in general, something that is mutual, or which is returned equally on both sides, or that affects both parties alike.

RECIPROCAL Terms, among logicians, are those which have the same signification; and consequently are convertible, or may be used for each other.

in mathematics, is applied to quantities. Reciprocal ties which multiplied together produce unity. Thus \( \frac{1}{x} \) and \( \frac{1}{y} \), \( x \) and \( y \), are reciprocal quantities. Likewise \( \frac{1}{x} \) is said to be the reciprocal of \( x \), which is again the reciprocal of \( \frac{1}{x} \).

**Reciprocal Figures**, in geometry, those which have the antecedents and consequents of the same ratio in both figures.

**Reciprocal Proportion**, is when in four numbers the fourth is less than the second by so much as the third is greater than the first, and vice versa. See **Proportion** and **Arithmetic**, chap. vi. Great use is made of this reciprocal proportion by Sir Isaac Newton and others, in demonstrating the laws of motion.

**Recital**, in law, means the rehearsal or making mention in a deed or writing of something which has been done before.

**Recitativo**, or **Recitative**, in music, a kind of singing, that differs but little from ordinary pronunciation; such as that in which the several parts of the liturgy are rehearsed in cathedrals; or that wherein the actors commonly deliver themselves on the theatre at the opera, when they are to express some action or passion; to relate some event; or reveal some design.

**Reckenhauen**, a strong town of Cologne, in Germany, in the middle territory of that name. The abbeys of its nunnery has power of punishing offenders with death, and she alone is obliged to the vow of chastity.

**Reckoning**, or **Ship's Reckoning**, in navigation, is that account whereby at any time it may be known where the ship is, and on what course or courses she is to steer, in order to gain her port; and that account taken from the log-board is called the **dead reckoning**. See **Navigation**.

**Reclaiming**, or **Reclaiming**, in our ancient customs, a lord's purifying, prosecuting, and recalling, his vassal, who had gone to live in another place without his permission.