Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies, Part 1 |
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Page 3
... principles , and leading the pupil , by gradual and easy steps , to a knowledge of the ele- ments of the science . The ... principle analyzed , in order that the mind of the pupil may be disciplined and strengthened so as to prepare him ...
... principles , and leading the pupil , by gradual and easy steps , to a knowledge of the ele- ments of the science . The ... principle analyzed , in order that the mind of the pupil may be disciplined and strengthened so as to prepare him ...
Page 4
... principles on which the rules are founded , and of the results which they produce . .Throughout the work , the aim has been , to combine the clear , explanatory methods of the French mathematicians , with the prac- tical exercises of ...
... principles on which the rules are founded , and of the results which they produce . .Throughout the work , the aim has been , to combine the clear , explanatory methods of the French mathematicians , with the prac- tical exercises of ...
Page 5
... Principles Definitions of Terms , and Explanation of Signs Examples to illustrate the use of the Signs Addition Subtraction · Observations on Addition and Subtraction Multiplication - Rule of the Coefficients Rule of the Exponents 1-15 ...
... Principles Definitions of Terms , and Explanation of Signs Examples to illustrate the use of the Signs Addition Subtraction · Observations on Addition and Subtraction Multiplication - Rule of the Coefficients Rule of the Exponents 1-15 ...
Page 7
... principle ; but that it is more convenient to represent the quantity we wish to find , by a single letter , than by one or more words . In the same manner , let the learner continue to use the letter x to represent the smallest of the ...
... principle ; but that it is more convenient to represent the quantity we wish to find , by a single letter , than by one or more words . In the same manner , let the learner continue to use the letter x to represent the smallest of the ...
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... may be applied to the solution of problems . We shall now proceed to consider the subject in a regular and scientific manner . ELEMENTS OF ALGEBRA . CHAPTER I. PRELIMINARY DEFINITIONS AND PRINCIPLES 24 RAY'S ALGEBRA , PART FIRST .
... may be applied to the solution of problems . We shall now proceed to consider the subject in a regular and scientific manner . ELEMENTS OF ALGEBRA . CHAPTER I. PRELIMINARY DEFINITIONS AND PRINCIPLES 24 RAY'S ALGEBRA , PART FIRST .
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Common terms and phrases
acre added algebraic quantities apples arithmetical progression arithmetical series binomial Binomial Theorem bought bushels coefficient common difference complete equation Completing the square cost Divide the number dividend division dollars entire quantity equal EQUATIONS CONTAINING exactly divide exponent expressed extract the square Find a number Find the cube Find the product Find the square Find the sum find the value following examples fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges perfect square polynomial positive quantity preceding principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result second degree second power solution solving square root three numbers tities Transposing twice unknown quantity whole number yards
Popular passages
Page 60 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 178 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 124 - 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 ? Let x be the number of leaps taken by the hound.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 64 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.