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4th power added antecedent arithmetical progression binomial Binomial Theorem breadth called co-efficient common denominator common difference common index completing the square compound quantities contains cube root Day's Algebra denoted Divide the number dividend division divisor dollars dols Eeduce equal factors equal quantities Euclid EXAMPLES FOR PRACTICE expressed Find the square find two numbers four quantities fraction gallons geometrical progression given quantity greater Hence improper fraction inches integer inverted involution last term Legendre Legendre's Geometry less letter merator Mult multiplicand negative quantity number of terms numbers 1 Prob parallelogram perpendicular positive preceding prefixed principles problem quadratic equation quan quantities are proportional Quest.—How Quest.—What quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder Required the cube right angled triangle schools and academies sides square root substituting subtracted subtrahend third Thomson's three numbers tion tities Transposing twice unknown quantity
Page 234 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 212 - 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 53 - 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 62 - RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator: then reduce the new fraction to its lowest terms.
Page 200 - When there is a 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 254 - It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84.
Page 194 - COMPOUND RATIO is THE RATIO OF THE PRODUCTS, OF THE CORRESPONDING TERMS OF TWO OR MORE SIMPLE RATIOS.* Thus the ratio of 6...
Page 47 - 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, may be set aside.