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Page 291 - In any proportion, the product of the means is equal to the product of the extremes.
Page 90 - 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 96 - Any term may be transposed from one member of an equation to the other, provided its sign be changed.
Page 293 - 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 289 - 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 46 - The same number, or equal numbers, may be added to both members of an equation without destroying the equality. 2.
Page 95 - Both members of an equation may be multiplied by the same number without destroying the equality.
Page 292 - 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 86 - 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 293 - 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.