Which algebraic problem was essential for medieval Islamic astronomers to accurately orient an astrolabe given observed star altitude?

💡 Explanation

To orient an astrolabe by star altitude, the astronomer had to calculate Local Time by using known star declinations. When solving the almucantar intersection via ratios, quadratic equations result from trigonometric identities, thus solving quadratic equations is required. Therefore, solving quadratic equation relates altitude to time instead of solving triangles or using positions requiring function calculation.

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