(14)![{\displaystyle ax+1=s^{2},\quad bx+a=t^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/780dd1376b6ae8f58931bfa0782a33d058e4c601)
(15)![{\displaystyle 2(x^{2}-y^{2})+3=s^{2},\quad 3(x^{2}-y^{2})+3=t^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d24ea3fef8d33450085abc25b02ddd1264c1bec8)
(16)![{\displaystyle ax^{2}+by^{2}=s^{2},\quad ax^{2}-by^{2}+1=t^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/922215f666962b3c3986620c7a243e5a5504ba59)
(17)![{\displaystyle x^{2}+y^{2}\pm 1=s^{2},\quad x^{2}-y^{2}\pm 1=t^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46e598b5ca253cee9664de17233f9d2319dd75b5)
(18)![{\displaystyle x^{2}-a\equiv x^{2}-b\equiv o~Mod.~c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b13210de5c8c99f9cabdc2edfcfbdf77076e5d44)
(19)![{\displaystyle ax^{2}+b\equiv o~Mod.~c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ecbeaa058fdeed5c1604cb3e96ebf01affcb3fac)
(20)![{\displaystyle x+y=s^{2},\quad x-y=t^{2},\quad xy=u^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e10e78e845d6087829964bdc2115ad316769223)
(21)![{\displaystyle x^{3}+y^{3}=s^{2},\quad x^{2}+y^{2}=t^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92fda06847cdc8ffc4a2514a227bb083d8a0c5ff)
(22)![{\displaystyle x-y=s^{3},\quad x^{2}+y^{2}=t^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfffc842bd807f5c5a18c0a23e77fd045eeff7c0)
(23)![{\displaystyle x+y=s^{2},\quad x^{3}+y^{2}=t^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/132b868436c1a69ba2002cd9d52d3c0bc6e77837)
(24)![{\displaystyle \scriptstyle {x^{3}+y^{2}+xy=s^{2},\quad (x+y)s+1=t^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/597b378710fb6a296300c52c9760c78f6ed2991f)
(25)![{\displaystyle \scriptstyle {ax+1=s^{3},\quad as^{2}+1=t^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4340a0755cb0fbd7b87a98ef93f8fad469e5a727)
(26)![{\displaystyle \scriptstyle {wxyz=a(w+x+y+z)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f4a3a95e2fb6f698ba6d45ad8c04a8e81188fa4)
(27)![{\displaystyle \scriptstyle {x^{3}-a\equiv o~Mod.~b}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb379789e88c0106238adc42168b5b78f7260146)
(28)![{\displaystyle {\begin{aligned}\\&\scriptstyle {x+y+3=s^{2},~x-y+3=t^{2},~x^{2}+y^{2}-4=u^{2},}\\&\scriptstyle {x^{2}-y^{2}+12=v^{2},\ {\frac {xy}{2}}+y=w^{3},}\\&\scriptstyle {s+t+u+v+w+2=z^{2}}\\\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f57644a3c03b54a838ec45d24acafaa27f17f04)
(29)![{\displaystyle \scriptstyle {{\frac {\sqrt[{3}]{xy+y}}{2}}+{\sqrt {x^{2}+y^{2}}}+{\sqrt {x+y+2}}+{\sqrt {x-y+2}}+{\sqrt {x^{2}-y^{2}+8}}=t^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c031eed431e1ee03561bcfd4b11fec669659f26)
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14. Rational right-angled triangles.—The Indian mathematicians of this period seem to have been particularly attracted by the problem of the rational right-angled triangle and give a number of rules for obtaining integral solutions. The following summary of the various rules relating to this problem shows the position of the Indians fairly well.