ABSTRACT
The twelfth century saw the earliest considerable infiltrations of Graeco-Arabic mathematical learning into Western Christendom. These chiefly took the form of translations, by Christian or Jewish scholars, of such textbooks as were current in the Moorish schools of Spain. An important achievement of sixteenth-century algebra was the solution of equations involving the cube of the unknown quantity. The ancients were acquainted with geometrical problems analogous to that of solving cubic equations, e.g. the classic problems of duplicating the cube, of trisecting the angle, and of dividing the sphere in a given proportion by means of an intersecting plane. An extremely important advance in the art of calculation was made early in the seventeenth century with the invention of logarithms, whereby multiplication and division were reduced to addition and subtraction, and the extraction of roots to simple division.
