man- 
ner as it respects these demonstrations, is much more con- 
cise, but it is too abstract, and difficult to be seized; and 
Cavalleri’s method of indivisibles is not sufficiently igorées 
to be used in elementary geometry. 
After what has been said, it is scarcely necessary to ob- 
serve, that American mathematical science, is under great 
obligations to the translator, for giving Legendre’s elements 
in so handsome an English dress. The only fault we have 
to charge him with, is, that he did not furnish us with the 
entire work, as it came from the hands of the author. Con- 
siderable of that part which in the original is printed in fine 
type, and almost all the ss are omitted in the transla- 
tion. These omissions we very much regret. By pre- 
serving the original difference in type, the work would 
have been equally convenient for academical instruction, 
and the additional expense of printing the parts omitted, 
would have been quite trifling. As it now is, we are pur- 
suaded, that all lovers of mathematical pclae y after hav- 
ng perused the translation, will feel induced to go to the 
expense of sending out for the original, for the sake of those 
parts, which the translation does not contain. The notes 
are a great curiosity, _— a be likely to inspire a taste 
for the higher mathemati 
The translation is cancited faithfully, and it is accurate- 
ly printed. A list of errata, however, to some extent 
might be made out, though none is given. In the demon- 
