Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[blocks in formation]
[blocks in formation]

Plus, or
more,

[merged small][ocr errors][merged small]

S Minus,

{

}

following Work.

Significations.

the Sign of Addition, as 2+4, signifies that 2 and 4 are to be added together. the Sign of Subtraction, as 8-3 signi or less,fies that 3 is to be subtracted from 8. multiplied the Sign of Multiplication, as 7x5 signifies that 7 is to be multiplied into or by 5.

into, or

by,

divided

by

the Sign of Division, as 9÷3, signifies that 9 is to be divided by 3; and , or 3)9, signifies the same.

the Sign of Equality, as 9=9, signifies that 9 is equal to 9; or 5+4—2=7 signifies, that 5, increased by 4 and diminished by 2 is equal to 7. The equal to line or vinculum, over the 5 and 4, serves as a chain to liuk them together, and shews, that they are to be added together, before the num. ber 2 is subtracted.

Propor-24 :: 8: 16 signifies, that 2 is to 4 as 8 is to 16.

tion.

The other characters are explained among the Defini. tions in the Work.

ERRATA.

Page 83, Ex. 7, read of

89,

103,
134,

19, for read

17, for 51.75 read 21.75 feet
25, for 3 read 32

252, the equation corrected will stand thus,

[merged small][merged small][merged small][merged small][ocr errors][merged small]

THE

COMPLETE PRACTICAL

ARITHMETICIAN.

PART I.

DEFINITIONS.

1. ARITHMETIC is the art of computing by numbers; and consists of two parts, viz. whole numbers, and frac tions vulgar or decimal.

2. Arithmetic in whole numbers consists of entire quantities, which are not divided into parts less than an unit.

3. Arithmetic in fractions consists of parts of some whole quantity, or of an unit.

4. Number is either an unit, or a collection of units; viz. it is the name of that idea, or notion, we conceive of things considered as one, or many.

Note 1. When we consider numbers simply, without applying them to any particular subject, the idea we form of them is called abstract. Thus, if we speak of the number three, four, five, or any other num ber, abstractedly, we mean three, four, five, &c. units of any thing whatever. But, when we consider number not in its general nature, but as a number of certain particular things, as four yards, five inches,

B

&c. we call it a concrete or an applicate number. Example, the num ber four is less than five abstractedly considered; yet, taking the numbers in an applicate sense, it is not always so; thus, the quantity of four yards is not less than five inches.

5. A whole number is an unit, or a multiple* of one or more units.

6. A mixed number is a whole number with some part, or parts, annexed.

7. An even number is that which can be divided into two equal whole numbers.

8. An odd number is that which cannot be divided into two equal whole numbers.

9. A prime number is that which can only be divided by itself, or by an unit, without a remainder.

10. Numbers are said to be prime to each other when only an uuit measures, or divides, them both even.

11. A square number is the product of a number by itself.

12. A cube number is the product of a number and its square.

13. A composite number is that produced by multiplying two or more numbers together.

14. A perfect number is that which is equal to the sum of all its aliquot parts.

Note 2. There are several other numbers, which have particular names, as figurate, abundant, deficient, &c. but their chief use is in the higher parts of the mathematics.

15. An aliquot part is that which is contained a precise number of times in another.

16. An aliquant part is such as is contained in another a certain number of times, with some part, or parts,

over.

One number is said to be a multiple of another, when the former contains the latter a certain number of times without a remainder thus, 4 is a multiple of 2, and 8 is a multiple of 2, and of 4, &c.

17. An integer is any whole quantity or number; as, a pound, a yard, &c. or, 1, 2, 3, &c.

18. Digits, or figures, are the marks by which numbers are expressed, and are the nine following, viz. 1 one, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine, to which we may add the cipher 0, or nought, which is of no value when taken by itself; yet, when it is placed on the right or left hand of any figure, increases or diminishes it tenfold.

19. The nature of all arithmetical operations is by some quantities that are given, to find out others that are required.

20. The principal, or fundamental, rules of Arithmetic are Notation and Numeration.

21. Notation is the art of expressing numbers by figures; and teaches us to read, or write down, any number, and to have a clear and distinct idea of every figure in it.

22. Numeration informs us in what manner we are to exercise and accommodate numbers to the various purposes of business; it consists principally of four parts, viz. Addition, Subtraction, Multiplication, and Division.

Note 3. The operations of arithmetic in general are only of two kinds, viz. increasing and diminishing; for, multiplication is only a compendious method of performing addition, and division performs the work of many subtractions.

23. A proposition is something proposed to be done, or proved.

24. An axiom is self-evident, and cannot be rendered more plain by demonstration.

25. A theorem is a demonstrative proposition, wherein the nature and property of a thing is proposed to be proved.

[merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][ocr errors][ocr errors][ocr errors][ocr errors][merged small]

8 7.6 5 4,3 2 1 7.6 5 4,3 2 1.9 8 7,6 5 4 3 2 1 9 8 7.6 5 4,3 2 1

[ocr errors]

Note 1. The table above may be extended to any lenghth by conti nually prefixing a period of six figures towards the left hand, and writ ing the word quintillions, sextillions, septillions, octillions, uonillions, decillions, &c. over the unit's place of each of these periods: but the table of nine figures, which is printed on a larger type than the rest, is. sufficient for common use.

Note 2. To write down any number. Rule: write down ciphers to as many periods and places as are named in the given number; then begin at the left hand, and observe, at each place, what significant figure is named; take away the cipher, and put the significant figure in its place. Ex. Write down ten million fifty thousand three hundred and one, thus:

00,000,000 Proceed in this manner for any other number.

210,050,301 S

3. To read any number of figures when written down. Rule: divide the figures, from the right hand to the left, into threes by a comma and a period alternately, writing m over the figure to the left

« ΠροηγούμενηΣυνέχεια »