tinguished ;-units, tens, hundreds, are the simple names of figures. A Compound Name, or Term, is a word by which three or six places of figures are called, when all, or a part of the places are supplied with figures ;-thousands, millions, billions, trillions, &c. A Period is six places of figures, reckoning from the right hand. Each period is divided into two parts, having three places of figures in each. NOTE.--It should be observed that the word unit or units is used in several different senses. It is used to express the right hand place of figures, the three right hand figures of every period : it is also the name of the right hand period. But in all cases, except in the right hand period, it denotes more than simple ones ; thus, when we say 1 million, our meaning is one in the period of millions, yet this 1 million implies ten hundred thousand simple units. Reading figures is expressing by words, a number represented in figures. If one figure is to be expressed by a word, we have only to repeat its common name. If two figures are to be read, we first repeat the tens by their contractions and the common name of the right hand figure. When three places of fig. ures are to be read, we commence at the left hand, call the figure in that place by its common name, then add the word hundred, and read the other two as before directed. The three left hand figures of every period express thousands, and are read in the same manner as the three right hand ones, with the addition of the word thousand. All the other periods are read the same as the right hand one, and then the name of the period is repeated. After the pupil has learned to read the six right hand places of figures, or the first period, he has only to learn the names of the other periods to be able to read with ease any number of figures. The right hand period is called Units, the next Millions, then Billions, Trillions, Quatrillions, Quintillions, Sextilions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions. An unit of any period implies ten hundred thousand of the units in the next right hand period. The names of the periods are not names of different denominations, strictly speaking, because any figure in either of the periods denotes ten times as many units, as it would if it stood in the next right hand place, which is the peculiar arrangement of simple numbers. REMARK. The periods and the subdivisions of the periods are now generally divided by a comma. This practice is objectionable ; for when the three right hand figures are decimals, as decimals are separated from whole numbers by commas, the schoIar generally labours under a difficulty, to determine whether they are whole numbers or decimals, and in any case they tend to confuse his conceptions of the subject. In this work, the periods and half periods are separated by apostrophes, and decimals by commas. The method of reading figures is exhibited in a condensed form in the following table. The words at the right hand express the same numbers as the figures standing against them. Tens, Millions, Hụndreds of Millions, Tens of Millions, Thousands, 1 One. 1 2 3 One hundred and twenty-three. 1 2 3 4 5 6 One hund. 23 thous. 456. 1 2 3 4 5 6 7 1 million 234 thous. 567. i 2 ' 3 4 5 6 7 8 12 millions 345 thous. 678 1 2 3 4 5 6 7 8 9 One hundred twenty-three mil. lion four hundred fifty-six thou sand seven hundred eighty-nine. When any place is supplied by a cipher, the cipher is not mentioned, and the other figures are read as before directed. S Millions, Hundreds of Millions, Tens of Millions, Hundreds, Thousands, 1 2 Two. 3 0 2 Three hundred and two. 4 0 0 3 Four thousand and three. 50 '04 0 Fifty thousand and forty. 6 05 0 0 0 Six hundred five thousand 7 0 0 0 000 Seven million. 8 0 7 0 0 6 0 0 80 million 700 thous. 600. 908'706' 5 0 4 Nine hundred and eight million 7 hundred and six thous. 5 hundred and four. Let the scholar be required to read the following numbers. 76 76'543 20'000'000 100'000'000'000 765 222'222 10'000'010 404'404'303'303 87'654 999'999 66'065'064 742'921'532'119 Period Period Period Period Period of of The above five Periods of figures are read as follows :-nine hundred eight thousand, seven hundred sixty-five quatrillion, four hundred thirty-two thousand, one hundred and nine trillion, eight hundred seventy-six thousand, five hundred and fortythree billion, two hundred ten thousand, nine hun. dred eighty-seven million, six hundred fifty-four thousand, three hundred and twenty-one. In reading the right hand period, the word units is not generally repeated, for it is always understood to be units unless the name of the period is mentioned. NOTATION. Notation is writing in figures any number expressed by words. If a number of units less than ten, are to be written, we make use of one figure ;-thus, nine is expressed by the figure 9. If more than nine units are to be written, we must set as many units in the second place as there are tens, because each one in the second place represents ten, and the other units at the right hand. Thus, twenty-two is written 22 because in twenty there are two tens ; so, thirty-six is written 36; forty-eight, 48. When three figures are to be written, place as many units in the third place as there are hundreds expressed, and the other two figures as before directed, If thousands are to be written, place the figures in the left division of the period, in the same manner as those in the right division. All the other periods are written in a similar manner. Let the scholar be requested to write on his slate in figures, the following numbers, Twenty-nine. Forty-five million, four hundred nine thousand and eight. Five hundred million, seven hundred one thousand and nineteen, Thirty-five billion, fourteen million, seven hundred thousand and forty. SECTION II. DEFINITIONS. A Question or Example is that which is required to be done. A Rule is the direction by which a question or example is to be done. An Answer is the result obtained by the correct performance of any question; or, it is the number demanded in the question. Proof is the method of ascertaining whether a question has been correctly performed A Principle is the fundamental truth on which a rule is founded. Illustration is the explanation of the principles or reasons on which any rule is established. Addition is the collecting or putting several things or numbers together; thus, when we say 2 put with 1 makes 3, we add these two numbers together; so, if we take 2 dollars and put them with 3 others, we dd two quantities together Subtraction is taking one number or one quantity from another; or it is taking a part of a number or quantity from a whole number or quantity. If we take 2 from 5, we take away 2 units which were contained in the 5, and there is 3 left; if we take 2 dollars from 5, we take away a part of the quantity ; and in both cases we subtract. Stating a Question is setting down numbers in a proper manner for the operation of a question. Operation is the working or performing of a question, |