164 
and the versed sine utcramajya. These terms seem to be 
derived from the word jya, which signifies the chord of an 
arc, from which the name of the radius, or sine of 90°, 
vis. trijya, is also taken. This regularity in their trigo- 
nometrical language, is not unworthy of remark ; but what 
is of more consequence to be observed is the use of sines, as 
it was unknown to the Greeks, who calculated by the help 
of the chords, and this forms a striking difference between 
theirs and the Indian trigonometry." The table of sines 
exhibits them to every twenty-fourth part of the quadrant ; 
the table of versed sines does the same : in each, the sine, 
or versed sine, is expressed in minutes of the circumference, 
neglecting fractions. Thus, the sine of 3° 45' is 225 ; the 
sine of 7° 30' is 449 ; and so on. The rule for the compu- 
tation of the sines is curious ; it indicates a method of 
computing a table by means of their second differences, — 
a considerable refinement in calculation, and first practised 
by the English mathematician Briggs."* (Wallace.) 
The Surya Siddhanta, continues the author of the 
abridged essay on Hindoo Mathematics in British India, 
ii. p. 463, does not give the demonstration of the truth of 
the rule ; but the commentary gives direct geometrical 
means for their calculation. In the progress of science, 
the invention of trigonometry is a step of great importance, 
and of considerable difficulty. He who first formed the 
idea of exhibiting, in arithmetical tables, the ratio of the 
sides and angles of all possible triangles, must have been a 
man of profound thought, and of extensive knowledge. 
However ancient, therefore, any book may be, in which 
we meet with a system of trigonometry, we may be assured 
that it was not written in the infancy of the science. We 
may therefore conclude, that geometry must have been 
known in India long before the writing of the Surya 
Siddhanta. Professor Playfair, speaking of the Indian 
