Page:Aryabhatiya of Aryabhata, English translation.djvu/60

30 How Kaye gets "If the first and second be bisected in succession the sine of the half-chord is obtained" is a puzzle to me. It is impossible as a translation of the Sanskrit.

13. The circle is made by turning, and the triangle and the quadrilateral by means of a karna; the horizontal is determined by water, and the perpendicular by the plumb-line.

Tribhuja denotes triangle in general and caturbhuja denotes quadrilateral in general. The word karna regularly denotes the hypotenuse of a right angle triangle and the diagonal of a square or rectangle. I am not sure whether the restricted sense of karna limits tribhuja and caturbhuja to the right-angle triangle and to the square and rectangle or whether the general sense of tribhuja and caturbhuja generalizes the meaning of karna to that of one chosen side of a triangle and to that of the diagonal of any quadrilateral. At any rate, the context shows that the rule deals with the actual construction of plane figures.

Paramesvara interprets it as referring to the construction of a triangle of which the three sides are known and of a quadrilateral of which the four sides and one diagonal are known. One side of the triangle is taken as the karna. Two sticks of the length of the other two sides, one touching one end and the other the other end of the karna, are brought to such a position that their tips join. The quadrilateral is made by constructing two triangles, one on each side of the diagonal.