CONIC SECTIONS TREATED GEOMETRICALLY - Classical Geometry

In this review of CONIC SECTIONS TREATED GEOMETRICALLY, the book is judged as a focused, classical treatment of conic curves suited to students and instructors who want a definition-driven, construction-based approach. The author frames conics with reference to a focus and directrix and derives the most important properties from that definition, so the single biggest reason to buy is its clear logical development that links construction to key results such as the ratio involving ordinates and rectangle distances.

Key Features

• Focus and directrix definition: The book defines conic sections with respect to a focus and directrix, giving a precise foundation that guides subsequent proofs.
• Construction-first approach: The first chapter presents a constructive method to determine points on a conic, which leads directly to important analytic relations.
• Derivation of ordinate relations: The text demonstrates the constancy of the ratio of the square on the ordinate to the rectangle under its distances from the vertices, clarifying a common algebraic fact geometrically.
• Immediate asymptote directions: For the hyperbola, the construction makes the directions of the asymptotes follow naturally, giving geometric intuition for asymptotic behavior.
• Classical methods: Several arguments echo the classical Wallace methods, situating the work within established geometric tradition for historical context.

Who It's For

The book is best for undergraduate students of geometry, instructors seeking a classical presentation, and self-learners who appreciate constructions and deductive development from definitions. Readers who value seeing how geometric construction yields analytic consequences will find the approach especially useful.

It is less suitable for those wanting a modern coordinate-geometry textbook with extensive exercises or numerical applications, and readers seeking introductory high-school level intuition without rigorous derivations may prefer a more elementary treatment.

Pros & Cons

Pros

• Clear use of the focus and directrix gives a tight foundational definition for conics.
• The construction in chapter one connects geometry to analytic properties in a direct, instructive way.
• Immediate geometric explanation of hyperbola asymptotes provides strong visual intuition.

Cons

• The treatment is classical and compact, so readers seeking many worked exercises or modern applications may find the book limited.

Specifications

Title	CONIC SECTIONS TREATED GEOMETRICALLY
Author	W. H. Besant
Primary focus	Conic sections via focus and directrix
Approach	Construction-based geometric deductions
Includes	Derivations of ordinate and asymptote properties
Style	Classical, deductive, referencing Wallace methods

Our Verdict

CONIC SECTIONS TREATED GEOMETRICALLY is a compact, rigorous resource for anyone who wants a classical, construction-led understanding of conics. It is good value for students and teachers who prefer geometric proofs tied to definition rather than a modern exercises-heavy text.

Frequently Asked Questions

Does the book use coordinates?
Answer. The emphasis is on geometric construction from focus and directrix, with analytic consequences derived from those constructions rather than a coordinate-first approach.

Is it suitable for beginners?
Answer. It suits beginners with some mathematical maturity, but complete newcomers may prefer a more elementary introduction with more examples.

Does it cover hyperbola asymptotes?
Answer. Yes, the construction in the first chapter leads directly to the directions of the hyperbola asymptotes.