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Elementary Algebra: Embracing the First Principles of the Science
Πλήρης προβολή - 1856
ac ac added to twice algebraic expression algebraic quantities arithmetical arithmetical means arithmetical progression binomial Binomial Theorem called cents Charles coefficient common denominator common difference completing the square contain contrary sign cube denote the number dividend division divisor dollars example exponent extracting the square figure Find the factors Find the square Find the sum Find the values find three numbers following RULE fraction geometrical progression give a sum Give the rule Given Given Given given number greater Hence incomplete equation last term least common multiple Let the number letters logarithm minus mixed quantity monomial Multiply negative number added number of terms perfect square progression proportion question quotient ratio remainder second degree second term similar terms simplest form square root Substituting this value subtractive terms sum equal third transposing trinomial twice the number twice the product units expressed unknown quantity Verification whence yards
Σελίδα 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 231 - Quantities are said to be in proportion by alternation, or alternately, when antecedent is compared- with antecedent and consequent with consequent. Thus, if we have the proportion 3 : 6 : : 8 : 16, the alternate proportion would be 3 : 8 : : 6 : 16. QUEST. — 147. When are three quantities proportional ? What is the middle one called ? — 148. When are quantities said to be in proportion by inversion, or inversely?
Σελίδα 155 - Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Σελίδα 234 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Σελίδα 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 273 - A person has four casks, the second of which being filled from the first, leaves the first four-sevenths full. The third being filled from the second, leaves it one-fourth full, and when the third is emptied into the fourth, it is found to fill only nine-sixteenths of it. But the first will fill the third and' fourth, and leave 15 quarts remaining.
Σελίδα 79 - Ibs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and t.ail together : what was the weight of the fish ? Let 2x = the weight of the body, in pounds.