Kiselev's Geometry — Book I: Planimetry
by A. P. Kiselev
Translated by Valery Manokhin, PhD
The first complete English translation of Kiselev's proof-based Euclidean geometry. 269 sections across 6 chapters: basic concepts, triangles, circles, similarity, regular polygons, and areas. Digital edition, paperback and hardcover.
6 chapters· 269 numbered articles· 220 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
Not sure this is the right first book? Start here →Full curriculum table — every book by school year →| United States | 8–10 | Geometry — the whole course except coordinate geometry and transformations |
|---|---|---|
| England | Years 8–11 | KS3 → GCSE Higher; circle theorems are Higher-only |
| Canada (Ontario) | Ontario 8–10 | MPM2D (less its analytic unit) · BC Geometry 12 · QC Secondary II–IV |
Not covered in this book
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
- Kiselev's Arithmetic$44.95
Covers much of the same ground
One volume covering this and the solid geometry together, with 450 figures — but without the chapter on the trigonometric functions of an acute angle.
- Davidov's Geometry$59.95
Davidov's puts plane and solid geometry in one 324-page volume of 305 numbered sections, with solutions to all 256 problems — but it has no chapter on the trigonometric functions of an acute angle.
- Rashevsky's Geometry$54.95
Rashevsky's puts plane and solid geometry in one 276-page volume — 20 chapters of plane geometry, 10 of solid — with 406 numbered articles and 367 exercises, printed without answers.
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
Problems to work alongside it
- Perelman's Geometry$44.95
What comes next
- Kiselev's Stereometry$49.95
Further reading
- Fuss's Geometry$44.95
A historical text to read beside the course, not a substitute for it.
Table of contents
29 section headings — the printed contents page in full.
Translator's Preface
Introduction3 sections
- The Plane
- The Straight Line
- The Concept of a Circle
The Straight Line6 sections
- Angles
- Mathematical Propositions
- Triangles
- Basic Construction Problems
- Parallel Lines
- Parallelograms and Trapezoids
The Circle7 sections
- Shape and Position of a Circle
- Arcs, Chords, and Distances of Chords from the Centre
- Relative Position of a Line and a Circle
- Relative Position of Two Circles
- Inscribed and Certain Other Angles. Construction of a Tangent
- Inscribed and Circumscribed Polygons
- Four Remarkable Points of a Triangle
Similar Figures9 sections
- The Concept of Measurement of Magnitudes
- Similarity of Triangles
- Similarity of Polygons
- Similarity of Arbitrary Figures
- Some Theorems on Proportional Segments
- Metric Relations Between Elements of a Triangle and Certain Other Figures
- Proportional Lines in a Circle
- Trigonometric Functions of an Acute Angle
- On the Application of Algebra to Geometry
Regular Polygons and the Circumference2 sections
- Regular Polygons
- Computation of the Circumference and Its Parts
Measurement of Areas2 sections
- Areas of Polygons
- Area of a Circle and Its Parts
Formats and editions
| Format | List price (USD) | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Digital edition | $59.95 | — | Gumroad · Read online | Buy → |
| Kindle | $54.95 | — | Amazon | Buy → |
| Paperback | $49.95 | 978-1-919012-05-6 | Amazon | Buy → |
| Hardcover | $79.95 | 978-1-919012-06-3 | Amazon | Buy → |
List price: the US publisher list price in USD, shown for reference. Amazon sets its own price in each store — see the current price on Amazon. The Gumroad price is the price charged.
The digital edition is read online in the Gumroad reader. It is not a downloadable file.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 220 pages
- First published
- 2026-07-14
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
More in This Series
Kiselev's Arithmetic
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The foundational arithmetic textbook used in Russian schools for over a century, in complete English translation. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation. Paperback, hardcover and Kindle on Amazon; the digital edition is read online in Gumroad; there is no file to download.
Kiselev's Algebra I
by A. P. Kiselev
US grades 7–9 · UK Years 8–10
6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.
Kiselev's Algebra II
by A. P. Kiselev
US grades 9–12 · UK Years 10–13
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.