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Page 189 - That is, in any proportion either extreme is equal to the product of the means divided by the other extreme; and either mean is equal to the product of the extremes divided by the other mean.
Page 72 - ... in geometrical proportion, the product of the two extremes is equal to the product of the two means :" a principle which is at the foundation of the Rule of Three in arithmetic.
Page 217 - Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 156 - The equality of the two sides is not affected by this alteration, because we only change one quantity x for another •which is equal to it. By this means we obtain an equation which contains only one unknown quantity.
Page 233 - 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.
Page 33 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Page 124 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 83 - Four places are situated in the order of the letters A, B, C, D. The distance from A to D is 34 miles. The distance from A to B is to the distance from C to D as 2 to 3. And ^ of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances'!
Page 325 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Page 20 - If the same quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered. 6. If a quantity be both multiplied and divided by another, the value of the former...

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