The Principles of Elliptic and Hyperbolic Analysis (Classic Reprint)

Exploring the principles that unite elliptic and hyperbolic analysis, with a fresh look at space using versors.

This book extends the theory of vector and versor analysis to elliptic and hyperbolic forms, applying them to spheres, ellipsoids, and hyperboloids while deriving complete trigonometric results for these surfaces. It presents a coherent development of the subject and its foundational theorems, including rotations and their generalized forms.

The work foregrounds how spherical, ellipsoidal, and hyperboloidal versors interact, and shows how to express product versors, excircular axes, and their components. It includes methods for forming and proving key identities in spherical and non-spherical settings, and introduces exponential series and logarithmic versors in a unified framework.

• Clear, step-by-step treatment of spherical, ellipsoidal, and hyperboloidal versors
• Techniques for computing product versors and their geometric interpretations
• Explanations of excircular axes, normal planes, and related trigonometric theorems
• Connections between classical spherical trigonometry and generalized space analysis

Ideal for readers of advanced mathematics and the history of analysis, this edition suits those seeking a rigorous, accessible path through a specialized topic.