Algebra
that department of mathematics which enables one, by the aid of certain symbols, to generalize, and, therefore, to abbreviate, the methods of solving questions relating to numbers.
It is now regarded as the most extensive department of mathematics. It was called by Isaac Newton universal arithmetic, employing letters of the alphabet as symbols of known or unknown quantities and signs (+, -, √, etc.), to indicate addition, subtraction, and similar arithmetical processes. Of the letters, those near the beginning of the alphabet (a, b, c, d, etc.) usually stand for known quantities, and those toward its end for unknown ones. The difference between algebra and arithmetic consists in the universality of the former, its conclusions being true for any number of specific cases, while the results of an arithmetical process can be applied to a single case only. The earliest extant treatise on algebra is that of Diophantus (4th century A. D.).
The Hindus transmitted the science to the Arabs, whose writings on the subject were brought to Italy by Leonardo Fibonacci (1202 A. D.) of Pisa.