पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४५४

256 GANITASĀRASANGRAHA. The rule for arriving at the numerical value of the diameter of a (given) circle when the numerical values of the (related) bow-string line and the arrow line are known :-- 229. The quantity representing the square of the value of the bow-string line is divided by the value of the arrow line as multiplied by four. Then the value of the arrow line is added (to the resulting quotient). What is so obtained is pointed out to be the measure of the breadth of the regular circle measured through the centre. An example in illustration thereof. 230. In the case of a regular circular figure, it is known that the arrow line is 2 dandas in measure, and the bow-string line 8 dandas. What may be the value of the diameter in respect of this (circle)? When two regular circles cut each other, there arises a fish- shaped figure. In relation to that fish-shaped figure, the line going from the mouth to the tail (thereof) should be drawn. With the aid of this line, there will come into existence the outlines of two howe applied to each other face to face. The line drawn from the mouth to the tail (of the fish-figure) happens to be itself the bow-string line in relation to both these bows. The two arrow lines in relation to both these bows are themselves to be understood as forming the two arrow lines connected with the mutually overlapping circles And the rule here is to arrive at the values of the arrow lines connected with the overlapping portion when two regular circles cut each other :- 231. With the aid of the values of the two diameters (of the two cutting circles) as diminished by the value of (the greatest breadth of) the overlapped portion (of the circles), the operation of praksēpaka should be carried out in relation to this (known) value of (the greatest breadth of) the overlapped portion (of the circles). The two results (so obtained) are in the matter 231. The problem here contemplated may be seen to have been also solved by Áryabhata, and the rule given by him coincides with the one under reference here.