Islamic mathematical achievements were many as here outlined by Sabra. Islamic scholars devised and successfully applied new and elaborate techniques of computations; they constructed sophisticated mechanical computers; devised methods for calculating with decimal fractions; took significant steps toward extending the concept of number inherited from the Greeks, so as to include irrational magnitudes as well natural numbers and common fractions; added to the limited, ad hoc trigonometric methods they learned from the Greeks (Ptolemy’s chord function) and from the Indians (the sine and tangent functions) and eventually developed them into an independent discipline no longer subservient to astronomy. They recast the algebraic modes of solving numerical problems found among the Greeks and the Indians, thereby creating a new form of algebraic discourse and setting the science of algebra on a new course (but without introducing a symbolic calculus), and they went a long way in exploiting the use of higher geometry (conic sections) in the solution of higher-thanquadratic equations.
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