عنوان مقاله [English]
The story of Archimedes and the crown is narrated by Vitruvius but he doesn’t explain how Archimedes succeeded to solve the problem. Menelaus speaks about Archimedes’ balance that’s an instrument for solving the problem. Later scholars were conscious of the difficulties of making such an instrument and doing exact experiments by it and so they tried to find another method. Menelaus found some mathematical methods for solving this problem. For solving the problem by these methods, we need some input data concerning the weights of three equi-volume pieces of pure metals and their alloy, but the scholars were aware of difficulties of casting such pieces. Aḥmad ibn Faḍl invented a casting method for making equi-volume pieces but Bīrūnī says that this method isn’t sufficiently precise. Bīrūnī’s efforts for finding the weights of equi-volume pieces result in inventing an instrument that he calls the “conic-shaped instrument”. After gathering the data, Bīrūnī decided to use this instrument for knowing gems. His method and the results of his experiments are reported in his treatise Fī al-Nisab allatī Bayn al-Filizzāt wa al-Jawāhir fī al-Ḥajm. In this article the efforts of Bīrūnī for improving Bukhārī’s method and the effect of these efforts on Bīrūnī’s mineralogy are explained.