 Discussion on "Dinanath Atmaram Dalvi" by Amod Dalvi (@mmd1525, 0)

Rao Saheb Dinanath Atmaram Dalvi (1844 – 10 February 1897), was my great-great grandfather an Indian judge and mathematicianHe obtained his BA degree in 1865 from Elphinstone College in Bombay. He was then selected as senior scholar and obtained the MA degree from Elphinstone College in 1866. He obtained his LLB degree in 1868 and was a Senior Dakshina Fellow in 1868.In the 1860’s he systematically examined Newton's rule for finding the number of imaginary roots and in 1869 published his book titled "An Examination of Sir Isaac Newton's Rule for finding the Number of Imaginary Square Roots in an Equation" in which he provides mechanical and geometric theorems and gives a direct and complete proof and disproof of the equation.D.A Dalvi states that the chief aim of his own rule was to find out the limit beyond which imaginary roots cannot exceed. He goes on to prove that if imaginary roots exist at all, they cannot exceed a certain number and in this show the superiority of the “Dalvi Rule “so referred to in the Times of India 9. He states that however it must not be supposed that this affords us the means by which to ascertain the exact number of imaginary roots any given equation may have, nor whether even one imaginary root exists in an equation. Newton’s rule may hence fail to detect imaginary roots in an equation when they actually exist in an equation and the roots may fall short of the number but be all real. He however agreed that when imaginary roots of an equation are all equal Newton’s criterial fully applies and although Newtons law is true for some values of the literal co-efficient of the general terms in an equation, it is not universally true.