Davidov's Elementary Geometry
by A. Yu. Davidov
Translated by Valery Manokhin, PhD
The geometry course written by the founding president of the Moscow Mathematical Society, in first faithful English translation from the original Russian edition. Two parts, thirteen chapters and 305 numbered sections. The planimetry treats straight lines and angles; figures, the equality of triangles, perpendicular and oblique lines; parallel lines, parallelograms and trapezoids; similarity and the ratio of lines; the circle — chords and tangents, the measurement of angles, proportional lines, inscribed and circumscribed polygons, the relative position of two circles, the four remarkable points of a triangle, reciprocal points and polars; regular polygons; the measurement of areas, with the surveying of a plan; and the circumference and area of the circle by limits. The stereometry covers lines and planes in space; dihedral, polyhedral and trihedral angles; prisms, pyramids, symmetric and regular polyhedra; volumes; the cylinder, cone and sphere, the spherical triangle, and the conic sections. 344 figures and 256 problems, with solutions to all of them. A digital edition, read online in Gumroad Reader.
13 chapters · 305 numbered articles · 256 exercises · 324 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; no trigonometry; closes with the conic sections |
|---|---|---|
| United Kingdom | Years 9–12 | KS3 → GCSE Higher → A-level enrichment (polars, the spherical triangle) |
| 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 · metric units — some problems use old Russian measures (versts, sazhens, arshins, poods)
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
- Elementary Geometry$69.95
Kiselev's single volume runs to 380 pages, 450 figures and 370 exercises, against 324 pages, 344 figures and 256 problems here. This book prints solutions to every problem and closes with the spherical triangle and the conic sections; neither book has a trigonometry section.
- Kiselev's Planimetry$59.95
Planimetry is the plane geometry alone — 220 pages, 269 sections — and has a chapter on the trigonometric functions of an acute angle, which this book does not. The solid geometry is in its companion volume, Stereometry.
- Rashevsky's Geometry$54.95
Rashevsky's covers the same plane and solid geometry in 276 pages and 406 numbered articles, adds a chapter of basic trigonometry and one on surveying and levelling, and gives 367 exercises without answers. This book prints solutions to all 256 of its problems.
- 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. This book’s five solid-geometry chapters add the spherical triangle and the conic sections.
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
- Davidov's Trigonometry$49.95
- Rashevsky's Trigonometry$39.95
Further reading
A historical text to read beside the course, not a substitute for it.
Table of contents
46 section headings — the printed contents page in full.
Introduction
Part I. Planimetry
1 On straight lines and angles
2 On figures3 sections
- On figures in general
- Equality of triangles
- Properties of a perpendicular and oblique lines
3 Parallel lines3 sections
- Parallel lines
- Some consequences of the theory of parallel lines
- Parallelograms and trapezoids
4 Similarity4 sections
- Similarity of triangles
- Similarity of polygons
- The Ratio of Lines
- Some propositions about the triangle
5 On the circumference of a circle8 sections
- Chords and tangents
- Measurement of angles
- Proportional lines in a circle
- Inscribed and circumscribed polygons
- The relative position of two circles
- The four remarkable points of a triangle
- Reciprocal points
- Polars
6 On regular polygons1 section
- Regular polygons inscribed and circumscribed
7 Measurement of areas3 sections
- Measurement of areas of rectilinear figures
- Some propositions on triangles, quadrilaterals, and regular polygons
- Surveying a plan
8 Definition of the circumference and area of a circle1 section
- On limits
Part II. Stereometry
1 On lines and planes in space5 sections
- Determination of the position of a plane
- Lines perpendicular to a plane
- Lines parallel to each other
- Lines parallel to a plane
- Planes parallel to one another
2 On angles formed by planes4 sections
- The angle of two lines and the angle of a line with a plane
- Dihedral angles
- Polyhedral angles
- Equality and symmetry of trihedral angles
3 On polyhedra5 sections
- Prisms, parallelepipeds, and pyramids
- Equality of prisms and pyramids
- Symmetric polyhedra
- Regular polyhedra
- Similarity of polyhedra
4 Measurement of volumes of solids2 sections
- Volume of a parallelepiped, prism, and pyramid
- Volumes of similar polyhedra
5 On round bodies5 sections
- On the cylinder and the cone
- On the sphere
- On the spherical triangle
- Similarity of round bodies
- Conic sections
Solutions to the Problems2 sections
- Part I. Planimetry
- Part II. Stereometry
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $59.95 | — | Gumroad · Instant download | 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
- 324 pages
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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