पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५२

256 GANITASARASANGRAHA The rule for arriving at the numerical value of the diameter of a (given) cirole 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 arov line as multiplied by you. 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 ecommple in allustration there0 . 230]. In the case of a regular circular figure, it is known that the arrow line is 2 depics in measure, and the bow-string line a demsWhat 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 bowe 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 circlesAnd the rule here is to arrive at the values of the anow lines connected with the overlapping portion when two regular circles cut each other 281छै. With the aid of the values of the two diameters (of the two cutting oircles) as diminished by the value of (the greatest breadth of) the overlapped portion (of the circles), the operation of prakspacket 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 2818. The problem here contomplated may be seen to have been also colved by Aryabhata, and the rule given by him coinoidea with the one under reference here.