Indian Mathematics c11.2

c11.2

The earliest Chinese work that deals with mathematical questions is said to be of the 12th century B.C. and it records an acquaintance with the Pythagorean theorem. Perhaps the most celebrated Chinese mathematical work is the *Chin-chang Suan-shū* or "Arithmetic in Nine Sections" which was composed at least as early as the second century B.C. while Chang T'sang's commentary on it is known to have been written in A.D. 263. The "Nine Sections" is far more complete than any Indian work prior to Brahmagupta (A.D. 628) and in some respects is in advance of that writer. It treats of fractions, percentage, partnership, extraction of square and cube-roots, mensuration of plane figures and solids, problems involving equations of the first and second degree. Of particular interest to us are the following: The area of a segment of a circle=½ (c+a)a, where ‘c’ is the chord and ‘a’ the perpendicular, which actually occurs in Mahāvīra’s work; in the problems dealing with the evaluation of roots, partial fractions with unit numerators are used (*cf.* paragraphs 5 and 7 above); the diameter of a sphere=[3]16/9, which possibly accounts for Āryabhaṭa’s strange rule; the volume of the cone=(circumference/6)² which is given by all the Indians; and the correct volume for a truncated pyramid which is reproduced by Brahmagupta and Srīdhara. One section deals with right angled triangles and gives a number of problems like the following: