Forsyth on Calculus of Variations

It is therefore wholly to its credit tha t Bell's book is so largely abstract . In this way he has secured the utmost generality and hence insured permanency to his work. There is also the following important immediate gain. After constructing abstract theories for various classes of problems, he was in a position to decide if those theories are distinct or are (abstractly) identical. In the latter case we have not merely the often astonishing conclusion tha t two quite different theories are really equivalent, but the great advantage of being able to apply in a particular case whichever of the two theories is best adapted to it. The book is however not abstract for the sake of being abstract, but because it gives the essence of a vast array of concrete results traced to their t rue sources and easily deduced from these few sources. I t is not to be overlooked tha t the author has a minute first-hand acquaintance with the vast array of concrete facts in the theory of numbers. It would require many volumes to expound them and the result would bewilder the reader. How much better to have a brief book which epitomizes all these facts under a few abstract theories. This original and scholarly book is an honor to American mathematics.