<Dl> <Dd> sin ⁡ A a = sin ⁡ B b = sin ⁡ C c . (\ displaystyle (\ frac (\ sin A) (a)) \, = \, (\ frac (\ sin B) (b)) \, = \, (\ frac (\ sin C) (c)).) </Dd> </Dl> <Dd> sin ⁡ A a = sin ⁡ B b = sin ⁡ C c . (\ displaystyle (\ frac (\ sin A) (a)) \, = \, (\ frac (\ sin B) (b)) \, = \, (\ frac (\ sin C) (c)).) </Dd> <P> where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see figure). </P> <P> Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power . He used this to find the volume of a paraboloid . He could find the integral formula for any polynomial without having developed a general formula . </P>

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