Geometry, Algebra, and Trigonometry by Thomas Kirkman
Geometry, Algebra, and Trigonometry - Table of Contents
- 1. Parallelogram Symmetries & Line Equations
- 2. Parallel Diverging Lines & Incommensurables
- 3. Intersection of Two Lines & Elimination
- 4. Distance Formula & Rectangular Circle Equations
- 5. Quadratic Equations & Imaginary Quantities
- 6. Circle Centre, Chords, Tangents & Secants
- 7. Circular Functions & Definitions of p
- 8. Law of Cosines & Sine/Cosine Addition Formulas
- 9. Trigonometric Formulae & Triangle Areas
- 10. Solution of Plane Triangles & Perpendiculars
- 11. Inscribed, Circumscribed & Escribed Circle Radii
- 12. Similar Polygons & Squaring the Circle
- 13. First Notions of Exponents
- 14. Logarithms and Computational Tables
- 15. Applied Geometry and Trigonometry Problems
- 16. Polygon Areas via Vertex Coordinates
- 17. Oblique Coordinate System Transformations
- 18. Arithmetic, Harmonic & Geometric Progressions
- 19. Permutations & Combinations
- 20. Binomial Theorem
- 21. Conic Curves of Second Degree
What You Will Learn in Geometry, Algebra, and Trigonometry
Geometry, Algebra, and Trigonometry by Thomas Penyngton Kirkman is an authoritative, classic 19th-century educational treatise published by John Weale that provides students with a unified, cross-disciplinary foundation bridging synthetic Euclidean geometry, Cartesian analytic geometry, elementary algebra, and plane trigonometry. This comprehensive volume guides readers through parallelogram symmetries, line slope equations, linear elimination, algebraic vinculum rules, distance formulas, rectangular circle equations, quadratic root classifications, imaginary numbers, chord and tangent properties, circular goniometrical definitions, trigonometric addition formulas, oblique triangle solving, circumscribed and inscribed circle radii, polygon area coordinate methods, oblique coordinate transformations, arithmetic and harmonic progressions, permutations, combinations, the binomial theorem, and five-point conic curve determinations with exceptional pedagogical clarity and logical precision.
Designed for undergraduate mathematics students, secondary educators, surveying apprentices, and history of mathematics researchers, this classic work bridges elementary synthetic proofs directly with Cartesian coordinate analysis and algebraic manipulation. Kirkman details step-by-step geometric constructions, determinant-style area expansions from vertex coordinates, logarithmic computation procedures, and explicit triangle center derivations. Whether you are reviewing historical methods of Victorian British mathematics instruction, mastering unified coordinate methods, or studying classical plane trigonometry, this book offers an indispensable roadmap.
Recognized globally as an ambitious early attempt to synthesize synthetic, analytic, and trigonometric branches into a single seamless curriculum, it stands as one of the best historical references for integrated coordinate geometry and trigonometry. By connecting algebraic equation solving directly to geometric constructions and conic section determination, it serves as an essential tool for learning classical geometry, algebra, and trigonometry with confidence.
Book Details & Specifications
Title:
Geometry, Algebra, and Trigonometry by Thomas Kirkman
Publisher:
John Weale
Year:
1852
Pages:
212
Type:
PDF
Language:
English
ISBN-10 #:
1164646710
ISBN-13 #:
978-1164646716
License:
Public Domain Work
Amazon:
Amazon
About the Author: Thomas Penington Kirkman
The author Thomas Penington Kirkman
(1806–1895) was an eminent British mathematician, Fellow of the Royal Society, and Rector of Croft, widely celebrated for his pioneering research in combinatorics, Kirkman's schoolgirl problem, knot theory, polyhedral geometry, and innovative educational textbooks.
Through Geometry, Algebra, and Trigonometry, Kirkman delivers a masterfully structured, integrated presentation of continuous and discrete mathematical foundations. His rigorous geometric derivations, clear algebraic algorithms, and unified coordinate treatments make this volume a classic reference for coordinate geometry, elementary algebra, and plane trigonometry valued by educators and mathematicians worldwide.
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