By Leonard Euler

[Reprint of the fifth version Longman, Orme, and Co., London 1840. edition]

In 1770, one of many founders of natural arithmetic, Swiss mathematician Leonard Euler (1707-1783), released components of Algebra, a arithmetic textbook for college students. This version of Euler's vintage, released in 1822, is an English translation inclusive of notes further by way of Euler's coach, Johann Bernoulli, and additions by means of Joseph-Louis Lagrange, either giants in eighteenth-century arithmetic, in addition to a brief biography of Euler. half 1 starts with effortless arithmetic of determinate amounts and comprises 4 sections on basic calculations (adding, subtracting, department, multiplication), after which progresses to compound calculations (fractions), ratios and proportions and algebraic equations. half 2 comprises 15 chapters on analyses of indeterminate amounts. the following, Euler indicates the reader a number of how one can clear up polynomial equations as much as the fourth measure. This landmark ebook confirmed scholars the wonderful thing about arithmetic, and extra considerably, the best way to do it.

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**Example text**

Abed. It shews that 5 must be multiplied by 7, and that this product is to be again multiplied by 8; that we are then to multiply this product of the three numbers by a, next by b, then bye, and lastly by d. 8, we may write its value, 280; for we obtain this number when we multiply 35 (the product of 5 by 7) by 8. 30. The results which arise from the multiplication of two or mOI'e numbers are called products; and the numbers, or individual letters, are called factors. 3]. Hitherto we have considered only positive numbers; and there can be no doubt, but that the products which we have seen arise are positive also: viz.

VIII. Of the Calculation of Irrational Quantities. • •. IX. Of Cubes, and of the Extraction of Cube Roots X. Of the higher Powers of Compound Quantities XI. • XII. •.... XIII. Of the Resolution of Negative Powers Chap. I. II. II I. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. S ECTIO N III. Of Ratios and Proportions. ••• Of Arithmetical Proportion. • • . • . . . • • . ••.. Of the Summation of Arithmetical Progressions.. •.... ••••.. •••••. ••. • Of Infinite Decimal Fractions.. . . • .

The only other occasional yet solid analyses of EULER's work I have found in languages other than Russian are included in Chapter VII of C. R. BOYER's History of Analytic Geometry, New York, Scripta Mathematica, 1956, and in six articles in the Archive for History of Exact Sciences: J. E. HOFMANN, "Uber zahlentheoretische Methoden Fermats und Eulers, ihre Zusammenhange und ihre Bedeutung", 1(1960/1962): 122-159 (1961 ). O. B. SHEYNIN, "On the mathematical treatment of observations by,L. Euler", 9 (1972): 45-56, H, J.