For Ramchundra's autobiographical notes see THIS LINK.
For De Morgan's Preface to Ramchundra's book see THIS LINK.
For Ramchundra's Preface to his 1850 edition, see THIS LINK.
For The Calcutta Review of the 1859 book, see THIS LINK.
Review of Ramchundra's 1850 book.
It is with sincere regret that we are compelled to speak with very limited approval of the merits of this work, both as regards its object and its execution. The very nature of the problems of Maxima and Minima involves the idea, which is the fundamental one of the Differential Calculus; and, however it may be disguised, that idea must pervade all investigations of the problems. What then is the use of a cumbrous, and often inelegant, process of doing that without the Calculus, which, in reality, it is the proper duty of the Calculus to do, and which it does so much more simply and elegantly? We can see no advantage, in an educational point of view, in teaching this cumbrous method of dispensing with the acquisition of that, which is at once so easy of acquisition and so worthy of it, as Taylor's Theorem. In any other point of view, the thing is equally useless. In actual practice, problems of Maxima and Minima never occur, except in investigations which, we may safely state, are never carried on by persons ignorant of the principles of the Calculus. Moreover, the author is in error, in supposing that he has succeeded in inventing a method applicable to the solution of all problems of the kind in question. His method may be applicable to all problems involving only algebraical functions; but these are in reality only a small portion of the problems that continually occur. Those that involve logarithmic and trigonometrical functions are left untouched.
While we are thus compelled to express our doubts, as to the utility of the object of the book, we cannot be much more complimentary as to the mode of its execution, which is, in general, clumsy and school-boy-like. We very gladly, however, exempt from this censure the "new method" of finding the value of a variable, which gives a maximum or minimum value to an algebraic function of it of the third, or any higher, degree. This is an original and neat application of a familiar principle; and had there been any utility in the application, and had the details of the application been as well executed, as the conception itself is ingenious, we should have been spared the task of expressing our disapproval of the work, and should have had, instead, the far more gratifying one of chronicling an ingenious device of one of a class of Mathematicians, in whose success we feel the liveliest interest. As it is, we state with much pleasure our conviction, that the mind, which formed this conception, is capable of far better things than are achieved in the work before us.
Our author gives two solutions of each problem; but the second is in every case no solution at all. It is merely a proof of the ac curacy of the result ; inasmuch, as it consists in assuming the un known quantity as equal to the result obtained by the former method, with the addition of some indeterminate quantity, and then, showing that that indeterminate quantity is equal to nothing.
Our author has laboured under a disadvantage, resulting from his distance from the press. A list of errata corrects ninety-two blunders ; but a careful perusal of a considerable portion of the book warrants our saying that there are four or five times as many left uncorrected : and these not of trifling moment, but such as make absolute nonsense of the passages, in which they occur.
If these remarks should fall under the notice of Ramchundra, or any of the class to which he belongs, we trust that they will receive them as a token of the interest, that we take in their progress. We have spoken our sentiments freely, as becomes those who are en gaged in researches on abstract truth. We have cheerfully accorded commendation, when we conscientiously could; and we have expressed our disapprobation as tenderly as our conviction would permit.