Synthetic & Analytical Geometry for High Schools by A.H. McDougall
Synthetic & Analytical Geometry for High Schools - Table of Contents
Part-I Classical Geometry
1. Theorems of Menelaus and Ceva
2. Medial Section
3. Harmonic Ranges and Pencils
Part-II Elementary Analytical Geometry
1. Cartesian Coordinates
2. The Straight Line
3. The Straight Line Continued
4. The Circle
What You Will Learn in Synthetic & Analytical Geometry for High Schools
"Advanced Geometry for High Schools: Synthetic and Analytical" by "A.H. McDougall" is a classic mathematics textbook designed to give high school students a deeper understanding of geometry. The book combines "synthetic geometry" (traditional Euclidean methods) with "analytical geometry" (algebraic and coordinate-based problem solving), offering a bridge between classical and modern approaches.
The text is divided into two main sections "Synthetic Geometry" and Analytical Geometry covering theorems, constructions, coordinate systems, and three-dimensional figures. It emphasizes logical reasoning, step-by-step proofs, and includes numerous exercises to strengthen problem-solving skills. The language is formal but clear, reflecting the rigorous standards of early 20th-century education while remaining useful for modern learners who seek mathematical precision.
Ideal for advanced students, educators, and enthusiasts, McDougall’s book remains a valuable resource for mastering geometric concepts and understanding the foundations of higher mathematics. Though the style may differ from modern textbooks, its timeless structure and challenging problems make it a strong tool for self-study, exam preparation, or enrichment. This historical yet practical text continues to inspire those who appreciate the beauty and logic of geometry.
Book Details & Specifications
Title:
Synthetic & Analytical Geometry for High Schools by A.H. McDougall
Publisher:
Copp, Clark
Year:
1919
Pages:
232
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Public Domain Work
Amazon:
Amazon
About the Author: Alexander Hiram McDougall
The author
Alexander Hiram McDougall
was a Canadian educator and Principal of Ottawa Collegiate Institute. He is known for writing "Advanced Geometry for High Schools: Synthetic and Analytical". His goal was to make geometry easier for high school students to understand by combining traditional geometric proofs with modern coordinate methods.
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