Fuss

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.

This is the algebra course he wrote for the schools of the Russian Empire, published in 1820 and drawn, as its own title page says, from the foundations of the science laid down by Euler. It is how Euler's algebra reached Russian classrooms — the ancestor of the textbook tradition that later produced Kiselev, and through Kiselev, the Soviet mathematical school. In two hundred years it has never appeared in English.

WHAT THE BOOK COVERS

Four divisions, 59 chapters, 570 numbered sections.

Division I — Simple quantities. Addition through division. Fractions and decimals. Squares, square roots, irrational and imaginary numbers. Cubes and cube roots. Powers, calculation with powers, roots of powers, fractional exponents. Logarithms, logarithmic tables and their use.

Division II — Compound quantities. The four operations on compound quantities. Resolution of fractions into infinite series. Squares, cubes and higher powers, with their roots. The permutation of letters, on which the proof of the binomial rests. Expansion of irrational and negative powers into series.

Division III — Equations. Equations of the first degree, in one unknown and in several, including indeterminate problems. Pure and complete equations of the second degree, with a full discussion of their properties. The third degree, including the irreducible case. The fourth degree, incomplete and complete. The approximate solution of equations.

Division IV — Ratios and progressions. Arithmetical ratio and proportion. Arithmetic progressions and their sums. Geometrical ratio, compound ratios, geometric proportions. Geometric progressions and their sums, applied to compound interest and annuities.

WHY IT MATTERS

Euler wrote the algebra. Fuss turned it into a course. What follows in Russian school mathematics — Kiselev above all — is built on this ground. It also stands alone as a complete first course, from the meaning of a letter standing for a quantity to the irreducible cubic.

WHAT YOU GET

- The complete work in English, professionally typeset, 217 pages
- Faithful to the original — no pedagogy modernised, no proofs glossed, no problems rewritten
- Paperback and hardcover

WHO THIS IS FOR

- Self-learners who want algebra built on reasoning rather than recipes
- Homeschoolers teaching a classical curriculum from primary sources
- Historians of mathematics, and anyone working on Euler's reception
- Readers of the Kiselev course who want to see where it came from

WHO THIS IS NOT FOR

- Anyone wanting modern abstract algebra — this is classical elementary algebra, by design
- Anyone wanting a solutions manual — worked examples throughout, no answer key

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