# 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. So far there is no mention of the decimal point, 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.

Ian
Bruce. August 10^{th} , 2018 latest revision. Copyright : I reserve
the right to publish this translated work in book form. However, if you are a
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