Kiselev's Elementary Geometry: The Classic Mathematics Textbook — First Complete English Translation (Russian Math Classics — English Editions)

For over 70 years, A. P. Kiselev's Geometry was the standard secondary-school geometry textbook in Russian and Soviet schools, the book from which tens of millions of students learned to reason. This volume presents the complete course in plane and solid geometry as a single English edition.

First published in 1892 and refined over Kiselev's lifetime, the Geometry became, alongside his Arithmetic and Algebra, part of the foundation of Russian mathematical education. Its method is simple and demanding: definitions are precise, theorems are proved, constructions are justified, and each new idea is prepared by what comes before it.

What makes Kiselev's Elementary Geometry different from a modern survey textbook:

Proof from first principles. The course begins with geometric figures, the straight line, the plane, axioms, and the structure of mathematical propositions. Angles, triangles, parallel lines, congruence, and the principal theorems of plane geometry are developed through proof.

The circle treated whole. Chords, arcs, central and inscribed angles, tangents, secants, and the relations between circles are developed in sequence, with the constructions and theorems connected rather than isolated.

Similarity, proportion, and limits. Similar triangles lead to proportional segments and the treatment of incommensurable ratios. Limits then provide the basis for the length of the circumference, regular polygons, and the calculation of the circumference and its parts.

Areas derived, not memorised. The area of the rectangle, parallelogram, triangle, trapezoid, and circle is established through geometric reasoning. The Pythagorean theorem, the ratios of areas in similar figures, and the relations involving inscribed and circumscribed circles are treated as mathematics to be understood.

Geometry in space. Stereometry develops the position of planes, perpendicular and oblique lines, parallel lines and planes, dihedral and polyhedral angles, polyhedra, prisms, pyramids, regular solids, cylinders, cones, and the sphere. Surface areas and volumes are derived by the same proof-led method.

Construction as a mathematical method. The concluding collection explains the principal methods of solving geometric construction problems, including the method of loci, auxiliary constructions, and the analysis of whether a problem has no solution, one solution, or several.

380 pages. Five books of Planimetry, three books of Stereometry, a complete sequence of exercises and construction problems, and 450 figures.

This is the first complete English translation. Kiselev's continuous section numbering, mathematical sequence, worked proofs, exercises, formulas, and figures are retained. The typography is modern; the mathematics and pedagogical order are Kiselev's.

Readers who own Kiselev's Arithmetic and Algebra will find here the complementary geometry course, applying the same proof-led method to figures, constructions, measurement, and space.

Ideal for homeschool families using a classical or rigorous mathematics curriculum, parents supplementing their children's geometry education, teachers seeking a proof-based course, advanced students preparing for higher mathematics and competition, adults rebuilding their mathematical foundations, and readers interested in the tradition of the Russian school of mathematics.

Part of Russian Math Classics: English Editions. Translated by Valery Manokhin, PhD (Royal Holloway, University of London). Published by Northern Star Academic Press. Full catalogue at russianmathbooks.com.