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added algebra altitude arithmetic means arithmetic progression Axiom base binomial called Centigrade Check circle coefficient common factor common multiple contains cross products cube root cubic foot cubic inches decimal denominator density difference digits distance divided dividend division divisor equal EXERCISES Find exponent factor x Fahrenheit feet per second Find the dimensions Find the numbers following indicated formula fraction fulcrum gain graph harmonic means Hence hypotenuse Illustrative Problem integers length less letters logarithm longitude means miles per hour million minuend minus monomial multiplied negative numbers number expressions obtained Perform the following polynomial population positive pounds Principle quadratic equation quotient radicand radius rectangle rectangular reduced remainder represent result rods satisfy side signed numbers solution Solve the equation Solve the following square inches square root substituting subtract temperature three numbers triangle trinomial twice unknown weight width zero
Page 88 - 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 206 - If squares are constructed on the two sides, and also on the hypotenuse of a right-angled triangle, then the sum of the squares on the sides is equal to the square on the hypotenuse. This is proved in geometry, but may be verified by counting squares in the accompanying figure. This proposition was first discovered by the great philosopher and mathematician Pythagoras, who lived about 550 BC Hence it is called the Pythagorean proposition.
Page 280 - 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 279 - In any proportion, the product of the means equals the product of the extremes.
Page 358 - If x = ч does not reduce D to zero, then R is not zero, and the division is not exact. That is, x — a is not a factor of D. Hence : If a polynomial in x reduces to zero when a particular number a is substituted for x, then x — a is a factor of the polynomial, and if the substitution of a for x does not reduce the polynomial to zero, then x — a is not a factor.
Page 303 - Axioms (1) If equal numbers are added to equal numbers, the sums are equal.
Page 294 - В can do a piece of work in 12 days, В and С in 20 days, A and С in 15 days.
Page 474 - The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.
Page 473 - Whence x — y is the logarithm m of — . QED n 180. Prop. 3. — The logarithm of a power of a number is the logarithm of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m.