Elements of Algebra

Leonhard Euler, John Hewlett, Francis Horner, Jean Bernoulli, Joseph Louis Lagrange

Longman, Orme, 1822 - Algebra - 593 pages

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Selected pages

Of the Different Methods of calculating Simple Quantities Chap I Of Mathematics in general	1

Explanation of the signs + plus and minus	3

Of the Multiplication of Simple Quantities	6

Of the nature of whole Numbers or Integers with respect to their Factors	10

Of the Division of Simple Quantities	15

Of the properties of Integers with respect to their Divisors	16

Of Fractions in general	20

Of the Properties of Fractions	24

Of the Squares of Compound Quantities	97

Of the Extraction of ItooU applied to Com	100

the demonstration of the preceding Rule	115

Of the Resolution of Negative Powers	123

Of Arithmetical Proportion	129

Of Geometrical Proportions	152

SECTION IV	186

Of the Solution of Questions relating to the pre	194

Of the Addition and Subtraction of Fractions	27

Of the Multiplication and Division of Fractions	30

Of Square Numbers L	36

Of Square Roots and of Irrational Numbers re sulting from them	38

Of Impossible or Imaginary Quantities which arise from the same source	42

Of Cubic Numbers	45

Of Cube Roots and of Irrational Numbers re sulting from them	46

Of Powers in general	48

Of the Calculation of Powers	52

Of Roots with relation to Powers in general	54

Of the Method of representing Irrational Num bers by Fractional Exponents	56

Of the different Methods of Calculation and of their Mutual Connexion	60

Of Logarithms in general	63

Of the Logarithmic Tables that are now in use	66

Of the Method of expressing Logarithms	69

SECTION II	76

Of the Subtraction of Compound Quantities	78

Of the Multiplication of Compound Quantities	79

Of the Division of Compound Quantities	84

Of the Resolution of Fractions into Infinite Series	88

Of the Resolution of two or more Equations	206

Of the Resolution of Pure Quadratic Equations	216

of the Resolution of Mixed Equations of	222

Of the Extraction of the Roots of Polygonal	230

Of the Nature of Equations of the Second	244

Of the Resolution of Complete Equations	253

Of the R ule of Cardan or that of Scipio Ferreo	262

Of the Resolution of Equations of the Fourth	272

PART II	299

Of Compound Indeterminate Equations in which	317

Of the casesin which the Formula a + bx +	335

Of the Cases in Integer Numbers in which	342

Of a particular Method by which the Formula	351

Of the Method of rendering the Irrational Formula	361

Of the Method of rendering rational the incom	368

Of the Method of rendering rational the irrational	379

Of the Resolution of the Formula axxbry+cy	387

Of the Transformation of the Formula ax1+cy	396

Of some Expressions of the Form ax + In	405

Common terms and phrases

Algebra already arithmetical progression become a square bers biquadrate calculation CHAP coefficient common divisor consequently consider contains continued fraction crowns cube root decimal fraction deduce denominator determine difference divided divisible ducats equal evident example exponent expressed factors farther formula geometrical progression given number gives greater number greatest common divisor Hence infinite number infinite series integer numbers irrational last term lastly less let us suppose letters likewise logarithm manner means method multiplied negative number of terms numbers sought observed obtain perceive positive numbers preceding prime numbers proposed question quotient ratio reduced remainder represented required to find resolve rule second degree second term shew solution square number square root substitute subtract third degree tion tiplied transform unity unknown quantity vulgar fraction wherefore whole numbers

Popular passages

Page 153 - Three, then, is based on the principle, that the product of the extremes is equal to the product of the means...

Appears in 101 books from 1807-2005

Page 33 - Multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor ; the first product "will be the numerator of the quotient, and the second wiU be its denominator.

Appears in 127 books from 1756-2003

Page 205 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Appears in 72 books from 1775-1896

Page 139 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.

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Page 205 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? 56.

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Page 206 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?

Appears in 51 books from 1782-1894

Page 4 - The manner in which we generally calculate a person's property, is a good illustration of what has just been said. We denote what a man really possesses by positive numbers, using, or understanding the sign + ; whereas his debts are represented by negative numbers, or by using the sign — Thus, when it is said of any one that he has 100 crowns, but owes 50, this means that his property really amounts to 100 — 50 ; or, which is the same thing, + 100 — 50, that is to say 50.

Appears in 15 books from 1821-1896

Page 254 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three by three ; and so on, the signs of the...

Appears in 13 books from 1769-1961

Page 223 - The general rule, therefore, which we deduce from this, in order to resolve the equation xx = — px + g, is founded on this consideration : That the unknown quantity x is equal to half the coefficient, or multiplier of x on the other side of the equation, plus or minus the square root of the square of this number, and the known quantity which forms the third term of the equation.

Appears in 14 books from 1813-1914

Page 26 - mb 90. In order therefore to reduce a given fraction to its least terms, it is required to find a number by which both the numerator and denominator may be divided. Such a number is called a common divisor, and so long as we can find a common divisor to the numerator and the denominator, it is certain that the fraction may be reduced to a lower form ; but, on the contrary, when we see that except unity no other common divisor can be found, this shews that the fraction is already in the simplest...

Appears in 11 books from 1821-1873

Bibliographic information

Title	Elements of Algebra
Authors	Leonhard Euler, John Hewlett, Francis Horner, Jean Bernoulli, Joseph Louis Lagrange
Edition	3
Publisher	Longman, Orme, 1822
Original from	Harvard University
Digitized	Sep 29, 2005
Length	593 pages

Export Citation	BiBTeX EndNote RefMan

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