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Mathematics.
See also: Thabit number

In mathematics, Thābit derived an equation for determining amicable numbers. His proof of this rule is presented in the Treatise on the Derivation of the Amicable Numbers in an Easy Way. This was done while writing on the theory of numbers, extending their use to describe the ratios between geometrical quantities, a step which the Greeks did not take. Thābit's work on amicable numbers and number theory helped him to invest more heavily into the Geometrical relations of numbers establishing his Transversal (geometry) theorem.

Thābit described a generalized proof of Phythagoras' Theorem. He provided a strengthened extension of Phythoras' proof which included the knowledge of Euclid's Fifth Postulate, which states that the intersection between two straight line segments combine to create two interior angles which are less than 180 degrees. These method of reduction and composition result in a combination and extension of contemporary and ancient knowledge on this famous proof. Thābit believed that geometry was tied with the equality and differences of magnitudes of lines and angles, also that ideas of motion should be included in geometry and more widely physics.

The continued work done on geometric relations and the resulting exponential series allowed Thābit to calculate multiple solutions to chessboard problem s. This problem was less to do with the game itself, and more to do with the number of solutions or the nature of solutions possible. In Thābit's case, he worked with combinatorics to work on the permutations needed to win a game of chess.

In addition to Thābit's work on Euclidian Geometry there is evidence that he was familiar with Archimedean geometry as well. His work with Conic Sections and the calculation of a paraboloid shape (cupola), show his proficiency as an Archimedean geometer. This is further embossed by Thābit's use of the Archimedean Property in order to do a rudimentary approximation of the volume of a paraboloid. The use of uneven sections while simple shows a critical understanding of both Euclidean and Archimedean geometry. Thābit was also responsible for a commentary on Archimedes' Libera Assumpta.