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12 rods abscissa added algebraic antecedent applied arithmetical arithmetical progression become binomial Binomial Theorem breadth calculation called co-efficients common difference Completing the square compound quantity consequent contains cube root cubic equation curve diminished Divide the number dividend division divisor dollars equa Euclid evident Expand exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multi multiplicand multiplied or divided negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principles Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tities Transposing twice unit unknown quantity varies whole number
Page 59 - FRACTIONS, MULTIPLY THE NUMERATORS TOGETHER, FOR A NEW NUMERATOR, AND THE DENOMINATORS TOGETHER, FOR A NEW DENOMINATOR.
Page 188 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 231 - 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 290 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Page 134 - Two travellers A and B set out to meet each other, A leaving the town C, at the same time that B left D.
Page 216 - If the first term of an increasing arithmetical series is 3, the common difference 2, and the number of terms 20 ; what is the sum of the series 1 Ans.
Page 185 - When there ka series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c. are all equal ; the quantities are said to be in continued proportion.
Page 42 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the 'dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factor a and bd .will produce the dividend. The first of these, being a divisor, maybe set aside.
Page 224 - There are three numbers in geometrical progression, the greatest of which exceeds the least by 15; and the difference of the squares of the greatest and the least,. is to the sum of the squares of all the three numbers as 5 to 7. What are the numbers 1 Ans.