The Principles and Application of Imaginary Quantities, Vol. 1: To Which Are Added Some Observations on Porisms (Classic Reprint) - Hardcover

Benjamin Gompertz

9780332452135: The Principles and Application of Imaginary Quantities, Vol. 1: To Which Are Added Some Observations on Porisms (Classic Reprint)

Hardcover

ISBN 10: 0332452131 ISBN 13: 9780332452135

Publisher: Forgotten Books, 2018

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Explore the strange world of imaginary quantities and see how they reshape algebra and geometry.

This early-19th-century treatise introduces imaginary and impossible quantities as tools for solving equations and exploring geometric problems. It discusses how these expressions can illuminate methods for roots beyond the real numbers, while weighing debates among mathematicians about their meaning and validity. The work blends practical rules with philosophical notes, offering historical context and concrete examples that show how imaginary roots can influence problem solving in algebra and geometry.

Readers will encounter explanations of rules of operation, geometric interpretations, and the use of these ideas in solving quadratic and cubic equations. The text also surveys how projections and functional representations help to connect algebraic form with geometric insight, and it reflects on the evolving view of what is mathematically possible.

Foundations and motivation for imaginary quantities in algebra
Rules of operation and how to handle imaginary roots
Connections between algebra and geometry through examples and projections

Ideal for readers of the history and foundations of mathematics who want a window into early discussions about imaginary quantities and their practical use.

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