Page:Indian mathematics, Kaye (1915).djvu/77

 49. In the case of a longish quadrilateral figure the perpendicular side is 55, the base is 48 and then the diagonal is 73. What are the elements here? Answer—3, 8. 50. Intelligent friend, if thou knowest well the spotless Līlāvatī, say what is the area of a circle the diameter of which is measured by seven, and the surface of a globe or area like a net upon a ball, the diameter being seven, and the solid content within the same sphere? Answer—Area $$\scriptstyle{38\frac{2423}{5000}}$$; surface $$\scriptstyle{153\frac{1173}{1250}}$$; volume $$\scriptstyle{179\frac{1487}{2500}}$$ 51. In a circle whose diameter is ten, what is the circumference? If thou knowest, calculate, and tell me also the area? Answer—$$\scriptstyle{\sqrt{1,000}}$$, $$\scriptstyle{\sqrt{6250}}$$. 52. The measure of Rāhu is 52, that of the moon 25, the part devoured 7. Answer—The arrow of Rāhu is 2, that of the moon 5. This is an eclipse problem and means that circles of diameters 52 and 25 intersect so that the portion of the line joining the two centres common to the two circles is 7. The common chord cuts this into segments of 5 and 2. 53. The combined sum of the measure of the circumference, the diameter and the area is 1116. Tell me what the circumference is, what the calculated area, and what the diameter? Answer—108, 972, 36. The rule given is circumference$$\scriptstyle{=\sqrt{12(\text{combined sum}+64)}-\sqrt{64}}$$ which assumes that $\scriptstyle{\pi=3}$. L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.