284 Cambridge Course of Mathematics. 
Calculus; and various academical memoirs. In the late 
reat trigonometrical surveys in France and England, op- 
erations which have contributed so much to our knowl- 
edge of the earth we inhabit, and to the honor of the na- 
tions engaged in them; the instruments used were of such 
exquisite construction, that the angles were measured to a 
fraction ofa second. Hence, the spherical excess, that is, 
the excess of the three angles of the triangles, measured in 
these surveys on the surface of the earth, above two right 
angles, became apparent. It was necessary, therefore, to 
estimate this excess. The prompt genius of M. Legendre 
stration of this very valuable theorem, in the appendix to 
his Trigonometry. 
The Elements of Geometry now under. consideration, 
were composed during that period.of the French history, 
when the ancient foundations of society and government 
were undermined, and the political edifice throughout Eu- 
rope, rocked with fearful convulsions on its base. The 
great French philosophers and mathematicians saw plainly, 
that in order to conciliate the popular favor, and avoid the 
jealousy of the reigning authority, they must, as far as p0S- 
sible, render their favorite pursuits subservient to objects of 
immediate and practical utility. They had seen the eml- 
nent talents and conspicuous virtues of Lavoisier, insufhi- 
cient to save him from the scaffold ; and the illustrious but 
unfortunate Bailly, who had formerly been the idol of the 
French nation, and who had devoted his life to the inter- 
