Rashevsky's Systematic Course of Geometry
by K. N. Rashevsky
Translated by Valery Manokhin, PhD
A complete school course in plane and solid geometry in one volume, in first faithful English translation from the original Russian edition. Two parts, thirty chapters and 406 numbered articles. The planimetry runs from the straight line, polygons and the circle through the three cases of equality of triangles, parallel lines, parallelograms and trapezoids and construction problems; the method of loci, parallel translation and rotation; ratio and common measure, angles in a circle, proportional segments, similarity and homothety; the basic trigonometric functions of the right triangle; regular polygons, areas, the concept of a limit, the circumference and area of the circle, and algebra applied to geometry. The stereometry covers the position of a plane, perpendicular and parallel lines and planes, dihedral and polyhedral angles, polyhedra and their volumes, the cylinder, cone and sphere, incommensurable quantities, and closes with practical work: making a plan and levelling. 338 figures and 367 exercises in ten graded sets.
30 chapters · 406 numbered articles · 367 exercises · 276 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 | 8–11 | Geometry, plane and solid, complete; adds right-triangle trigonometry and closes with surveying and levelling |
|---|---|---|
| United Kingdom | Years 9–12 | KS3 → GCSE Higher (right-angled trigonometry included) → A-level enrichment |
| Canada | Ontario 8–11 | MPM2D (less its analytic unit) · BC Geometry 12 · QC Secondary III–V |
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 Algebra I$44.95
- Rashevsky's Arithmetic$39.95
Covers much of the same ground
- Elementary Geometry$69.95
Kiselev's single volume runs to 380 pages and 450 figures, against 276 pages and 338 figures here, with about the same number of exercises — 370 to 367. This book adds a chapter on the basic trigonometric functions, which that volume does not carry.
- Davidov's Geometry$59.95
Davidov's is longer — 324 pages, 305 numbered sections, 344 figures — and prints solutions to all 256 of its problems; this book's 367 exercises carry no answers. Davidov's has no trigonometry and closes with the conic sections; this book closes with surveying and levelling.
- Kiselev's Planimetry$59.95
Planimetry is the plane geometry alone — 220 pages, 269 sections in six chapters — and, like the first part of this book, includes the trigonometric functions of an acute angle and algebra applied to geometry. The solid geometry is in its companion volume, Stereometry.
- Kiselev's Stereometry$49.95
Stereometry is the solid geometry alone, 112 pages, with a chapter on orthogonal projection and a supplement on the axioms of geometry, neither of which this book has. Its plane geometry is in the companion volume, Planimetry.
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
What comes next
- Rashevsky's Trigonometry$39.95
Table of contents
39 section headings — the printed contents page in full.
Translator's Preface
Brief Historical Notes
Introduction1 section
- Basic concepts and definitions
Part I. Planimetry
1 On the straight line1 section
- Angles
2 Polygon and circle1 section
- Units of measurement for angles and arcs
3 Three cases of equality of triangles3 sections
- Relation between the sides and angles of a triangle
- Properties of the perpendicular and obliques
- Equality of right triangles
4 Parallel lines
5 Parallelograms and trapezoids
6 Construction problems
7 The circle5 sections
- Property of a diameter perpendicular to a chord
- Relative position of two circles
- Method of loci
- Parallel translation
- Rotation about a point
8 Ratio and common measure
9 Measurement of angles in a circle
10 Inscribed and circumscribed triangles and quadrilaterals
11 Proportional segments
12 Similarity of polygons
13 Numerical relations and proportional segments
14 Homothety. (Similar arrangement of figures.)2 sections
- Method of similitude
- Method of reversal
15 Basic trigonometric concepts and formulas
16 Regular polygons
17 Measurement of areas2 sections
- To measure an area means to find its ratio to an area taken as unity
- Comparison of areas
18 The concept of a limit
19 Circumference and area of a circle
20 The concept of applying algebra to geometry
Part II. Stereometry
1 Determination of the position of a plane
2 A straight line and a plane perpendicular to it
3 Parallel lines and planes3 sections
- Parallel lines
- A line and a plane parallel to it
- Parallel planes
4 Dihedral angles2 sections
- Perpendicular planes
- The angle between a line and a plane
5 Polyhedral angles1 section
- Equality of trihedral angles
6 Polyhedra4 sections
- Regular polyhedra
- Prism
- Parallelepiped
- Pyramid
7 Volume of a prism and a pyramid2 sections
- Equality of prisms and pyramids
- Similarity of polyhedra
8 Surfaces and solids of revolution6 sections
- Cylinder
- Cone
- Frustum of a cone
- Similar cylinders and cones
- The sphere
- Surface and volume of a sphere and its parts
9 Incommensurable quantities4 sections
- Proportionality of segments
- Proportionality of central angles and their corresponding arcs
- Area of a rectangle
- Volume of a rectangular parallelepiped
10 Practical applications of geometry2 sections
- Making a plan
- The concept of leveling
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $54.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $54.95 | 978-1-80910-042-9 | Amazon | Buy → |
| Paperback | $54.95 | 978-1-80910-042-9 | IngramSpark · direct | Buy → |
| Hardcover | $84.95 | 978-1-80910-043-6 | Amazon | Buy → |
| Hardcover | $79.95 | 978-1-80910-043-6 | IngramSpark · direct | Buy → |
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IngramSpark prints and ships direct orders to the US, UK and Australia. Libraries, schools and bookshops can order the same ISBNs through Ingram: ordering for libraries →
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 276 pages
- First published
- 2026-10-12
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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