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ELEMENTARY ARITHMETIC,

WITH BRIEF NOTICES OF ITS HISTORY.

SECTION I.

OF NUMBERS.

BY ROBERT POTTS, M.A.,

TRINITY COLLEGE, CAMBRIDGE,

HON. LL.D. WILLIAM AND MARY. COLLEGE, VA., U.S.

CAMBRIDGE:

PUBLISHED BY W. METCALFE AND SON, TRINITY STREET.

LONDON:

SOLD AT THE NATIONAL SOCIETY'S DEPOSITORY, WESTMINSTER.

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INTRODUCTION.
NUMBERS.

IT has been remarked, that one of the most important, and yet one of the most neglected branches of every science, is its history. The following brief notices of the history of the science of number make no pretence to completeness. If they invest the subject with interest to the mind of the intelligent student, and lead him to further inquiries, the object of the writer will have been answered.

In what age of the world the science of number had its origin— who first devised the method of counting by tens-who first invented symbols of notation, and separated the idea of number from the qualities of objects with which it was associated, are questions more easily proposed than answered satisfactorily.

It is highly probable that the origin of number was coeval with the origin of spoken language, and that, long before figures were invented, some rude methods of reckoning were devised, at first limited, but afterwards extended and improved as the wants and necessities of human society increased. The classifying by pairs would seem to suggest the simplest mode of reckoning. The counting by fives was probably the next step in numeration, and the practice of numbering by the five fingers on the two hands was the origin of counting by tens, as almost all children may be observed to do in their first efforts in counting. In the oldest writings which have been preserved to modern times, there is found a full recognition of this principle of counting by tens, tens of tens, tens of hundreds, and so on. Language still betrays by its structure the original mode of proceeding, and it is probable that the primitive words denoting numbers did not exceed five.

It was by abstracting or separating the idea of number from the ideas of the qualities of the things themselves, and expressing this abstraction in language, that the names of numbers have arisen, and the names of numbers being thus separated, could afterwards be applied to things with other qualities. The information, however, which can be collected from what remains on this subject, is both scanty and unsatisfactory. Some ancient languages recognised a dual number in the names of things, and the English words pair and brace are employed not universally, but only to some particular things; the same remark may be made on the word leash, applied to three particular things.

It is uncertain whether the earliest forms of written language were hieroglyphical or alphabetical, whether the letters denoting elementary sounds were formed from hieroglyphical characters; it is, however, certain that the initial letters of the names of numbers were in very early times employed as symbols of numbers. The brief notices here given of tho early history of numbers, will be restricted to those peoples who have chiefly contributed by their discoveries and writings to our civilisation and advancement in knowledge.

In the fifteenth section of his Problems, Aristotle puts forth the following questions, touching the opinions held by philosophers of his time, as to the origin of counting by tens:

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