lements of Analytical Geometry and Differential and Integral Calculus by Gerardus Docharty
Analytical Geometry and Calculus - Table of Contents
1. Analytical Geometry
2. Differential Calculus
3. Elements of The Integral Calculus
What You Will Learn in Analytical Geometry and Calculus
"Elements of Analytical Geometry, and of the Differential and Integral Calculus" by Gerardus Beekman Docharty is a classic "mathematics textbook" first published in 1865. It provides a structured introduction to "analytical geometry", covering points, straight lines, circles, and conic sections, and gradually connects these geometric ideas to the principles of "calculus". The book reflects the 19th-century approach to teaching, combining clear explanations with numerous examples to help learners bridge algebra, geometry, and calculus.
The book begins with the fundamentals of analytical geometry, exploring coordinate systems, transformations, and the properties of curves. It then introduces "differential calculus", including derivatives, maxima and minima, implicit functions, and methods for analyzing curves. Following this, Docharty moves into integral calculus, addressing definite and indefinite integrals, areas, volumes, and applications of integration to geometric and physical problems. The content is presented in a logical progression that allows students to build a strong foundation in both geometry and calculus simultaneously.
Docharty’s work is notable for its clarity and educational approach, making it accessible for students of the era while remaining valuable for modern readers interested in the historical development of mathematical instruction. Its combined focus on analytical geometry and calculus offers a comprehensive resource that illustrates the unity of algebraic and geometric thinking, demonstrating the evolution of mathematical pedagogy in the 19th century.
Book Details & Specifications
Title:
lements of Analytical Geometry and Differential and Integral Calculus by Gerardus Docharty
Publisher:
Harper & brothers
Year:
1867
Pages:
312
Type:
PDF
Language:
English
ISBN-10 #:
0484319361
ISBN-13 #:
978-0484319362
License:
Public Domain Work
Amazon:
Amazon
About the Author: Gerardus Beekman Docharty
The author Gerardus Beekman Docharty
was a 19th-century American "mathematics educator" and textbook author. He served as a professor of pure mathematics at New York Free Academy and contributed significantly to mathematics education in the United States. His teaching focused on clarity, logical progression, and bridging algebra, geometry, and calculus. Docharty authored several influential works, including "Elements of Analytical Geometry, and of the Differential and Integral Calculus", "The Institutes of Algebra", and texts on geometry and trigonometry. His books remain valuable for understanding the historical development of mathematical instruction and the structured approach of classical "mathematics textbooks".
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