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 8
... called the sign of addition . Also , instead of writing the word equal , we use the sign = , which means the same , and is called the sign of equality . 10. John , James , and Thomas , are each to have equal shares of 12 apples ; if x ...
... called the sign of addition . Also , instead of writing the word equal , we use the sign = , which means the same , and is called the sign of equality . 10. John , James , and Thomas , are each to have equal shares of 12 apples ; if x ...
Page 25
... called magnitude , when presented or con- sidered in an undivided form , such as a quantity of water . ART . 4. Quantity is called multitude , when it is made up of indi- vidual and distinct parts , such as three cents , which is a ...
... called magnitude , when presented or con- sidered in an undivided form , such as a quantity of water . ART . 4. Quantity is called multitude , when it is made up of indi- vidual and distinct parts , such as three cents , which is a ...
Page 26
... called symbols . DEFINITION OF TERMS , AND EXPLANATION OF SIGNS . ART . 16. Known quantities are those whose numerical values are given , or supposed to be known : unknown quantities are those whose numerical values are not known . ART ...
... called symbols . DEFINITION OF TERMS , AND EXPLANATION OF SIGNS . ART . 16. Known quantities are those whose numerical values are given , or supposed to be known : unknown quantities are those whose numerical values are not known . ART ...
Page 27
... called the signs ; the former is called the positive , and the latter the negative sign ; they are said to be contrary or opposite . ART . 23. Every quantity is supposed to be preceded by one or the other of these signs . Quantities ...
... called the signs ; the former is called the positive , and the latter the negative sign ; they are said to be contrary or opposite . ART . 23. Every quantity is supposed to be preceded by one or the other of these signs . Quantities ...
Page 28
... called factors . The continued product of several factors , means that the product of the first and second is to be multiplied by the third , this product by the fourth , and so on . Thus , the continued product of a , b , and c , is ...
... called factors . The continued product of several factors , means that the product of the first and second is to be multiplied by the third , this product by the fourth , and so on . Thus , the continued product of a , b , and c , is ...
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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.