Abstract
How was it that the physical science emerging in the seventeenth century ‘fitted’ so conveniently into the form of traditional algebra? Greek and early modern numerical and algebraic concepts, embodied in their respective notations, call for examination. The concept of number replacing that of the Greeks, which is at the base of traditional modern algebraic concepts, is whole and self‐determining, in contrast to the variegated wholeness and monodic dependence of the latter. Following on the various co‐existing sign‐systems of the Renaissance, Descartes’ Geometry provided that which became standard. His earlier Regulae ad Directionem Ingenii interweaves concepts of quantity, extension, dimension, unit and figure to enable (perhaps justify) the emergence, in Rule XVIII, of algebraic quantities free of geometrical constraints, and reveals the concepts embodied in the symbolism of early modern algebra. The new algebra, particularly in the form of the real variable, a consequence mainly of the continued connec...
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