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Ra·ti·o n.

1. Math. The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by *a* to *b* by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a.

Note: ☞ Some writers consider __ratio__ as the quotient itself, making ratio equivalent to a number.

The term __ratio__ is also sometimes applied to the __difference__ of two quantities as well as to their __quotient__, in which case the former is called __arithmetical ratio__, the latter, __geometrical ratio__. The name __ratio__ is sometimes given to the __rule of three__ in arithmetic. See under Rule.

2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress.

**Compound ratio**, **Duplicate ratio**, **Inverse ratio**, etc. See under Compound, Duplicate, etc.

**Ratio of a geometrical progression**, the constant quantity by which each term is multiplied to produce the succeeding one.

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In·verse a.

1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct.

2. Bot. Inverted; having a position or mode of attachment the reverse of that which is usual.

3. Math. Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with ⁻¹ as an index. Thus *sin*⁻¹ *x* means the arc or angle whose sine is *x*.

**Inverse figures** Geom., two figures, such that each point of either figure is inverse to a corresponding point in the order figure.

**Inverse points** Geom., two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius.

**Inverse ratio**, *or* **Reciprocal ratio** Math., the ratio of the reciprocals of two quantities.

**Inverse proportion**, *or* **Reciprocal proportion**, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : ⅓ : ⅙, or 4 : 2 : : 3 : 6, __inversely__.