Fuss: Foundations of Pure Mathematics – Part II, Geometry
by N. I. Fuss
Translated by Valery Manokhin, PhD
The geometry of Fuss's course of pure mathematics, the volume that follows his Algebra, in first complete English translation. Two parts, twelve chapters and 460 numbered sections. Planimetry: definitions and axioms; straight lines, angles and the sides of rectilinear figures; the circle and the figures inscribed in it and circumscribed about it; proportional lines and similar figures; the comparison and measurement of figures; the transformation and division of figures. Stereometry: the position of planes and of lines drawn outside them; the surface, comparison and volume of solids; and the five regular solids. 107 theorems with their proofs, 61 construction problems with their solutions and 158 corollaries. All 230 figures are reproduced on the nine engraved plates.
12 chapters · 460 numbered articles · 166 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 | 8–12 | A primary source, not a course — plane and solid Geometry content without coordinates |
|---|---|---|
| United Kingdom | Years 9–13 | No qualification maps to it cleanly; content runs KS3 → GCSE Higher, solids to A-level enrichment |
| Canada | Ontario 8–12 | historical reading |
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
exercises — this volume is exposition only · coordinate geometry · transformations on a grid · vectors · 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 Algebra$54.95
Covers much of the same ground
Raykovsky covers plane and solid geometry in 112 pages and 310 numbered articles, with 157 figures on five plates, and opens with an explanation of algebraic signs. It has no chapter on the transformation and division of figures and none on the regular solids, both of which this book carries. Neither has exercise sets.
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
What comes next
Further reading
- Elementary Geometry$69.95
- Kiselev's Planimetry$59.95
- Kiselev's Stereometry$49.95
A historical text to read beside the course, not a substitute for it.
Table of contents
12 section headings — the printed contents page in full.
Translator's Preface
Preliminary Explanations
Part I. Planimetry6 sections
- Definitions, Axioms, and Preliminary Explanations
- On Straight Lines, Angles, and Sides of Rectilinear Figures
- On the Circle and Figures Inscribed in It and Circumscribed About It
- On Proportional Lines and on the Similarity of Figures
- On the Comparison and Measurement of Figures
- On the Transformation and Division of Figures
Part II. Stereometry6 sections
- Definitions, Axioms and Preliminary Explanations
- On the Mutual Position of Planes, and Also on the Position of the Same with Respect to Straight Lines Drawn Outside Them
- On the Surface of Solids
- On the Comparison of Solids
- On the Volume of Solids
- On Regular Solids
Figure Plates
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Kindle | $49.95 | — | Amazon | Buy → |
| Paperback | $44.95 | 978-1-919012-94-0 | Amazon | Buy → |
| Hardcover | $69.95 | 978-1-919012-95-7 | 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
- 166 pages
- First published
- 2026-09-23
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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