# The Principles of Algebra

J. Davis, 1796 - Algebra

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Pages à faire: 34 et 37.

### Contents

 Addition 8 Diviſion 21 Reſolution of Equations 34 Fraćtions 49 Decimal Fraćtions 64 Powers and Roots of Numbers 82 Equations of the Second Order 100
 Equations of the Third Order 128 Queſtions producing Equations of the Third 146 On the Nature of a Series of Numbers Arithmetical 165 Geometrical Series continued 188 On the Application of Algebra to Geometry 201 Cardans Rule 210 253

### Popular passages

Page x - ... intractable; though the whole world should be destroyed, one will be one, and three will be three, and no art whatever can change their nature. You may put a mark before one, which it will obey ; it submits to be taken away from another number greater than itself, but to attempt to take it away from a number less than itself is ridiculous. Yet this is attempted...
Page x - You may put a mark before one, which it will obey; it submits to be taken away from another number greater than itself, but to attempt to take it away from a number less than itself is ridiculous. Yet this is attempted by algebraists, who talk of a number less than nothing, of multiplying a negative number into a negative number, and thus producing a positive number, of a number being imaginary.
Page 99 - Add the quotient, last found, to the number belonging to that error, when its supposed number is too little, but subtract it when too great, and the result will give the true root nearly. 4. Take this root and the nearest of the two former, or any other that may be found nearer; and, by proceeding in like manner as above, a root will be had still nearer than before.
Page x - ... to book debts and other arts. Now when a person cannot explain the principles of a science, without reference to a metaphor, the probability is, that he has never thought accurately upon the subject. A number may be greater or less than another number : it may be added to, taken from, multiplied...
Page x - Now when a person cannot explain the principles of a science, without reference to a metaphor, the probability is, that he has never thought accurately upon the subject. A number may be greater or less than another number : it may be added to, taken from, multiplied into...
Page xi - ... positive number, of a number being imaginary. Hence they talk of two roots to every equation of the second order, and the learner is to try which will succeed in a given equation : they talk of solving an equation which requires two impossible roots to make it soluble : they can find out some impossible numbers, which being multiplied together produce unity. This is all jargon, at which common sense recoils; but from its having been once adopted, like many other figments, it finds the most strenuous...
Page 209 - TF a ftraight line be divided into any two parts, the ,*" fquare of the whole line is equal to the fquares of the two parts, together with twice the rectangle contained by the parts. Let the ftraight line AB be divided into any two parts in C; the fquare of AB is equal to the fquares of AC, CB and to twice the rectangle contained by AC, CB. Book II. Upon AB ikforibe a the fquare ADEB, and join BD, and thro...
Page 98 - ... of the unknown quantity, marking the errors which arise from each of them. 2. Multiply the difference of the two numbers, found by trial, by the least error, and divide the product by the difference of the errors, when they are alike, and by their sum when they are unlike.
Page 516 - A Remark on an Error in the Reasoning of the late learned French Mathematician, Monsieur Clairaut, in that Part of his Elements of Algebra in which he endeavours to prove the Rules of Multiplication laid down by Writers on Algebra concerning Negative Quantities.
Page 466 - ... to be performed : and, as to the negative roots of an equation, they are in truth the real and pofitive roots of another equation confiding of the fame terms as the firft equation, but with different figns + and — prefixed to fome of them ; fo that, when writers of Algebra...