ADDITION. 
arithmetic. 
ter II. and wlio died in the year 1,003, 
brought this notation from the Moors of 
Spain into France, long before the time of 
his death, or, as some think, about the year 
960 ; and it was known among us in Bri- 
tain, as Dr. Wallis has shewn, in the begin- 
ning of the eleventh century, if not some- 
what sooner. As literature and science 
advanced in Europe, the knowledge of 
numbers was also extended, and the writers 
in this art were very much multiplied. The 
next considerable improvement in this 
branch of science, after the introduction 
of the numeral figures of the Arabians or 
Indians, was that of decimal parts, for 
which we are indebted to Regiomontanus ^ 
who about the year 1464, in his book ot 
« Triangular Canons,” set aside the sexage- 
simal subdivisions, and d ivided the radius into 
60,000,000 parts ; but afterwards he alto- 
gether waved the ancient division into 60, 
and divided the radius into 10,000,000 parts ; 
so that if the radius be denoted by 1, the 
sines will be expressed by so many places 
of decimal fractions as the cyphers follow- 
ing 1. This seems to have been the first 
introduction of decimal parts. To Dr. 
Wallis we are principally indebted for our 
knowledge of circulating decimals, and also 
for the arithmetic of infinites. The last, 
and perhaps, with regard to its extensive ap- 
plication and use, the greatest improvement 
which the art of computation ever received, 
was that of logarithms, which we owe to 
Baron Neper or Napier, and Mr. Henry 
Briggs. See Logarithms. 
Arithmetic, theoretical, is the science 
of the properties, relations, Sec. ot numbers, 
considered abstractedly, with the reasons 
and demonstrations of the several rules. 
Euclid furnishes a theoretical arithmetic, in 
the seventh, eighth, and ninth books of his 
elements. 
Arithmetic, practical, is the art of num- 
bering or computing ; that is, from certain 
numbers given, of finding ceitain others, 
whose relation to the former is known. As, 
if two numbers, 10 and 5, are given, and 
we are to find their sum, which is 15, their 
difference 5, their product 50, their quo- 
tient 2. 
The method of performing these opera- 
tions generally we shall now proceed to 
shew, reserving for the alphabetical ar- 
rangement those articles which, though de- 
pendent on the first four rules, do not ne- 
cessarily make a fundamental part of aiith- 
nietic. 
Addition is that operation by which we 
find the amount of two or more numbers. 
The method of doing this in simple cases is 
obvious, as soon as the meaning of number 
is known, and admits of no illustration. A 
young learner will begin at one ot the num- 
bers, and reckon up as many units separately 
as there are in the other, and practice will 
enable him to do it at once. It is impossi- 
ble, strictly speaking, to add more than 
two numbers at a time. We must first find 
the sum of the first and second, then we 
add the third to that number, and so on. 
However, as the several sums obtained are 
easily retained in the memory, it is neither 
necessary nor usual to mark them down. 
When the numbers consist of more figures 
than one, we add the units together, the 
tens together, and so on. But if the sum of 
the units exceed ten, or contain ten several 
times, we add the number of tens it contains 
to the next column, and only set down the 
number of units that are over. In like 
manner we carry the tens of every column 
to the next higher. And the reason of this 
is obvious from the value of the places ; 
since an unit in any higher places signifies 
the same thing as ten in the place immedi- 
ately lower. 
Rule. Write the numbers distinctly, units 
under units, tens under tens, and so on. 
Then reckon the amount of the right-hand 
column ; if it be under ten mark it down ~ 
if it’ exceed ten mark the units only, and 
carry the tens to the next place. In like 
manner carry the tens of each column to the 
next, and mark down the full sum of the 
left-hand column. 
Ex. 1. 
Ex 2. 
Ex. 3. 
432 
10467530 
. 457974683217 
215 
37604 
2919792935 
394 
63254942 
47374859621 
260 
43219 
24354642 
■109 
856757 
925572199991 
245 
2941275 
473214 
132 
459 
499299447325 
694 
41210864 
10049431 
317 
52321975 
41 
492 
4686 
5498936009 
243 
43264353 
943948999274 
Ans. 3833 
As it is of great consequence in business to 
perform addition readily and exactly, the 
learner ought to practise it till it become 
