Mr. Wuisu on the Hindi Quadrature of the Circle. 521 
“ According to the genius of the rules which we have laid down for the circumference 
** of the circle, the are of any given sine may be found thus: take a given sine multiplied 
“« by radius, and divided by the cosine to the given sine for the first quote ; let the square 
“© of the sine be a constant multiplier, and the square of the cosine a constant divisor, 
“© the quotes obtained by multiplying and dividing (by these) the first quote, must be 
“* placed in order one under the other, and divided in succession by the odd numbers 1, 3, 
«5, 7, 9, 11, &c.; then subtract the sum of the even from that of the odd quotes, 
** and the remainder will be the are whose sine was taken. If the sine of the given arc 
** be greater than its cosine, call thut the cosine, and the cosine to it the sine.” 
Having thus submitted to the inspection of the curious eight different 
infinite series, extracted from Bréhmanical works for the quadrature of the 
circle, it will be proper to explain by what steps the Hindé mathematician 
has been led to these forms, which have only been made known to Euro- 
peans through the method of fluxions, the invention of the illustrious 
Newton. Let us first, however, know the age of these works; and as far 
as can be determined, the authors. First, then, it is a fact which I have 
ascertained beyond a doubt, that the invention of infinite series of these 
forms has originated in Malabar, and is not, even to this day, known to 
the eastward of the range of Ghdts which divides that country, called in 
the earliest times Céralam, from the countries of J/adura, Coimbatore, 
Mysore, and those in succession, to that northward of these provinces. 
The author of the Sadratnamdlah is Sancara Varma, the younger brother 
of the present Rdja of Cadattandda near Tellicherry, a very intelligent man 
and acute mathematician. This work, which is a complete system of 
Hindi astronomy, is comprehended in two hundred and eleven verses of 
different measures, and abounds with fluxional forms and series, to be 
found in no work of foreign or other Indian countries. 
The author of the Carana Padhati, whose grandson is now alive in his 
seventieth year, was Parnumana Séma Yau, a Nambitiri Bréhmana of 
Tirusteapura (Trichar) in Malabar. In the first verse of the commentary 
on his work, he is thus mentioned : 
Nutuna griha sama sutarachitayah carana padhatervidusha 
Bhasham vilichati caschit balanam bhodhanarthamalpadhiyam. 
«The Carana Padhati, a path to arithmetic, composed by Nurunacrina Soma 
« Sura, [ now proceed to explain in the common tongue, to adapt it to the genius of 
“* young scholars,” 
