This concise treatise, from The Cambridge Mathematical Journal, introduces how algebra can represent geometric quantities and the rules that govern their combination. It emphasizes magnitude and direction, covering linear, plane, and solid forms, and shows how transference of operations can illuminate geometric relations. The work also delves into how to pass from general symbols to the projections on coordinate planes, highlighting symmetry and the underlying structure of geometric problems.

Learn the core idea that an algebraic symbol can represent an operation in geometry only if it obeys the same laws of combination as the operation itself.
See concrete explorations of lines of curvature on an ellipsoid, the nature of stationary points, and the geometric meaning of optimization conditions.
Discover methods for solving geometric questions symbolically, including the theory of maxima and minima of functions of two variables and related curvature analyses.
Explore applications to other topics, from the calculation of formulas in diffraction to the broader method of algebraic elimination and transformation.

Ideal for readers of history and development of mathematics, as well as those seeking a bridge between algebra and geometry in classical research.

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