# 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 22^{nd} , 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
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