Rashevsky's Systematic Course of Geometry

A complete school course in plane and solid geometry, in a single volume — now in English for the first time.

In 1923 K. Rashevsky published A Systematic Course of Geometry, a textbook that grew out of his daily work in schools and teacher-training institutions. It takes the reader from the first notions of point, line and plane through triangles, circles, proportion and areas, and on into planes, polyhedra, volumes and solids of revolution. Four hundred and six numbered articles, each one preparing the tools for the next.

The word in the title is the whole method. Systematic. Definitions come before they are used. Every proof shows its steps. Difficulty arrives one stage at a time, and nothing is asserted without a reason.

WHAT MAKES THIS COURSE DISTINCTIVE

Plane and solid geometry as one continuous argument. The solid geometry is built directly on the plane geometry that precedes it, article by article.

Trigonometry inside the geometry. Sine, cosine and tangent are introduced as ratios in the right triangle and put to work at once on the theorems already proved.

Limits made explicit. Areas, circumferences and volumes are derived through a careful treatment of the limit concept, not handed over as formulas.

Geometry in the field. The final chapter turns to practical work: measuring inaccessible heights, leveling, surveying ground, and the instruments that make it possible.

WHAT IS INSIDE

Plane geometry — the straight line, polygons and the circle, the cases of triangle equality, parallel lines, parallelograms and trapezoids, construction problems.

Proportion and similarity — ratio and common measure, angles in a circle, inscribed and circumscribed figures, proportional segments, similar polygons, homothety.

Trigonometry — the basic concepts and formulas, developed from the right triangle.

Areas and limits — regular polygons, measurement of areas, the concept of a limit, algebra applied to geometry.

Solid geometry — the plane, perpendicularity, parallel lines and planes, dihedral and polyhedral angles, polyhedra, the volume of the prism and the pyramid, surfaces and solids of revolution.

Practical applications — surveying, heights and leveling.

Twenty-eight chapters, 406 numbered articles, 339 figures, 276 pages.

IDEAL FOR

- Homeschool families following a classical, proof-based mathematics curriculum
- Students who want plane and solid geometry in one coherent sequence
- Teachers and tutors who put proof at the centre of the course
- Olympiad and entrance-exam students building construction technique
- Adults returning to geometry who want to understand why, not only what
- Readers interested in the history of mathematics education

This edition preserves Rashevsky's article numbering, the order of his chapters, his proofs and problems, and his notation — including sn, cs and tg for sine, cosine and tangent. All 339 figures are set beside the passages that reference them.

Translated by Valery Manokhin, PhD, and published by Northern Star Academic Press as part of the Russian Math Books programme.

For more English translations of classical Russian mathematics, visit russianmathbooks.com