Geometry, Algebra, and Trigonometry by Thomas Kirkman - PDF

About this book :-
"First Mnemonical Lessons in Geometry, Algebra, and Trigonometry" by "Thomas Penyngton Kirkman" is a 19th-century educational text designed to teach the fundamentals of "geometry", "algebra", and "trigonometry" in a clear and structured manner. Kirkman’s approach emphasizes both understanding and memorization, making it easier for learners to grasp essential mathematical concepts. The book is aimed at students and self-learners who want a strong foundation in these core areas of mathematics. The "geometry" section covers the basics of points, lines, angles, polygons, circles, and Euclidean principles. It introduces learners to spatial reasoning and geometric problem-solving in a systematic way. The "algebra" portion explains operations, equations, functions, and symbolic manipulation, bridging arithmetic and higher-level mathematics. Kirkman uses step-by-step examples and exercises to help learners apply concepts practically and build confidence in solving problems. In the "trigonometry" section, the book explores trigonometric functions, triangle properties, identities, and practical applications. A unique feature of Kirkman’s work is the use of "mnemonics" to aid memory, helping readers retain formulas and procedures effectively. This combination of clear explanation, practical examples, and memory techniques makes the book a valuable resource for understanding foundational mathematics. Its pedagogical approach ensures learners develop strong problem-solving skills while mastering the essentials of "mathematics".

Book Detail :-
Title: Geometry, Algebra, and Trigonometry by Thomas Kirkman - PDF
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 Author :-
The author Thomas Penington Kirkman (1806–1895) was an English "mathematician" and clergyman known for his work in "geometry", "algebra", and "combinatorics". Despite his clerical duties, he made significant contributions to mathematics, publishing over 60 papers on polyhedra, group theory, and combinatorial problems. He is famous for "Kirkman’s schoolgirl problem" and pioneering research in combinatorial design. Kirkman also focused on "mathematics education", producing works like his mnemonical-style textbook on geometry, algebra, and trigonometry to help students learn and retain concepts effectively.

Book Contents :-
1. Symmetry of the Parallelogram, Coordinates of a Point, Law of the Right Line and Forms of its Equation, Rule of Signs in Multiplication and Division, Symbol of an Infinite Number 2. Sections by Parallels of Diverging Lines, Height of a Tower, Square of the Hypotenuse, Incommensurable Numbers, Product of Two Lines 3. Intersection of Two Lines, Elimination between Two Linear Equations, Explicit Equation of the Line through Two Given Points, Vinculum Untied 4. Area of Parallelogram and Triangle, Expression of the Distance between Two Points, ((a \pm b)^2) and ((a + b)(a - b)), Rectangular Equation of the Circle, Quadratic Equations 5. Examples of Quadratic Equations, Signification of the Coefficients, Imaginary Quantities 6. Radius and Centre of Circle Found from its Equation, Perpendicular from Centre on Chord and Tangent, Isosceles Triangle, Angles at Centre and Circumference on Equal Arcs, Inscribed Quadrilateral, Segments of Secant or Chord through a Given Point 7. Expression of Angles by Numbers, the Number p, Definitions and First Notions of Circular Functions 8. (c^2 = a^2 + b^2 - 2ab \cos B), Expansion of (\sin(A \pm B)) and (\cos(A \pm B)) 9. Trigonometric Formulae, Area of Triangle in Terms of the Sides 10. Similar Arcs of Circles, Solution of Plane Triangles, Sides and Perpendiculars on Them from the Angles in Terms of Each Other 11. Bisectors of the Sides, Bisectors of the Angles, Perpendiculars at the Mid-sides, Simple Theorems on Proportion, Product of Diagonals of Inscribed Quadrilateral, Drawing a Circle through Three Given Points, Radii of Circumscribed, Inscribed, and Escribed Circles, Area in Terms of These Radii 12. Similar Polygons, Ratio of Circumference to Diameter, Squaring the Circle 13. First Notions of Exponents 14. Logarithms and the Tables 15. Problems in Geometry and Trigonometry 16. Area of a Polygon in Terms of the Coordinates of its Vertices, Perpendicular from a Given Point on the Line (y - mx - b = 0) 17. Meaning of (e) in (y - mx - b = 0) for Any Axes, Distance between Two Points for Oblique Coordinates, Equation of the Line Perpendicular to a Given One, Equations of the Bisectors of Sides and Angles of a Triangle and Those of the Perpendiculars, Intersections of These Lines, General Property of Segments of the Sides of a Triangle Made by Three Lines from the Angles to a Fourth Point, Expression of a Sought Line 18. Arithmetical, Harmonical, and Geometrical Progressions 19. Permutations, Combinations, and Variations 20. The Binomial Theorem 21. Explicit Circle through Three Points, and Curve of Second Degree through Five Points

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