Fuss: Foundations of Pure Mathematics – Part III
by N. I. Fuss
Translated by Valery Manokhin, PhD
The third part of Fuss's course of pure mathematics, after the Algebra and the Geometry, in first faithful English translation from the original Russian edition. Four divisions, 32 chapters and 480 numbered sections. The application of algebra to geometry: geometric questions solved by equations of the first to the fourth degree. Plane trigonometry: the trigonometric lines and their properties, the solution of triangles, questions of practical geometry, further formulas, and the solution of cubic equations by trigonometry. Conic sections: the sections of a cone, curved lines in general, the circle, the ellipse, the parabola and the hyperbola. The foundations of the differential and integral calculus: differentials of algebraic and transcendental functions, tangents, points of inflection, greatest and least quantities, integrals, the length and quadrature of curves, the surfaces and volumes of solids of revolution, and the inverse method of tangents. 219 questions are worked with full solutions; the 157 figures are reproduced on twelve engraved plates.
32 chapters · 480 numbered articles · 289 pages
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | 11–12 and university | A primary source, not a course — Precalculus (trigonometry, conics) and Calculus content |
|---|---|---|
| United Kingdom | Years 12–13 and undergraduate | A-level Pure and Further Maths content; no qualification maps to it cleanly |
| Canada | Ontario 11–12 and university | historical reading beside MCR3U → MHF4U → MCV4U |
This book matches no modern course. It is worth reading for the mathematics; it will not put a mark on an exam paper.
Not covered in this book
graphs of the trigonometric functions and radian measure · vectors · series, parametric and polar calculus, and differential equations · exercises — this volume is exposition only · statistics and data handling · probability
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Work through first
- Fuss's Geometry$44.95
Further reading
- Derzhavin's Trigonometry$54.95
- Kiselev's Calculus$54.95
- Rashevsky's Trigonometry$39.95
A historical text to read beside the course, not a substitute for it.
Table of contents
32 section headings — the printed contents page in full.
Translator's Preface
Division I: Application of Algebra to Geometry4 sections
- On the solution of geometric questions leading to equations of the first degree
- On the solution of geometrical questions leading to equations of the second degree
- On the solution of geometric problems leading to equations of the third degree
- On the solution of geometric problems leading to equations of the fourth degree
Division II: Plane Trigonometry8 sections
- Definitions and preliminary explanations
- On the origin and properties of trigonometric lines
- On the application of the trigonometric lines to triangles
- On the solution of triangles
- On the use of the rules set forth above in the solution of certain questions pertaining to practical Geometry
- Further investigation of trigonometric formulas
- Application of the preceding formulas to the solution of geometrical questions
- On the solution of equations of the third degree by means of Trigonometry
Division III: Conic Sections6 sections
- On the various ways of cutting a cone by a plane
- On curved lines in general
- On the circle
- On the Ellipse
- On the Parabola
- On the Hyperbola
Division IV: Foundations of the Differential and Integral Calculus14 sections
- Definitions and preliminary explanations
- On finding the differentials of algebraic functions
- On finding the differentials of transcendental functions
- Application of these principles to curved lines
- On differentials of higher orders
- On points of inflection and of return
- On greatest and least quantities
- On Integrals in General
- On finding the integrals of compound differential formulas
- On finding the integrals of compound differential functions by means of transformation
- Application of the integral calculus to finding the length of curved lines
- Application of the integral calculus to finding the quadrature of curved lines
- Application of the integral calculus to finding the surfaces and volumes of solids of revolution
- Application of the integral calculus to questions of the so-called inverse method of tangents
Corrections to the Original Printing
Figure Plates
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $64.95 | 978-1-80910-040-5 | Amazon | Buy → |
| Hardcover | $109.95 | 978-1-80910-041-2 | Amazon | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 289 pages
- First published
- 2026-09-24
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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