Anoshchenko's Rectilinear Trigonometry
by P. M. Anoshchenko
Translated by Valery Manokhin, PhD
The 1905 secondary-school course in plane trigonometry, in first faithful English translation from the original Russian edition. Three parts: goniometry builds the measurement of angles and the trigonometric quantities from first principles across twelve chapters; rectilinear trigonometry proper solves the right triangle and then the oblique triangle, and closes with a full chapter on field triangulation; supplementary articles take up trigonometric equations, inverse trigonometric quantities, and maxima and minima. Sixty-three figures on eight plates.
25 chapters · 188 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 | 10–12 | Trigonometry / Precalculus; closes with field triangulation |
|---|---|---|
| United Kingdom | Years 10–13 | GCSE Higher (sine and cosine rules) → A-level Pure |
| Canada | Ontario 10–12 | MPM2D → MCR3U · QC Secondary IV–V SN |
Not covered in this book
graphs of the trigonometric functions and radian measure · statistics and data handling · probability · vectors
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
- Elementary Algebra$69.95
- Kiselev's Algebra II$54.95
Covers much of the same ground
- Derzhavin's Trigonometry$54.95
Derzhavin opens with the derivative and closes with the series for sine and cosine, the computation of π and Tables I–V bound in — none of which this book has. This book gives far more room to trigonometric equations, inverse trigonometric quantities and maxima and minima, and its 63 figures sit on eight plates rather than in the text.
- Rashevsky's Trigonometry$39.95
Rashevsky is the short course — 81 pages to 188 — and stops at the solution of triangles: no field triangulation and no chapter on trigonometric equations.
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
- Kiselev's Calculus$54.95
Table of contents
49 section headings — the printed contents page in full.
Part I. Goniometry29 sections
- INTRODUCTION
- The subject of trigonometry
- Measurement of angles
- Direction and signs
- Ends of arcs
- Trigonometric lines and quantities
- Difference between the values of trigonometric quantities and lines
- Independence of the trigonometric quantities from the length of the radius
- Construction of trigonometric quantities from arcs (angles)
- Construction of arcs (angles) from trigonometric quantities
- Inverse trigonometric quantities (or circular quantities)
- Variation of trigonometric quantities
- Reduction formulas
- Arcs corresponding to one and the same trigonometric quantity
- Fundamental relations among the trigonometric quantities of one and the same arc (angle)
- Generalization
- Addition and subtraction of arcs (angles)
- Addition
- Generalization
- Subtraction
- Consequences of the addition formulas
- Multiplication and division of arcs (angles)
- Multiplication
- Division
- Reduction of formulas to logarithmic form
- The auxiliary angle
- Computation of trigonometric quantities. Tables
- Corollaries
- Tables of logarithms of trigonometric quantities
Part II. Rectilinear trigonometry proper12 sections
- Relations between the sides and angles of a right triangle
- Solution of right triangles (fundamental cases)
- Relations between the angles and sides of an oblique triangle
- Solution of oblique triangles (basic cases)
- Areas
- Radii
- Altitude, bisector, median
- More complicated cases of solving triangles
- Solution of problems on more complicated cases of triangles
- Oblique triangle
- Isosceles triangle, regular polygons, parts of a circle, irregular polygons
- Operations on the terrain. Triangulations
Part III. Supplementary articles8 sections
- Solution of trigonometric equations
- Relations among inverse trigonometric quantities
- Computation of trigonometric quantities
- A remark on the solution of geometric problems by means of trigonometry
- Remark on the proof of identities (or inequalities), or on showing the validity of formulas
- The greatest or least values of formulas containing trigonometric quantities (maximum and minimum)
- Indeterminate expressions containing trigonometric quantities
- On the duality of signs in formulas containing trigonometric quantities, and on the number of values of trigonometric quantities of different angles
Figure Atlas
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $49.95 | 978-1-80910-018-4 | Amazon | Buy → |
| Hardcover | $74.95 | 978-1-80910-019-1 | Amazon | 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
- 188 pages
- First published
- 2026-09-18
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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