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Page 293 - In any proportion, the product of the means is equal to the product of the extremes.
Page 92 - 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 98 - Any term may be transposed from one member of an equation to the other, provided its sign be changed.
Page 295 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 291 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 48 - The same number, or equal numbers, may be added to both members of an equation without destroying the equality. 2.
Page 97 - Both members of an equation may be multiplied by the same number without destroying the equality.
Page 294 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third.
Page 88 - That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. For example, — = a*~".
Page 295 - 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.