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The Attention of the Conductors of Schools, and of Book

sellers in general, is invited to the following List OF NEW AND VALUABLE ELEMENTARY BOOKS.

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£. s. d. Blair's Practical English Grammar, with copious Exercises,

containing every thing essential, and nothing superfluous,
complete in this single Book

Class Book, or 365 English Lessons
Reading Exercises, for Junior Classes

Grammar of Natural Philosophy, by which the various branches of Science may, for the first time, be practically taught in Schools

Grammar of Chemistry, new edition

First Catechism, containing common things necessary to be known by all Children

School Dictionary, for learning by rote, containing none but inportant words, and omitting derivative, vulgar,

obscene, and trivial words
Smith's Grammar of Geometry
Mavor's Circle of the Arts and Sciences, containing the first
Principles of every Branch of Knowledge

0 Goldsmith's Grammar of the Laws and Constitution of England, for the Use of Schools and Junior Students of Law

· Grammarof Geography, including the Use of the Globes, numerous Exercises, Questions, &c., &c., with

Geographical Copy Book, or Sl:eleton Maps, to be filled in by the Student. Part I. Do. Do. Do. Part II.

- Popular Geography, containing all the interesting Features of that Science, with 60 plates

0 14
School Atlas,' or Key to the Geographical Copy
Books
Robinson's Grammar of History, by which that Subject may

now be practically taught in Schools .
Mortimer's Grammar of Trade and Commerce
Irving's Elements of English Composition
Gregory's Letters on Literature and Composition, 2 vols.
Thornton's Grammar of Botany, with numerous Plates

7 The Book of Trades, with sixty Engravings, descriptive of all the useful Arts, 3 vols., each

3 96 Morrison's Elements of Book-keeping, by Single and Double Entry, with Copper plate Forms, &c.

0 7 0 Crocker's Land Surveying in all its Branches and Varieties, with coloured Plates, dic.

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ARITHMETIC is the science which explains the various methods of computing by numbers.

Allits operations are perforined by Addition, Subtraction, Multiplication and Division.

NUMERATION OR NOTATION.

When two or more figures are placed together, the first, or right-hand figure is taken for its simple value; the second to the left signifies so many tens; the third so many hundreds; and the fourth so many thousands; and so on, uccording to the following Table :

Thus figures, besides their common value, have one which depends upon the place in which they stand when joined to others; 6 and 5 are read six and five; butif they stand together, 65, they are read sixty-five. The figure 5 on the right hand denotes its simple value only, but the 6, from its situation, becomes ten times greater than its simple value, or sixty, therefore the two together are called sixty-five.

If there be three figures, as 978, the first denotes its simple value, as eight; the second a value ten times greater than its simple value, as seventy; and the third is a hundred times greater than its simple value, as nine hundred: the figures together are read nine hundred and seventy-eight.

In this manner, the value of each figure to the left is always ten times greater than it would be if it stood in the next place on the right,

NOTE.

* The Tutor is recommended to direct the Pupil to commit to memory all the passages which are printed in Italic characters, and likewise all the tables,

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thus 6666, the first figure 6 is simply six, the next is sixty, the third six hundred, and the fourth six thousand; the whole number is read, Six thousand six hundred and sixty-six.

The first six figures in the table above are read, One hundred twenty. six thousand nine hundred and seventy-eight. The whole period of nine figures is thus read, Five hundred and forty three millions, one hundred and twenty-six thousand, nine hundred and seventy-eight.

The enumeration of figures may be carried much further according to the following Table:

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In large nuñbers it is common to divide them into periods of six figures each, and half periods of three figures. The foregoing three periods are read-One hundred twenty-three thousand, four hundred and fifty-six billions, four hundred eighty-seven thousand, nine hunelred and fitty one millions, four hundred sixty-two thousand, seven hundred and fifty-three.*

Hence the following general RULE. To the simple value of each figure, join the name of its place according to the situation in the series, as hundreds, thousünds, millions, billions, trillions, &c.

NOTE.

