Trigonometry, and Trigonometrical Analysis by Augustus De Morgan
Trigonometry, and Trigonometrical Analysis - Table of Contents
- 1. Single Angle Definitions & Identities
- 2. Formulas for Two or More Angles
- 3. Solution of Triangles & Goniometry
- 4. Symbol Extensions & Imaginary Quantities
- 5. Periodic Quantities & Function Inversion
- 6. Calculus Notions in Trigonometric Analysis
- 7. Trigonometric Functions
- 8. Analytical Trigonometry
- 9. Miscellaneous Additions & Analytical Topics
What You Will Learn in Trigonometry, and Trigonometrical Analysis
Trigonometry, and Trigonometrical Analysis by Augustus De Morgan is an authoritative, classic 19th-century analytical treatise published by Taylor and Walton that provides advanced students with a masterly, foundational transition from geometric plane trigonometry to abstract analytical analysis and early complex variable theory. This comprehensive volume guides readers through single-angle trigonometric definitions, fundamental Pythagorean and quotient identities, addition and compound angle theorems, triangle solution algorithms, symbolic extension principles, arithmetic of imaginary quantities and complex numbers, periodic function properties, inverse trigonometric mappings, calculus foundation concepts (limits, differentials, and series expansions), and advanced analytical applications linking trigonometric and exponential series with exceptional logical rigor and philosophical clarity.
Designed for undergraduate mathematics majors, secondary mathematics educators, historians of analysis, and theoretical physics researchers, this foundational work bridges elementary goniometric calculations directly with analytical algebra and infinite series expansions. De Morgan details step-by-step algebraic derivations, complex exponential identity proofs, periodic function inversions, and explicit trigonometric calculus limits. Whether you are reviewing historical foundations of British mathematical logic, studying the analytical unification of circular and exponential functions, or mastering classical analytical trigonometry, this book offers an indispensable roadmap.
Recognized globally as a landmark text in Victorian mathematical analysis, it stands as one of the best historical references for mastering analytical trigonometry and symbolic logic foundations. By connecting geometric trigonometric definitions directly to complex variable notation and calculus expansions, it serves as an essential tool for learning higher analytical algebra with confidence.
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 preeminent British mathematician, logician, and the first Professor of Mathematics at University College London, internationally celebrated for formulating De Morgan's laws in logic and set theory, as well as his foundational contributions to symbolic algebra, formal logic, and mathematical analysis.
Through Trigonometry, and Trigonometrical Analysis, De Morgan delivers a masterfully structured, philosophically deep presentation of circular functions and complex variable expansions. His rigorous symbolic logic pathways, clear calculus integrations, and historical context make this volume a classic reference for analytical trigonometry and symbolic algebra valued by mathematicians worldwide.
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