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OHAPTER VII- MEASUREMENT OF ARBAS.
229
(also) of the square. (That same) quotient, it multiplied by s6, gives rise to the required ineasure of the base of thu (equilatoral) triangle as also of the longisb quadrilateral figuro. Half (of this) is the measure of the perpendicular-side (in the case of the longisb quadrilateral figure).
An example in illustration thereof. 143-145. A king caused to be dropped an excellent carpot on the floor of (his) palace in the inner apartments of his zenana amidst the ladies of his harem. That (cnrpet) was in shape) # regular circle. It was held in band) by those ladies. The fistfuls of both their arms made each of them) acquire 15 (dandas ont of the total area of the carpot). How many are the ladies, and what is the diameter of the circle) here? What are the sides of the square (if that samo carpot be square ip shupo) ? and what the
magnitude. The stanza states a rule for finding out the measure of the diameter of the circle, or of the sides of the square, or the equilateral triangle or the oblong. Ilm represents the arou of ouch part and n the length of a part of the total porimeter, the formulas given in the rule aro
x 4 = diamotor of the circle, or side of the square ;
and "x 6 = side of the equilateral triangle or of the oblongi
and half of x 6 = the longth of the perpendicular-wide in the came of the oblong.
The rationals will bo cleur from the following aquations, where represents the nnulor of parts into which ench figure is divided, a in the length of the radius in the case of the circle, or the length of a side in the case of tho other figures ; and 6 is the vertical side of the oblouk :
x mwa In the case of the Cirolo ... =
X
2 !
Xm
In the case of the Square
=
X
1
In the case of the Equilateral Triangle = 2
1 x 1 3 In the cro of the Oblong
тх тахь =
; horu b is taken to be equal
* Xn2(a + b) nor to half of a It has to be noted that only the approximate value of the ares of the equilater triangle, w given in stanza 7 of this chapter, is adopted bero. Otherwise the formula given in the role will not hold good.
148-146. Wat is called Astful in this problem is cquivalent to four angulas in measure.
