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Perelman's Geometry and the Beginnings of Trigonometry cover
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Perelman's Geometry and the Beginnings of Trigonometry

by Ya. I. Perelman

Translated by Valery Manokhin, PhD

A practical course in plane and solid geometry for self-study, carried as far as the trigonometry of the right triangle, in first faithful English translation from the original Russian edition. Nine chapters: the straight line and the circle, with scales, circumferential speed, belts and gear wheels; angles and parallel lines, with the protractor; the triangle, its construction and the tests for equality; polygons and the parallelogram, with the vernier and slide calipers; chords, tangents, conjugation and the ellipse; similarity, Pythagoras’ rule and the square root; tangent, cotangent, sine and cosine, with their tables; areas, from the rectangle to the circle, the ellipse and irregular figures; and the surfaces, volumes and weights of solids. The main text rests on about forty theorems; 458 problems, about half the book, carry the rest, with solutions or answers to 423 of them. 230 figures.

9 chapters · 458 exercises · 166 pages

Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.

$44.95 Buy Now — Paperback Amazon Paperback Amazon Hardcover

Where this fits in school

Full curriculum table — every book by school year →
United States7–10Grade 7–8 geometry → Geometry, simplified to about 40 theorems, with right-triangle trigonometry
United KingdomYears 8–11KS3 → GCSE Foundation and Higher, right-angled trigonometry included
CanadaOntario 7–10MTH1W · MPM2D right-triangle trigonometry · BC Math 8–10

Not covered in this book

coordinate geometry · transformations on a grid · vectors · statistics and data handling · probability · graphs of the trigonometric functions and radian measure

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

Table of contents

124 section headings — the printed contents page in full.

Translator's Note

Author's Preface

How to Study with This Book

Introduction2 sections
  1. The science of geometry
  2. On measures
1 The Straight Line and the Circle19 sections
  1. Lines
  2. The straight line
  3. Drawing straight lines
  4. Denoting lines
  5. Latin letters
  6. The plane
  7. The length of a straight line. Scale
  8. Linear scale
  9. Numerical scale
  10. The circle. The center
  11. Radius, diameter; arc
  12. Circumference and circle
  13. Concentric circles
  14. The circumference of a circle
  15. Circumferential speed
  16. Cutting speed
  17. The endless belt
  18. Transmission
  19. Gear wheels
2 Angles and Parallel Lines18 sections
  1. Angles; their notation
  2. Comparison of angles
  3. A straight angle
  4. Adjacent angles. Right angle
  5. Perpendicular
  6. Vertical line
  7. Horizontal line
  8. Property of a right angle
  9. Property of adjacent angles
  10. Drawing right angles
  11. Acute and obtuse angles
  12. Opposite angles
  13. Measurement of angles
  14. Central angles
  15. The protractor
  16. Angular velocity
  17. Parallel lines
  18. Angles formed by parallel lines
3 The Triangle12 sections
  1. The sum of the angles of a triangle. The exterior angle
  2. Right triangle
  3. Construction of a triangle from three sides
  4. Relation between the lengths of the sides of a triangle
  5. Construction of an angle equal to a given angle
  6. Bisecting an angle. The bisector
  7. Construction of a triangle from two sides and the included angle
  8. Isosceles triangle
  9. Bisection of a segment
  10. Construction of a triangle from a side and two angles
  11. Tests for the equality of triangles
  12. Unequal sides and angles of a triangle
4 Polygons and the Parallelogram10 sections
  1. Polygon
  2. The sum of the angles of a polygon
  3. Regular polygons
  4. A network of regular polygons
  5. The parallelogram
  6. Sides and angles of a parallelogram
  7. Rectangle. Rhombus. Square
  8. Division of a segment into equal parts
  9. The vernier
  10. Slide calipers
5 The Straight Line and the Circle: The Ellipse15 sections
  1. Properties of chords
  2. Finding the center
  3. Tangents and secants
  4. Construction of tangents
  5. Center finder
  6. Common external tangents
  7. Common internal tangents
  8. Conjugation
  9. Basket-handle curve
  10. Inscribed polygon
  11. Circumscribed polygon
  12. Ellipse
  13. Foci of the ellipse
  14. Drawing an ellipse
  15. Axes and center of the ellipse
6 Similarity of Figures8 sections
  1. Similar figures
  2. Similarity of triangles
  3. Transverse scale
  4. Pythagoras' rule
  5. Extraction of the square root
  6. Sides of regular polygons
  7. Calculation of the radius of curvature
  8. The sagitta of an arc
7 Initial Information from Trigonometry9 sections
  1. Taper
  2. Tangent
  3. Cotangent
  4. Table of tangents and cotangents
  5. Examples of computations with tan and cot
  6. Sine
  7. Cosine
  8. Table of sines and cosines
  9. Examples of computations with sin and cos
8 Measurement of Areas18 sections
  1. Area
  2. The unit of area
  3. A grid overlay
  4. Computation of areas
  5. Area of a rectangle
  6. Trapezoid; its area and midline
  7. The area of a parallelogram
  8. The area of a triangle; its base and altitude
  9. Figures of equal area
  10. Area of a regular polygon. Apothem
  11. Area of a circular sector
  12. Area of a circle
  13. Area of a circular segment
  14. Area of an ellipse
  15. Table of areas
  16. Area of an irregular figure
  17. Areas of similar figures
  18. Calculation for rupture
9 Surface Area and Volume of Solids13 sections
  1. The cube
  2. Parallel planes. The right prism
  3. Right rectangular parallelepiped (bar)
  4. Pyramid
  5. The cylinder
  6. The cone
  7. The sphere
  8. Computing the surface of bodies
  9. Surfaces of similar solids
  10. Computation of volumes
  11. Volumes of similar bodies
  12. Extraction of the cube root
  13. Computing the weight of bodies

Solutions and Answers

Search the contents of every book →

Formats and editions

FormatPriceISBN-13WhereBuy
Paperback$44.95978-1-80910-007-8AmazonBuy →
Hardcover$69.95978-1-80910-008-5AmazonBuy →

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
166 pages
First published
2026-10-05

Published by Northern Star Academic Press · First faithful English translation from the original Russian edition

Browse the full Russian Math Classics series on Amazon →

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