Kiselev's Geometry - Book I, Planimetry

For more than a century, 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 children learned to reason with a straightedge and compass. This volume presents Book I, Planimetry (plane geometry), as a complete English translation.

First published in 1892 and continuously refined over Kiselev's lifetime, the Geometry became, alongside his Arithmetic and Algebra, the backbone of Russian mathematical education for generations. Its enduring appeal is the same one that made it famous: every result is proved, every construction is justified, and the exposition builds strictly from first principles.

What makes Kiselev's Geometry different from every modern textbook:

Proof from the very first page. The straight line, the angle, and the triangle are not merely defined and used — their properties are established by rigorous argument. Congruence is developed through superposition; the isosceles-triangle theorem and its converse are proved in full.

The circle, treated whole. Chords, arcs, central and inscribed angles, tangents, and the relationships between two circles are developed systematically, each theorem earning the next.

Similar figures and measurement. The theory of proportional segments, the fundamental property of similar triangles, and the careful passage from commensurable to incommensurable ratios — the conceptual heart of classical geometry, presented with a rigour modern courses defer to college.

Regular polygons and the circle's length. Inscribed and circumscribed regular polygons, the side of the regular decagon and pentagon, and the definition of the length of a circle as a limit — culminating in the number that relates circumference to diameter.

Areas, derived rather than memorised. The area of the rectangle, parallelogram, triangle, and trapezoid; the Pythagorean theorem by area; and the relationship of areas in similar figures — each formula proved, not simply stated.

230 pages. Five chapters: the straight line (angles, triangles, parallels, parallelograms, and trapezoids); the circle; similar figures; regular polygons and the length of a circle; and the measurement of areas. The complete Planimetry of Kiselev's Geometry, in a faithful English edition.

Pair with the companion problem book. Rybkin's Collection of Problems in Geometry, Part I: Planimetry is the set Russian students worked beside Kiselev's geometry — 970 problems in sixteen sections, in the order of this course: the straight line, the circle, similarity, regular polygons, areas.

For strong students, the next step in problem solving is Collection of Geometry Problems by Delone, Zhitomirsky and Fetisov — 85 problems, each solved in full by analysis, construction, proof and investigation.

Continue with Kiselev's Geometry – Book II, Stereometry, and Rybkin's Part II: Stereometry.

This translation preserves Kiselev's original section numbering, the structure of his exposition, and the precision of his prose. The typography is modern; the mathematics is Kiselev's.

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

Translated by Valery Manokhin, PhD (Royal Holloway, University of London) — independent machine learning researcher and translator of English editions of classic Russian mathematics textbooks.