* The names of the higher periods after Billions, are Trillions, Quadrillions, Quintillions, Sextillions, Septillions, Octillions, and Nonila lions, each period consisting of six places of figures. The first three of every period are so many Units of it, and the latter, or left hand part, so many Thousands. The following 's able contains the whole series:

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EXAMPLES IN NUMERATION AND NOTATION,
Read, or write down in 'words, the value of the following

Numbers :
Ex. 1. 19
Ex. 11. 40005

Ex. 21. 340
2. 244
12. 324060

22, 436901
3. 3045
13. 400369

23. 36945
4. 45060
14. 765

24. 9874000
5. 69305
15. 564001

25, 654328
6. 93614
16. 43976+

26. 4328764
7. 564875
17. 9300042

27. 856540
8. 4500342
18. 70000021

28. 43760000
9. 5687041
19. 35000

29 37004
10. 6843700
20. 50000000

30. 85600341
Ex. 31. 456074328

32. 5900007 643
33. 68670749004
34. 876430786453
35. 1000000843213
36. 34876543218764
37. 594632171834785
38. 87643285176487589
39. 1234567890001259

40. 987654321123456789
"Write down the figures answering to the following Examples,
Ex. 1. Thirty-nine.

2. Four hundred and sixty-nine.
3. Two thousand and one.
4. Thirty-five thousand and twenty-eight.
5. Three hundred and seventy-six thousand.
6. One million and fifty-nine.
7. Eighty-seven millions, five hundred and eighty thousand, one

hundred and nine.
8. Five hundred seventy-six millions, three hundred twenty-five

thousand, three hundred and ninety-one.
9. Eight hundred millions and eighty.
10. Three hundred and three millions and thirty-one.

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NOTE.

* Besides these ten examples, it will be desirable that the pupil should, after having written the preceding forty examples into words, write them back again into figures, without the assistance of the book. He should likewise be desired to mention the value of each line in the subsequent

in Addition, as well as the sum total ; by these means Numeration will, in both its parts, become perfectly familiar to him,

MISCELLANEOUS EXAMPLES. Ex. I. By the late enumeration of the people, the number of inhabitants in England is put down at nine millions, three hundred fortythree thousand, five hundred and seventy-eight; and the number found to be in London was eight hundred eighty-five thousand, five hundred and eighty-seven ;-How are these numbers expressed in figures?

Ex. 2. The world was created two thousand three hundred and fortyeight years before the Deluge; three thousand two hundred and fifty-one years before the building of Rome; four thousand and four years before the birth of Christ, and five thousand and fourteen years before the present time (1811):-Let each of these numbers be expressed in figures.

Ex. 3. Express in words the distances of the primary planets from the Sun, which are as follow : Mercury . 37,000,000 Venus

66,000,000 The Earth . 95,000,000

Mars

145,000,000 Jupiter . 493,000,000 Saturn 903,000,000

The Herschel . . 1,813,000,000 miles.* FRACTIONS, or broken numbers, are expressed in the following manner :-A halfpenny is denoted by }; a farthing, by !, being the onc-fourth of a penny; and three farthings by , being three-fourths of a penny. Thus it appears that a fraction is any part or parts of an unit, and is expressed by two numbers separated from each other by a short line. The lower number shows how many parts the unit is divided into, and the upper figure points out what number of these parts are contained in the fraction: thus 4, when standing for

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NOTE. * The ancient Romans, in their Notation of Numbers, made use of the following five letters: I, V, X, L, and C, which, singly, stood for one, five, ten, fifty, and a hundred. By repeating and combining these, any other numbers were expressed: thus II, signified two; III, three; XX. twenly; CC, two hundred, and so on. The rules for Roman Notation are as follow :

1. The annexing a letter of a lower value to one of a higher, increases its value, or denotes the sum of both, as VI, signifies six; XII, denotes twelve; LV, fifty-five; LXXVI, seventy-six; CLII, one hundred and fifty-two.

2. The prefixing a letter of a lower value, to one of a higher, subtracts their values, or shows their difference. thus, I prefixed to V, or IV, is four; IX, nine ; XL, forty; XC, ninety, &c.

For the sake of abbreviation, the Romans introduced these marks:--17, five hundred; Clɔ, a thousand : these, in process of time, were written DM, so that now the D signifies five hundred, and the M. a thousand; but in the titles of many old books we find the other mode of Notation. The following table will exhibit every thing necessary to be known on this subject :

Table.

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