Page:Indian mathematics, Kaye (1915).djvu/40

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 * + We conclude this section with a few illustrations transliterated from Sanskrit manuscripts.
 * | Indian Forms.
 * | Equivalents.
 * | References.
 * | 1.
 * | yā 6 rū 300 yā 10 rū $$\scriptstyle{1\dot{0}0}$$
 * | $$\scriptstyle{6x+300=10x-100}$$
 * | V. 104.
 * | 2.
 * | yāca 18 yā 0 rū 0 yāva 16 yā 9 rū 18
 * | $$\scriptstyle{18x^2+0x+0=16x^2+9x+18}$$
 * | Y. 133.
 * | 3.
 * | yā ra ra 1 yā va $$\scriptstyle{\dot{2}}$$ yā 400 rū 0 yā ra ra 0 yā va 0 yā 0 rū 9999
 * | $$\scriptstyle{x^4-2x^2+400x+0=0.x^4+0.x^2+0.x+9999}$$
 * | V. 138.
 * | 4.
 * | yā 197 kā $$\scriptstyle{1\dot{6}44}$$ nī $$\scriptstyle{\dot{1}}$$ rū 0 yā 0 kā 0 nī 0 rū 6302
 * | $$\scriptstyle{197x-1644y-z+0=0.x+0.y+0.z+6302}$$
 * | Br. xviii, 55.
 * | 5.
 * | ka 6 ka 5 ka 2 ka 3
 * | $$\scriptstyle{\sqrt{6}+\sqrt{5}+\sqrt{2}+\sqrt{3}}$$
 * | V. 37.
 * | 6.
 * | $$\begin{array}{|c|c|c|c|}\hline\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}\\\hline\scriptstyle{4}&\scriptstyle{3}&\scriptstyle{6}&\scriptstyle{12}\\\hline\end{array}$$
 * | $$\scriptstyle{\frac{1}{4}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}}$$
 * | S. 7.
 * | 7.
 * | $$\begin{array}{|c c|c c c|c c c c|}\hline\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}&\scriptstyle{1}\\\scriptstyle{1}&\scriptstyle{2}&\scriptstyle{1}&\scriptstyle{2}&\scriptstyle{3}&\scriptstyle{1}&\scriptstyle{2}&\scriptstyle{3}&\scriptstyle{5}\\\hline\end{array}$$
 * | $$\scriptstyle{1\times\frac{1}{2}+1\times\frac{1}{2}\times\frac{1}{3}+1\times\frac{1}{2}\times\frac{1}{3}\times\frac{1}{5}}$$
 * | 8.
 * | $$\begin{array}{|r|r|c|c c|}\hline\scriptstyle{10}&\scriptstyle{163}&\scriptstyle{4}&\scriptstyle{pha}&\scriptstyle{163}\\\scriptstyle{1}&\scriptstyle{60}&\scriptstyle{1}&&\scriptstyle{150}\\\hline\end{array}$$
 * | $$\scriptstyle{10:\overset{163}{60}::4:\overset{163}{150}}$$
 * | Bk. 27.
 * | 9.
 * | $$\begin{array}{|r|}\hline\scriptstyle{1}\\\scriptstyle{1}\\\scriptstyle{1}\\\scriptstyle{\dot{2}}\\\scriptstyle{2}\\\scriptstyle{\dot{9}}\\\scriptstyle{1}\\\scriptstyle{\dot{4}}\\\scriptstyle{6}\\\scriptstyle{\dot{10}}\\\hline\end{array}$$
 * | 10.
 * | $$\begin{array}{|r l|}\hline\scriptstyle{40}&\\\scriptstyle{1}&\\\scriptstyle{1}&\\\scriptstyle{3}&+\\\scriptstyle{1}&\\\scriptstyle{4}&+\\\scriptstyle{1}&\\\scriptstyle{5}&+\\\hline\end{array}$$
 * | 9. $$\scriptstyle{(1-\frac{1}{2})(1-\frac{2}{9})(1-\frac{1}{4})(1-\frac{6}{10})}$$ 10. $$\scriptstyle{40(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})}$$
 * | L. 53. Bk. 25.
 * }
 * | 8.
 * | $$\begin{array}{|r|r|c|c c|}\hline\scriptstyle{10}&\scriptstyle{163}&\scriptstyle{4}&\scriptstyle{pha}&\scriptstyle{163}\\\scriptstyle{1}&\scriptstyle{60}&\scriptstyle{1}&&\scriptstyle{150}\\\hline\end{array}$$
 * | $$\scriptstyle{10:\overset{163}{60}::4:\overset{163}{150}}$$
 * | Bk. 27.
 * | 9.
 * | $$\begin{array}{|r|}\hline\scriptstyle{1}\\\scriptstyle{1}\\\scriptstyle{1}\\\scriptstyle{\dot{2}}\\\scriptstyle{2}\\\scriptstyle{\dot{9}}\\\scriptstyle{1}\\\scriptstyle{\dot{4}}\\\scriptstyle{6}\\\scriptstyle{\dot{10}}\\\hline\end{array}$$
 * | 10.
 * | $$\begin{array}{|r l|}\hline\scriptstyle{40}&\\\scriptstyle{1}&\\\scriptstyle{1}&\\\scriptstyle{3}&+\\\scriptstyle{1}&\\\scriptstyle{4}&+\\\scriptstyle{1}&\\\scriptstyle{5}&+\\\hline\end{array}$$
 * | 9. $$\scriptstyle{(1-\frac{1}{2})(1-\frac{2}{9})(1-\frac{1}{4})(1-\frac{6}{10})}$$ 10. $$\scriptstyle{40(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})}$$
 * | L. 53. Bk. 25.
 * }
 * }