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algebraic arithmetical arithmetical series arrangements assigned constant B's chance binomial binomial theorem called cent coefficients cologarithm column common logarithms Complete the square complex number contains continued fraction cube root cubic decimal denominator denote determinant digits Divide divisible divisor equal numbers event Exercise exponent expression Extract the root Find the number function geometrical progression geometrical series given equation given number Hence infinite series infinitesimal left member less letters limit logarithm mantissa monomial Multiply negative number number of terms obtained orthotomic number periodic continued fraction polynomial positive integer positive number positive roots quadratic equation quantic quotient ratio real roots remainder represent Resolve into factors scalar number selected series is convergent solution square root Sturm's Theorem subtracted surd symmetrical Theorem third unknown numbers variable white ball written zero
Page 184 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, . ,. ... ' , ' ad be by dividing by bd, bd=bd
Page 257 - This is the same as the number of permutations of n things taken r at a time, and hence r!C(»,r) = P(«,r) '-- It is interesting to know that the number of combinations of n things taken r at a time is the same as the number of combinations of n things taken n — r at a time.
Page 79 - A person engaged to work a days on these conditions : for each day he worked he was to receive b cents, and for each day he was idle he was to forfeit c cents. At the end of a days he received d cents. How many days was he idle ? 76.
Page 90 - In the first term the exponent of a is the same as the exponent of the power to which the binomial is raised, and it decreases by one in each succeeding term.
Page 140 - A number consists of two digits whose sum is 13, and if 4 is subtracted from double the number, the order of the digits is reversed. Find the number. 58. The sum of the digits of a certain number of two figures is 5, and if 3 times the units, digit is added to the number, the order of the digits will be -reversed.
Page 182 - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 519 - The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Page 186 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 33 - Then divide the first term of the remainder by the first term of the divisor...