P. HISTORY OF ' AATHEMATICAL - School of Mathematics

INDIVIDUAL WRITERS 81
first unknown quantity multiplied by the cube of the second. A dot
is, in some copies of the text and its commentaries, interposed between
the fzctors, without any special direction, however, for this notation.lY1
Instead of ya va one finds in Brahmagupta and BhZskara also the
severer contraction ya v; similarly, one finds cav for the square of the
second unkno~n.~
It should be noted also that "equations are not ordered so as to
put all the quantities positive; nor to give precedence to a positive
term in a compound quantity: for the negative terms are retained,
and even preferably put in the first pla~e."~
According to N. Ramanujacharia and G. R. Ka~e,~ the content of
the part of the manuscript shown in Figure 33 is as follows: The
FIG. 33.-iridhara's Triscitika. Sridhara wrts born 991 A.D. He is cited by
Bhmkara; he explains the "Hindu method of completing the square" in solving
quadratic equations.
circumference of a circle is equal to the square root of ten times the
square of its diameter. The area is the square root of the product of
ten with the square of half the diameter. Multiply the quantity whose
square root cannot be found by any large number, take the square
root .of the product, leaving out of account the remainder. Divide
it by the square root of the factor. To find the segment of a circle,
take the sum of the chord and arrow, multiply it by the arrow, and
square the product. Again multiply it by ten-ninths and extract its
square root. Plane figures other than these areas should be calculated
by considering them to be composed of quadrilaterals, segments of
circles, etc.
Op. cit., p. 140, n. 2; p. 141. In this quotation we omitted, for simplicity,
some of the accents found in Colebrooke's transliteration from the Sanskrit.
Ibid., p. 63, 140,346.
Ibid., p. xii.
Bibliotheca malhematica (3d ser.), Vol. XI11 (1912-13), p. 206, 213,214.