## Ramchandra's *Treatise of Problems on Maxima And Minima*

In 1850 Ramchandra published in Calcutta, at his own expense,

For Ramchundra's autobiographical notes see THIS LINK.

For De Morgan's Preface to Ramchundra's book see THIS LINK.

For

For

*A Treatise of Problems on Maxima And Minima, Solved by Algebra*. The book was sent to Augustus De Morgan who republished the book in London in 1859. De Morgan added an Editor's Preface which contained De Morgan's thoughts on Ramchandra's book, Indian mathematics, the Hindu in India, and other related topics. This Editor's Preface also contained autobiographical notes that Ramchundra had sent De Morgan. We give below a version of Ramchandra's Preface to his 1850 work.For Ramchundra's autobiographical notes see THIS LINK.

For De Morgan's Preface to Ramchundra's book see THIS LINK.

For

*The Calcutta Review*of the 1850 book, see THIS LINK.For

*The Calcutta Review*of the 1859 book, see THIS LINK.**Ramchandra's Preface**

For the last four or five years I was desirous of solving almost all problems of Maxima and Minima by the principles of Algebra, and not by those of the Differential Calculus. All those problems which brought out equations of the second degree were of course easily solved by the method of imaginary roots given in some works on Algebra, particularly in Wood's Algebra by Lund, and the Encyclopaedia Metropolitana. But even these problems in several cases required particular artifices, without which it was impossible for me to solve them. All these problems are solved in the first chapter of this little work. Besides the method of imaginary roots, I have given another, quite independent of Imaginary quantities, quantities which to many beginners of Mathematics, appear somewhat mysterious and unintelligible. This latter method I may venture to call a

*new method*, because in all mathematical works which I have had access to, I have never seen a single problem of Maxima or Minima solved by it, though it is used to reduce an adfected quadratic to a pure one in a great many works on Algebra. Thus far I have spoken of the first chapter.

All the problems solved in the second chapter bring out cubic equations, the solution of which on the condition of Maximum or Minimum, required a new method, which I could not find, though I searched for it in several works enumerated hereafter. I then resolved to find out a method, and in intervals of leisure during three years I continually thought on the subject, and at last found it out. This is a method which appears extremely simple and easy, though it baffled all my endeavours for the space of three years. I may call it new, for I did not find it in any book I looked into.

The third and fourth chapters, and the supplement contain problems and general solutions of particular equations of the fourth, fifth, and the sixth degree, together with those problems in which two or three variable quantities enter. The methods used in these parts of the work, though more difficult and intricate than that used in the second chapter, were easily discovered.

This work contains about 130 problems taken chiefly from the following works: Simpson's Fluxions, Hall's Differential Calculus, Gregory's Examples, Connel's Differential Calculus, Walton's Differential Calculus, Ritchie's Differential Calculus, Young's Differential Calculus, Encyclopaedia Britannica, Hirsch's Geometry ,works on Mixed Mathematics, &c. Besides the problems solved here, many more may be solved by the methods given in this treatise.

I have also given definitions, formulae, and propositions necessary for the study of this work in the Introduction.

In conclusion, I flatter myself with the hope that my labours will be of some use to those Mathematical students who are not advanced in their study of the Differential Calculus, and that the lovers of science, both in India and Europe, will give support to my undertaking.

Owing to the necessity of having the work printed in Calcutta, and my consequent inability to superintend the sheets passing through the press, many errors, almost inseparable from a work of this nature, have unavoidably crept in; for these I must beg the indulgence of my readers.

RAMCHUNDRA

Delhi,

16th February, 1850.