Mr. Wursu on the Hindi Quadrature of the Circle. 523 
to his own period, he thus observes: ‘ Much difference having occurred 
** in astronomical calculations, in the year of the Caliyuga 4532 a Bréh- 
** man of high rank who lived on the coast of the western ocean, having 
** examined the heavens for twelve years, established what is laid down 
“in the Yantra-Sangraha.” This is the evidence of the author of the 
Yucti-Bhisha, the commentary on the Tantra-Sangraha, concerning the 
author of the latter work: the date of the Driccaranam is mentioned in 
the latter part of the work, wiz. the 783d of the Malabar era; and in the 
summary account of the periods of astronomy, it is written 4708 of the 
Caliyuga, both of which coincide with the year 1608 of the Christian era. 
A farther account of the Yucti-Bhdshd, the demonstrations of the rules 
for the quadrature of the circle by infinite series, with the series for the 
sines, cosines, and their demonstrations, will be given in a separate paper: 
I shall therefore conclude this, by submitting a simple and ears proof of 
the 47th proposition of Euciin, extracted from 
the Yucti-Bhashd. In the accompanying figure, 
let ABC be a triangle, having the angle at C ,, 
a right angle: on AC describe the square 
ACFN, and on BC describe the square 
BCDE: on ED take EG equal to AC, and 
on AD take AH equal to BC, draw HK 
perpendicular to AD and equal to AC, join 
BG, GK, and AK. 
E G 
The mathematician will easily prove that the three spaces AFO, PGD, 
and BEG, parts of the squares SACFN and BCDE not included in the 
figure ABGK, are equal to, and identical with, the spaces KHP, OBN, and 
AHK, not occupied by any parts of the above two squares; id est, that the 
sum of the two squares ACFN and BCDE equals the figure ABGK ; but 
this, from its construction, is a square, and is drawn upon the hypothenuse 
ABC. This is probably the form by which Pyruacoras discovered the 
celebrated problem, which Eucuip afterwards so beautifully illustrated in 
the 47th proposition of the first book of his ‘ Elements.’ 
VoL. BUG 3 ¥ 
