Trigonometry, and Trigonometrical Analysis by Augustus De Morgan
Trigonometry, and Trigonometrical Analysis - 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 Trigonometrical Analysis
"Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the Differential Calculus" it for Those who have Studied the Principles of Arithmetic and Algebra, and Six Books of Euclid by "Augustus De Morgan" is a classic mathematical text designed to build a strong foundation in "trigonometry", preparing students for "calculus". The book systematically introduces "trigonometric functions", exploring their geometric interpretations and algebraic properties. De Morgan emphasizes understanding the relationships between angles, triangles, and functions, helping learners see the logical structure behind trigonometric formulas rather than just memorizing them.
The book goes beyond basic trigonometry, introducing "trigonometrical analysis" to show how trigonometric functions behave and can be manipulated algebraically. This early analytical approach bridges the gap between geometry and calculus, providing students with tools to tackle differential calculus confidently. De Morgan carefully integrates examples and exercises, reinforcing concepts while connecting "algebra", geometry, and trigonometry.
Designed for students with prior knowledge of arithmetic, algebra, and geometry, the book is both rigorous and accessible. Its historical significance lies in its clear logical progression from elementary mathematics to advanced analysis. Even today, it serves as a valuable reference for those interested in classical approaches to trigonometry, the foundations of calculus, and the interplay between "geometry", "algebra", and analytical reasoning.
Book Details & Specifications
Title:
Trigonometry, and Trigonometrical Analysis by Augustus De Morgan
Publisher:
Taylor and Walton
Year:
1837
Pages:
258
Type:
PDF
Language:
English
ISBN-10 #:
1436833485
ISBN-13 #:
978-1436833486
License:
Public Domain Work
Amazon:
Amazon
About the Author: Augustus De Morgan
The author Augustus De Morgan
(1806–1871) was a pioneering British mathematician and logician known for his work in "trigonometry", "algebra", and "mathematical analysis". He served as the first mathematics professor at University College London and played a key role in advancing mathematics education. De Morgan authored influential textbooks, including "Elements of Trigonometry and Trigonometrical Analysis", emphasizing clarity, logical structure, and practical learning. He is also famous for "De Morgan’s Laws" in logic.
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