Mohammed ben Musa (c.780 c.850) was a Persian mathematician and
astronomer. The word 'algebra' derives from his Compendious Book on
Calculation by Completion and Balancing, which introduced modern
algebraic methods. First published in 1831, this translation from
Arabic into English was prepared by the German orientalist
Friedrich August Rosen (1805 37). The key algebraic methods
introduced are reduction, completion and balancing. To reduce an
equation is to change an expression to a simpler form; completion
is to remove a negative quantity from one side of the equation and
add it to the other; and balancing is to cancel like terms on
opposite sides of the equation. An account is also given of solving
polynomial equations up to the second degree. Rosen's introduction
and notes accompany the translation, which remains relevant in the
history of mathematics.
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