ARITHMETIC. 



aneofthe greatest improvements which 

 this science had received sinc the first 

 discovery of it. This method of notation, 

 now universally used, was probably de- 

 rived originally from the Indians by the 

 Arabians, and not, as some have supposed, 

 from the Greeks ; and it was brought 

 from the Arabians into Spain by the 

 Moors or Saracens, in the tenth century. 

 Gerbert, who was afterwards Pope, un- 

 der the name of Silvester IT. and who 

 died in the year 1003, brought this nota- 

 tion 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 Britain, as Dr. 

 Wallishas shewn, 'in the beginning 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 In- 

 dians, WHS that of decimal parts, for 

 which we are indebted to Regiomonta- 

 rms ; who, about the year 1464, in his 

 book of " Triangular Canons," set aside 

 the sexagesimal subdivisions, and divided 

 the radius into 60,000,000 parts; but af- 

 terwards he altogether 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 ex- 

 pressed by so many places of decimal 

 fractions as the cyphers following 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 per- 

 haps, with regard to its extensive applica- 

 tion and use, the greatest improvement 

 which the art of computation ever re- 

 ceived, 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. of num- 

 bers, 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 

 numbering or computing; that is, from 

 certain numbers given, of finding certain 

 others whose relation to the former is 

 known. As, if two numbers. W and 5, 

 are given, and we are to find their sum, 

 which : s 15, their difference 5, their pro- 

 duct 50, their quotient 2. 



The method of performing these ope- 

 rations generally we shall now proceed to 

 shew, reserving for the alphabetical ar- 

 rangement those articles, which, though 

 dependent on the first four rules, do not 

 necessarily make a fundamental part of 

 arithmetic. 



ADDITION. 



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 illus- 

 tration. A young learner will begin at 

 one of the numbers, 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 impossible, strictly speak- 

 ing, 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 re- 

 tained in the memory, it is neither neces- 

 sary 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 va- 

 lue of the places ; since an unit in any 

 higher places signifies the same thing as 

 ten in the place immediately 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 curry the tens to the next place. 

 In like manner carry the tens of each co- 

 lumn 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 



409 856757 925572199991 

 245 2941275 473214 



. 132 459 499299447325 



694 41210864 10049431 



317 52321975 41 



492 4686 5498936009 



24S 43264353 943948999274 



Ans.3833 



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