Fuss: Foundations of Pure Mathematics - Part II, Geometry: Classical Russian Math Textbooks - First Complete English Translation (Russian Math Classics — English Editions)

First faithful English translation from the original Russian edition.

Euler's assistant became Euler's successor at the lectern. Nicolas Fuss came to St Petersburg from Basel at seventeen to serve as the hand and eye of the nearly blind Leonhard Euler, stayed in Russia for the rest of his life, and from 1800 until his death in 1826 ran the Imperial Academy of Sciences as its permanent secretary. Along the way he wrote the mathematics course for the schools of the Russian Empire.

This is its second volume, published in 1823: the geometry. Part One had been the algebra of 1820. Where that book taught calculation, this one teaches proof — and it is the book standing behind the Russian school geometry tradition that runs through Kiselev into the Soviet classroom. In two hundred years it has never appeared in English.

WHAT THE BOOK COVERS

Two parts, twelve chapters, 460 numbered sections, 230 figures.

Part One - Planimetry. Definitions, axioms and preliminary explanations. Straight lines, angles, and the sides of rectilinear figures. The circle, and figures inscribed in it and circumscribed about it. Proportional lines and the similarity of figures. The comparison and measurement of figures. The transformation and division of figures.

Part Two - Stereometry. Definitions, axioms and preliminary explanations. The mutual position of planes, and their position with respect to straight lines drawn outside them. The surface of solids. The comparison of solids. The volume of solids. Regular solids - the five Platonic bodies, each constructed and measured.

107 theorems with their proofs, 60 problems with their solutions, 158 corollaries, and the remarks and supplements Fuss wrote to connect them.

WHY IT MATTERS

Euler wrote the algebra; Fuss turned it into a course. The geometry is Fuss's own. It is the volume where a Russian schoolboy first met a proof, and it set the pattern - numbered propositions, a figure for every argument, the theorem and the problem as the two things mathematics does - that Kiselev inherited and that Soviet textbooks kept for a century. It also stands on its own as a complete classical geometry, from what it means for two lines to be parallel to the volume of a sphere.

WHAT YOU GET

- The complete work in English, professionally typeset, 166 pages
- Nine engraved plates reproduced from the original - all 230 figures as Fuss's own engraver drew them, not redrawn
- Faithful to the original - original sequence, section numbering, and historical notation; no proofs glossed, no problems rewritten
- Paperback and hardcover

WHO THIS IS FOR

- Self-learners who want geometry as a chain of reasoning rather than a set of formulas
- Homeschoolers teaching a classical curriculum from primary sources
- Historians of mathematics, and anyone working on Euler's circle or Russian mathematical education
- Readers of Kiselev's Geometry who want to see the book it grew from

WHO THIS IS NOT FOR

- Anyone wanting modern axiomatic or analytic geometry - this is classical synthetic geometry, by design
- Anyone wanting a solutions manual - every problem is solved in the text, but there is no separate answer key

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

The full series: russianmathbooks.com