Attic measures of capacity for liquids reduced to English wine

measure

ibid.

Measures of capacity for liquids reduced to English wine mea

sure

ibid.

Jewish dry measure reduced to English

125

Jewish measure of capacity for liquids reduced to English wine

Of the principal gold and silver coins, containing their weights, fineness, pure contents, current value, &c.

126

peated.

As often as any character is repeated, so many times its value is re

† A less character before a greater diminishes its value.

‡ A less character after a greater increases its value.

* For every

affixed this becomes ten times as many.

† For every C and Ɔ put one at each end, it is increased ten times

A line over any number increases it 1000 fold.

ELEMENTARY TREATISE

ON

ARITHMETIC.

NUMERATION.

1. A COMPARISON of the different objects, that come within the reach of our senses, soon leads us to perceive, that, in all these objects, there is an attribute, or quality, by which they can be supposed susceptible of increase or diminution; this attribute is magnitude. It generally appears in two different forms. Sometimes as a collection of several similar things, or separate parts, and is then designated by the word number.

Sometimes it presents itself as a whole, without distinction of parts; it is thus, that we consider the distance between two points, or the length of a line extending from one to the other, as also the outlines and surfaces of bodies, which determine their figure and extent, and finally this extent itself.

The proper characteristic of this last kind of magnitude is the connexion or union of the parts, or their continuity; whilst in number we consider how many parts there are; a circumstance to which the word quantity at first had relation, though afterwards it was applied to magnitude in general, magnitude considered as a whole being called continued quantity, to distinguish it from number, which is called discrete, or discontinued quantity. 2. All that relates to magnitude is the object of mathematics; numbers, in particular, are the object of arithmetic.

Continued magnitude belongs to geometry, which treats of the properties presented by the forms of bodies, considered with regard to their extent.

3. Number, being a collection of many similar things, or many Arith.

1

distinct parts, supposes the existence of one of these things, or parts, taken as a term of comparison, and this is called unity.

The most natural mode of forming numbers is, to begin with joining one unity to another, then, to this sum another; and continuing in this manner, we obtain collections of units, which are expressed by particular names; the whole of these names, which varies in different languages, composes the spoken numeration.

4. As there are no limits to the extention of numbers, since however great a number may be, it is always possible to add an unit to it, we may easily conceive that there is an infinity of different numbers, and, consequently, that it would be impossible to express them in any language whatever, by names, that should be independent of each other.

Hence have arisen nomenclatures, in which the object has been, by the combinations of a small number of words, subject to regular forms, and therefore easily remembered, to give a great number of distinct expressions.

Those, which are in use in the [English language,] with few exceptions, are derived from the names assigned to the nine first numbers and those afterwards given to the collections of ten, a hundred, and a thousand units.

The units are expressed by

one, two, three, four, five, six, seven, eight, nine.

The collections of ten units, or tens, by

ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety. The collections of ten tens, or hundreds, are expressed by names borrowed from the units; thus we say,

hundred, two hundred, three hundred, . . . . nine hundred. The collections of ten hundreds, or thousands, receive their denominations from the nine first numbers and from the collections of tens and hundreds ; thus we say

thousand, two thousand ..

nine thousand,

ten thousand, twenty thousand, &c.

hundred thousand, two hundred thousand, &c.

The collections of ten hundred thousands, or of thousands of thousands, take the name of millions, and are distinguished, like the collections of thousands.