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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.
TACT I Cs.
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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