Education

1895

Normal Standard Arithmetic
Arithmetical Language

1. Arithmetic is the science of numbers and the art of computing with them.
   
2. A Unit is a single thing or one. A thing is a concrete unit; one is an abstract unit.
   
3. A Number is a unit or collection of units. Numbers are concrete and abstract.
   
4. A Concrete Number is one in which the kind of unit is names; as in two yards, five books.
   
5. An Abstract Number is one in which the kind of unit is not named; as, two, four, etc.
   
6. Similar Numbers are those in which the units are alike; as, two boys and four boys.
   
7. Dissimilar Numbers are those in which the units are unlike; as, two boys and four books.
   
8. Arithmetical Language is the method of expressing numbers.
   
9. Arithmetical Language is of two kinds, Oral and Written. The former is called Numeration and the latter is called Notation.
   
10. Numeration is the method of naming numbers, and of reading them when expressed by characters. It is the oral expression of numbers.
    
11. It would require too many words to give each number a separate name; numbers are therefore named according to the following simple principle:
    
    Principle - we name a few of the first numbers, and then form groups or collections, name these groups, and use the names of the first numbers to number these groups.
    
    
12. A single thing is named one; one and one more are named two; two and one more, three; three and one more, four; and thus we obtain the simple names: one, two, three, four, five, six, seven, eight, nine, ten.
    
13. Now regarding the collection ten as a single thing, we might count one and ten, two and ten, three and ten, etc., as far as ten and ten, which we would call two tens. By this principle were obtained the following numbers: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty.
    
14. Proceeding in the same way, we would have two tens and one, two tens and two, two tens and three, etc. By this principle were obtained the following numbers: twenty-one, twenty-two, twenty-three, twenty-four, twenty-five, twenty-six, twenty-seven, twenty-eight, twenty-nine.
    
15. Continuing in this same manner, we would have three-tens, four-tens, five-tens, etc. By this principle were derived the following ordinary names: thirty, forty, fifty, sixty, seventy, eighty, ninety.
    
16. A group of ten tens is call a hundred; a group of ten hundreds a thousand. The next group consists of a thousand thousands, and is called a million; the next group is a thousand millions, called a billion, etc.
    
17. After a thousand, the two groups coming between those having a distinct name are numbered by tens and hundreds, as ten thousand and hundred thousand.
    1. The above shows the principle by which the numbers were named. The names we use come from the Saxon or Gothic language.
       
    2. Eleven is from the Saxon endlefen, or Gothic ainlif (ain, one and lif, ten); twelve is from the Saxontwelif, or Gothic tvalif (tva, two and lif, ten).
       
    3. Twenty is from the Saxon twentig(twegin, two and tig, ten); thirty is from the Saxon thritig (thri, three and tig, ten), etc.
       
    4. Hundred is a primitive word; thousand is from the Saxon thusend, or Gothic thusundi (thus, ten and hund, hundred); million, billion, etc. Are from the Latin.