Fuss: Foundations of Pure Mathematics - Part III, Elementary Foundations of Pure Mathematics: Classic Russian mathematics textbook (Russian Math Classics — English Editions)

First faithful English translation from the original Russian edition.

In 1773 a seventeen-year-old from Basel arrived in St Petersburg to work for Leonhard Euler, who had just lost most of his sight. For the next decade Nicolas Fuss was the hand and the eye of the greatest mathematician of the age. He stayed in Russia for the rest of his life, and from 1800 until his death in 1826 he was permanent secretary of the Imperial Academy of Sciences. Along the way he wrote the mathematics course for the schools of the Russian Empire.

This is its third volume, published in 1823. Part One taught algebra; Part Two taught geometry. Part Three puts the two to work on each other - every geometric question turned into an equation and solved - and then carries the course on through trigonometry and the conic sections to the differential and integral calculus. In two hundred years it has never appeared in English.

WHAT THE BOOK COVERS

Four divisions, 32 chapters, 480 numbered sections, 157 figures, and 219 questions, each worked to its solution.

Division I - The application of algebra to geometry. Turning a geometric question into an equation, and choosing the unknown so the equation comes out simple: 84 questions leading to equations of the first to the fourth degree, each solved.

Division II - Plane trigonometry. The trigonometric lines; the solution of triangles, worked in logarithms; trigonometry in the field - the height of a tower whose foot cannot be reached, the distance between points no one can walk to; cubic equations solved by trigonometry.

Division III - Conic sections. The curves made by cutting a cone with a plane; curved lines and their equations; the circle, ellipse, parabola and hyperbola, each with its theorems, proofs and problems.

Division IV - The foundations of the differential and integral calculus. Differentials of algebraic and transcendental functions; tangents; higher differentials; inflection points and cusps; maxima and minima; integration, directly and by transformation; lengths of curves, areas, and the surfaces and volumes of solids of revolution, the cycloid among them; and the inverse method of tangents.

WHY IT MATTERS

Classical mathematics after arithmetic, as one continuous argument: algebra becomes the tool of geometry, trigonometry an instrument for measuring the world, the conics curves with equations - and the calculus finds their tangents, lengths, areas and volumes. It is the calculus as Euler's own assistant taught it: in differentials and infinitely small quantities, before limits.

WHAT YOU GET

- The complete work in English, professionally typeset, 289 pages
- Twelve engraved plates reproduced from the original - all 157 figures as Fuss's own engraver drew them, not redrawn
- Faithful to the original: its sequence, section numbering and notation; no proofs glossed, no problems rewritten
- A table of corrections to the 1823 printing
- Paperback and hardcover

WHO THIS IS FOR

- Self-learners who want trigonometry, conics and calculus built as one line of reasoning
- Homeschoolers teaching a classical curriculum from primary sources
- Historians of mathematics and of Euler's circle
- Readers of Parts One and Two who want to finish the course

WHO THIS IS NOT FOR

- Anyone wanting modern analysis - this calculus is built on infinitely small quantities, not limits, by design
- Anyone wanting a separate answer key - every question is solved in the text

Translated from Russian by Valery Manokhin, PhD. Northern Star Academic Press, Russian Math Classics - English Editions.

The full series: russianmathbooks.com