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rious alterations and material improve-
ments. This is to be confidered as the
outline of a large and important work,
which the author promises, of Mathema-
tical Analysis: we fincerely hope that he
may meet with no interruption in the pro-
secution of his laborious undertaking. Mr.
Vilant, in his Appendix, has reduced with
fingular ingenuity and neatness the fifth
book of Euclid's Elements into the lan-
guage of algebra.
Mr. How ARD has published A Trea-
tise of Spherical Geometry, containing its
fundamental Properties, the Doğrine of its
Loci, the Maxima and Minima of Spheres,
Lines, and Areas, with an Application of
ibose Elements to a Pariety of Problems.
This work is extremely valuable to the
learner; the arrangement is good, and the
demonstrations, generally speaking, are at
once elegant and perspicuous.
Mr. MANNING has published the se-
cond volume of his Introdoton to Arith-
metic and Agora; it evinces the same
accuracy, acuteness, and perspicuity, which
gave such merited reputation to the first.
An Elucidation of several Parts of his
Majesty's Regulations for the Formation and
Movements of Cavalry has lately been
printed for the War Office: it is reported
to have been drawn up by Colonel Le
MERCHANT, from the elementary in-
structions of General DAv ID DUNDAs,
in his Cavalry Movements: this latter
work is out of print.
The following publication, moreover, is
said to be written in elucidation of general

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