### Great Moments in Mathematics Before 1650 (Dolciani Mathematical Expositions 5)

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Rider And C. Bashmakova , Paul R. Efron's Dice. Reading, Mass. Paris: Hermann, Poetry and Mathematics. New York: Day, Thousands of teachers of mathematics have read these stories and anecdotes for their own enjoyment and used them in the classroom - to add entertainment, to introduce a human element, to inspire the student, and to forge some links of c Press, New York: Oxford University Press, Internally fine and clean.

A very attractive copy of one of Euler's rarer works. Petersburg Academy in , in which Euler announced his discovery of the quadratic reciprocity theorem, or the "Aureum Theorema" Golden Theorem , as Gauss referred to it. This theorem of modular arithmetic, which gives conditions for the solvability of quadratic equations modulo prime numbers, was first announced by Euler and later in by Legendre, but none of which were able to give a proper proof.

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The first proof of this famous law was first given by Gauss in his "Disquisitiones arithmeticae" see PMM Gauss was fascinated by this fundamental law and gave no less than eight different proofs himself. Today there are over two hundred published proofs of it. Petersburg Academy in the years The first volume was published in the year of Euler's death. De seriebus, in quibus producta ex minis terminis contiguis datam constituunt progressionem.

Varia artificia in serierum indolem inquirendi. Observationes circa divisionem quadratorum per numeros primos.

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Observationes analyticae. Disquitio accuratior circa residua ex divisione quadratorum altiorumque potestatum per numeros primos relicta. De eximio usu methodi interpolationum in serierum doctrina. Investigatio formulae integralis? Investigatio valoris integralis? A large wide-margined copy 25,5 x 20,5 cm. Later half calf, raised bands, title-labels with gilt lettering.

Top of spine professionally repaired.

### Great Moments in Mathematics Before 1650

Title in red and black with engraved title-vignette.. Some marginal browning. A faint dampstain to 9 leaves at end. Additamentum 1 with a dampstain to 6 leaves. Some marginal worm tracts to the middle and at the end. Some browning to 2 plates.

Timoshenko", one of the world's leading authorities on theoretical and applied mechanics, the father of modern engineering mechanics, and the famous author of "History of Strength of Material", N. Euler here in this work, brought it into a coherent mathematical discipline. He furthermore saw the importance of maxima and minima problems to the analysis of natural phenomena and in the second appendix Additamentum II, pp. Timoshenko pp. He also showed how these equations could be used to represent the positions of equilibrium of elastic and flexible lines, and formulated the first rigorous dynamical variational principle.

Craig G. Frazer in Landmark Writings in Western Mathematics.. On the curve of fastest descent in whatever resistent medium. On harmonic progressions. On infinite ly many curves of the same type, that is, a method of finding equations for infinite ly many curves of the same type. Addendum to the dissertation on infinite ly many curves of the same type. Petersburg, Typis Academiae, No wrappers.

In: "Classes Prima continens Mathematica. Euler's papers: pp.

Enestroem: E42, E43, E44 a. The origins of this paper would seem to be Proposition 15 of Vol. A method is developed for finding the modular equation for the first order equation that is extended to cover a number of cases; this in turn is extended to second and higher orders. The method involves finding suitable functions to integrate, starting from a part of the modular equation that is integrable, so that the whole equation is of this form. This paper is noteworthy in addition as it seems to be the first in which the function notation, albeit in a slightly different form from the modern meaning, is introduce.

I have not been able to check all the equations at this stage.

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Actorum Erud. Contemporary full vellum. Small stamps to title page and pasted library label to pasted down front free end-paper.

The lacking plate relates to a review-paper and not to Eulers paper. Euler's paper: pp.

## ISBN 13: 9780883853108

A widemargined copy with the usual scattered browning and brownspots. On the sums of series of reciprocals. A small brownspot in margin of first leaf, otherwise clean. On the surface of scalene cones and of other conic bodies. Theorems on divisors of numbers. On the nispidal points of the second kind of Mons. Research on imaginary roots of Equations. The first paper is Euler's discussion of "Cramers Paradox" and it contains his inventions of 2 kinds of curves, "Cusps of first kind" or keratoid cusp and "Cups of second kind" or ramphoid cusp.

Petersburg paradox, the Game Pharon. Book, , [4 , pp. Volume 2 only but complete in itself. Spine heavily damaged, backside not present frontside nearly detached. Rebinding is advised. Interior somewhat foxed but in very good condition. Notes, translation and additions by Bernoulli and Lagrange. Important and rare.