Notices respecting New Books. 7 
sd fully to establish his reputation as a mathematician, and 
to exhibit his dexterity in analytical investigations, as the 
work now before us. Convinced as we are that the higher 
parts of the doctrine of trigonometry are admirable instru- 
ments in many philosophical researches, and especially in 
_those which relate to physical astronomy, we trust we shall 
be benefiting many of our readers by introducing this va- 
luable performance to their notice. 
The work is preceded by an introduction of twenty-eight 
pages, containing a judicious, though concise, history of the , 
principal writings relative to trigonometry. The loga- 
rithmic and algebraic rules for all the cases of plane trian- 
gles, whether right or oblique, and a great variety of practi- 
cal examples, several of which are wrought out at length, 
occupy about seventy pages.) These are succeeded by the 
doctrine of spherical trigonometry, and its application to 
astronomical problems, comprised in two hundred pages. 
The distribution of this part of the subject is as follows: 
General properties of spherical triangles; on the ambiguous 
cases of spherical triangles; the affections and other pro- 
perties of right-angled spherical triangles; solutions of 
the six cases of right-angled spherical triangles, by con- 
struction, by calculation, and instrumentally ; a similar di- 
vision with respect to the six cases of quadrantal triangles ; 
and, a similar one relative to the six cases of oblique-angled 
spherical triangles ; logarithmic and analytic solutions of 
all the cases of right-angled, quadrantal, and oblique-an- 
gied spherical triangles; miscellaneous problems for exer- 
cise; application to the solution of astronomical problems; 
tables of right ascension, &c. useful in the preceding solu- 
tions; and, miscellaneous astronomical problems. This 
part of the work cannot fail to be of the highest utility ; for 
in the exhibition of the general rules of spherical trigono- 
metry, the author has struck into the happy medium be- 
tween the fatiguing prolixity of most writers on this branch 
of the subject, and that abstracted analytical process by 
which Euler, Gua, Lagrange, and others, have deduced all 
the practical theorems from one fundamental formula; 4 
process which, though it is so conducted as to be both gra- 
Vol. 26, No, 10%, Nov, 1606. M tifying 
