This book explores the extension of analysis to space, introducing vector analysis and quaternions. It presents the idea of a vector as a quantity that has magnitude and direction, considering how they can be combined and manipulated. The book traces the development of vector analysis from its foundations in the work of Argand and Warren, through the contributions of Moebius, Bellavitis, Grassmann, and others, to the insights of Hamilton and Tait. It discusses the relationship between vector analysis and quaternions, and demonstrates how quaternions can be used to represent rotations in 3D space. With its clear explanations and practical examples, this book is a valuable resource for students and researchers interested in vector analysis, quaternions, and their applications.

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Excerpt from Vector Analysis and Quaternions

Every proposition about quantities in space ought to re main true when restricted to a plane; just as propositions about quantities in a plane remain true when restricted to a straight line. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. Arts. 2-4 treat of the more restricted analysis, while Arts. 5 - 10 treat of the general analysis.

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