CHAPTER VII-MEASUREMENT OF AREAS. 255 Within the (known) numerical measure of the diameter of a regular circle, any known number being taken as the measure of an arrow, the rule for arriving at the numerical value of the string (of the bow) having an arrow of that same measure:- 225. The difference between (the given value of) the diameter and (the known value of) the arrow is multiplied by four times the value of the arrow. Whatever is the square root (of the resulting product), that the wise man should point out to be the (required) measure of the string (of the bow). An example in illustration thereof. 226. The diameter of the circle is 10. It is cut off by 2. O mathematician, give out, after calculating well, what may be the string (of the bow) in relation to (that) cut off portion (of the given diameter). The rule for arriving at the ramerical value of the arrow- line, when the numerical value of the diameter of a (given) regular circle and the value of a bow-string line (in relation to that circle) are (both) known :-- 227. That which happens to be the square root of the difference between the squares of the (known) values of the diameter and the bow-string line (relating to the given circle)- that has to be subtracted from the value of the diameter. Half of the (resulting) remainder should be understood to give (the required value of) the arrow-line. An example in illustration thereof. 228. The diameter of the (given) circle is 10 in measure. Moreover, the bow-string line inside is known to be 8 in measure. Give out, O friend, what the value of the arrow-line may be in relation to that (how-string). 225. The rules given in stanzas 225, 227, 229 and 231 are all based on the fact that in a circle the rectangles contained by the segments of two intersecting chords are equal.
