Trigonometry and Double Algebra by Augustus De Morgan
Trigonometry and Double Algebra - Table of Contents
1. Definitions and Fundamental Formulas of Trigonometry in the Case of One Angle
2. Formulas Connected with Two or More Angles
3. On the Solution of Triangles
4. On the Extension of the Meanings of Symbols and on the Square Roots of Negative Quantities
5. On the Distinction of Periodic Quantities, and Preliminary Considerations on the Inversion of Periodic Functions
6. Notions of the Differential and Integral Calculus, as Required in the Succeeding Chapters
7. Continuation of the Connection of Direct and Inverse Trigonometric Functions
8. Applications of the Preceding Chapters
9. Miscellaneous Additions to the Preceding Chapters
What You Will Learn in Trigonometry and Double Algebra
"Trigonometry and Double Algebra" by "Augustus De Morgan" is a classic 19th-century text that explores the foundations of "trigonometry" and extends algebra into a more general, symbolic framework known as "double algebra". The book presents trigonometric functions not merely as formulas to memorize but as objects with geometric and algebraic significance. De Morgan emphasizes logical reasoning and systematic understanding, helping learners see the connections between angles, triangles, and algebraic expressions.
The book’s "trigonometry" section covers sine, cosine, tangent, and related functions, along with their expansions, identities, and applications. De Morgan blends geometric interpretations with algebraic manipulations, showing how equations and expressions can be understood both visually and symbolically. The “double algebra” portion generalizes traditional algebra, treating symbols as representing not just numbers but also directed quantities or complex-like entities. This allows a deeper understanding of operations with negative numbers, imaginaries, and symbolic expressions.
Designed for students and educators interested in advanced mathematical reasoning, the book bridges "algebra", trigonometry, and geometry. Its rigorous approach provides a conceptual foundation for later developments in "complex numbers", "symbolic algebra", and analytic geometry. Even today, "Trigonometry and Double Algebra" remains a valuable resource for understanding the logical structure behind mathematical symbols and trigonometric reasoning.
Book Details & Specifications
Title:
Trigonometry and Double Algebra by Augustus De Morgan
Publisher:
Taylor
Year:
1849
Pages:
194
Type:
PDF
Language:
English
ISBN-10 #:
141818053X
ISBN-13 #:
978-1418180539
License:
Public Domain Work
Amazon:
Amazon
About the Author: Augustus De Morgan
The author Augustus De Morgan
(1806–1871) was a British mathematician and logician, best known for his work in "trigonometry", "algebra", and the development of "double algebra". He emphasized clear, logical reasoning and helped bridge geometry with symbolic mathematics. De Morgan formulated the famous "De?Morgan’s laws" and introduced systematic "mathematical induction", influencing both logic and algebra. As the first mathematics professor at University College London and co-founder of the London Mathematical Society, he shaped "mathematics education" for generations. His textbooks and writings remain valuable for understanding the foundations of algebra, trigonometry, and the logical structure of mathematics.
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