# Euler : E17

## Translated and annotated by Ian Bruce .

One of Euler's early books was, it appears, thrust upon him, as he describes in the Forward. However, the manner in which he sets about to enlighten the Russian youth of the time is from a level perhaps more advanced than usual for the run of the mill books on arithmetic. I hasten to add that the work is hardly run of the mill, and would perhaps be more suited to a rare intellect who had never heard of arithmetic, which seems unlikely. Euler's great love of numbers soon becomes apparent, which he treats as old friends, and his approach is essentially one where no knowledge of algebra is assumed or used. Thus the text is very verbose but comprehensive.

CONTENTS

Forward

Chapter I

Here we are introduced to the nomenclature of numbers, or how to express them in terms of units, tens, hundreds, etc verbally.

Chapter II

The traditional method for finding the sum of two or more whole numbers is presented here.

Chapter III

The traditional methods for finding the difference of two or more whole numbers is presented here.

Chapter IV

Euler spends quite some time in illustrating how to multiply numbers. The beauty of the base ten number system comes apparent as he proceeds.

Chapter V

Euler spends quite some time in illustrating how to divide numbers. There is no mention of the decimal point in this work, but long division is explained in great detail.

Chapter  VI

Having introduced the basic operations with whole numbers, Euler moves on to the development of fractions, and gets as far as the greatest common divisor of two numbers, in order to cancel fractions to their lowest form.

Chapter  VII

Here we have the details of adding and subtracting fractions explained in great detail.

Chapter  VIII&IX

Here we have the details of multiplication and division of fractions explained in great detail.

Ian Bruce. August 22nd , 2018 latest revision. Copyright : I reserve the right to publish this translated work in book form. However, if you are a student, teacher, or just someone with an interest, you can copy part or all of the work for legitimate personal or educational uses. Please feel free to contact me if you wish, especially if you have any relevant comments or concerns about this work.