500 Proceedings of Royal Society of Edinburgh. 
perfectly new point of view, added many results previously un- 
tliouglit of, and opened up a whole avenue of fresh investigation, 
one cannot but assign to him the place of highest honour among all 
the workers from 1693 to 1812. It is, no doubt, impossible to call 
him, as some have done, the formal founder of the theory. This 
honour is certainly due to Vandermonde, who, however, erected 
on the foundation comparatively little of a superstructure. Those 
who followed Vandermonde contributed, knowingly or unknowingly, 
only a stone or two, larger or smaller, to the building. Cauchy 
relaid the foundation, rebuilt the whole, and initiated new enlarge- 
ments j the result being an edifice which the architects of to-day 
may still admire and find worthy of study. 
Eetrospect of the Period 1693-1812. 
Prom what has just been said by way of estimate of Cauchy’s 
memoir, it will readily appear that a suitable opportunity has now 
presented itself for taking a general retrospect of the work done 
from the date at which the history commences. The system which 
has been pursued, of numbering the new advances made by eacb 
writer, enables us to do this very conveniently, and with a tolerable 
approximation to accuracy by means of a tabular form. The table,, 
herewith annexed, so far explains itself. The authors’ names, it 
will be seen, are arranged both vertically and horizontally in chrono- 
logical order ; and vertical and horizontal lines of separation are 
drawn so as to apportion to each name a gnomon-shaped space. The 
crediting of any entirely new result to an author is done by giving 
its number in Roman figures after his name in the vertical list.. 
On the other hand, any mere modification, fresh presentment, or 
extension of a previously known result, is notified to the right of 
the original number of the result, and under the new writer’s name 
in the horizontal series. Instead of the Arabic figures placed in 
the gnomon-shaped spaces, a cross or other uniform mark would 
have sufficed, but in order to increase the usefulness of the table, a 
number has been inserted, telling the page (counting from the 
commencement of the History) at which the result is to be found. 
For example, if we look to the space allotted to Bezout (1779), we 
find him credited with one entirely new result, numbered XXIII., 
and with some contribution toffiach of five previously known results. 
