of the two axes.

6. The rectangles of the parts of two parallel lines, terminated by the curve, are to one another, as the rectangles of the parts of any other two parallel lines, any where cutting the former. Or the rectangles of the parts of two intersecting lines, are as the squares of their parallel diameters, or squares of their parallel tangents.

7. All the parallelograms are equal which are formed between the asymptotes and curve, by lines parallel to the asymptotes.

For other properties, see the article CoNICS; and for the measure of hyperbolas, their arcs, &c. consult Hutton's Mensu

HYPERBOLE, in rhetoric, a figure, whereby the truth and reality of things are excessively either enlarged or diminished. Lord Kaims observes, that an object uncommon with respect to size, either very great of its kind or very little, strikes us with surprise; and this emotion forces upon the mind a momentary conviction, that the object is greater or less than it is in reality: the same effect precisely attends figurative grandeur or littleness; and hence the hyperbole, which expresses this momentary conviction. A writer, taking adVantage of this natural delusion, enriches his description greatly by the hyperbole; and the reader, even in his coolest moments, relishes this figure, being sensible that it is the operation of nature upon a warm fancy.

It cannot have escaped observation, that a writer is generally more successful in magnifying by a hyperbole than in diminishing. The reason is, that a minute object contracts the mind, and fetters its powers of imagination; but that the mind, dilated and inflamed with a grand object, moulds objects for its gratification with great facility. Longinus, with respect to a diminishing hyperbole, cites the following ludicrous thought from a comic poet: "He was owner of a bit of ground not larger than a Lacedemonian epistle." But, for the reason now given, the hyperbole has by far the greater force in magnifying objects; of which take the following examples:

For all the land which thou seest, to thee will I give it, and to thy seed for ever. And I will make thy seed as the dust of the earth:

so that if a man can number the dust of the earth, then shall thy seed also be numbered." Gen. xiii. 15, 16.

Illa vel intactæ segetis per summa volaret Gramina: nec teneras cursu læsisset aristas. Æneid. vii. 808. atque imo barathri ter gurgite

wastos

:

Eneid. iii. 571.

Hyperboles, says Seneca, lie without deceiving; they lead the mind to truth by ficthough by expressing it in terms which rentions they convey the sentiment intended, der it incredible. The hyperbole premises too much, in order to make you conceive enough. There is nothing faulty in an hy perbole, when it is ultrà fidem, as Quintilian says, provided that it be not ultrà modum,

Aristotle observes, that hyperboles are the favourite figures of young authors, who love excess and exaggeration; but that phi

losophers should not use them without a great deal of reserve.

The pitch to which an hyperbole may be carried, is a point of great delicacy; to carry it too far, is to destroy it: it is of the nature of a bow-string, which by immoderate tension, slackens; and frequently has an effect quite contrary to that intended.

Those hyperboles are best, which are latent, and are not taken for hyperboles. For this reason, they should scarce ever be used but in a passion, and in the middle of some important incident: such is the hyperbole of Herodotus, speaking of the Lacedæmonians, who fought at Thermopyla: "They defended themselves, for some time, with the arms that were left them, and at last with their hands and teeth: till the Barbarians, continually shooting, buried them, as it were, with their arrows." Now what likelihood is there, that naked men should defend themselves with their hands and teeth against armed men; and that so many persons should be buried under their enemies' arrows? Yet does there appear some probability in the thing, by reason it is not sought for the sake of the figure; but the hyperbole seems to arise out of the subject itself.

HYPERBO'LIC CONOID, a solid formed by the revolution of an hyperbola about its axis: it is otherwise called an hyperboloid.

HYPERBOLIC CYLINDROID, a solid formed by the revolution of an hyperbola about its conjugate axis, or line through the centre perpendicular to the transverse axis.

HYPERBOLIC LOGARITHM, a logarithm so called, as being similar to the asymptotic spaces of the hyperbola. The hyperbolic logarithm of a number, is to the common logarithm, as 2-3025850929940457 to 1, or as 1 to 4342944819032518. The first invented logarithms, by Napier, are of the hyperbolic kind; and so are Kepler's. See

LOGARITHM.

HYPERBOLICAL. a. (from hyperbola.)

HYPERBO'LIC.

1. Belonging to the hyperbola; having the nature of a hyperbola (Grew). 2. (from hyperbole.) Exaggerating or extenuating beyond fact (Boyle).

HYPERBOLICALLY. ad. 1. In form of a hyperbola. 2. With exaggeration or extenuation (Brown).

HYPERBOLIFORM. a. (hyperbola and forma, Latin.) Having the form, or nearly the form of the hyperbola.

HYPERBOREAN. a. (hyperboreus, Lat.)

HYPERICUM, (Hypericum, i. n. úæepuxov; from, over, and xv, an image or spectre; so named because it was thought to have power over and to drive away evil spirits.) St. John's wort.

In botany, a genus of the class polyadelphia, order polyandria. Calyx five-parted, inferior; petals five; filaments numerous, in three or five sets, united at the base; capsula many seeded. Eighty-seven species scattered over the globe, of which nine or ten are common to our country. The whole may be partitioned into those,

A with five styles.

B three styles; calyx very entire. C three styles; calyx and bractes with glandular serratures.

D

two styles.

H. perfoliatum, with three styles, stem somewhat two-edged, leaves ovate and clasping the stem, and cymed, sessile flowers, a native of our own country, was, on account of its supposed medicinal virtues, greatly esteemed by the ancients, but is now very rarely used. The late London Pharmacopoeia retain the flowers on account of the great proportion of resinous oily matter, in which the medical efficacy of the plant is supposed to reside.

One of the most beautiful species is H. hircinum, fetid St. John's wort, a native of Sicily, with lanceolate acute leaves, for which see Nat. Hist. Pl. CXXIX.

HYPERIDES, an orator of Greece, was the disciple of Plato and Isocrates, and go verned the republic of Athens. He defended with great zeal and courage the liberties of Greece; but was put to death by Antipater's order, 322 B. C. He composed many ora tions, of which only one now remains. He was one of the ten celebrated Greek ora. tors.

HYPERMETER. 8. (ύπερ and μέτρο.) Any thing greater than the standard requires (Add.).

HYPERMNESTRA, in fabulous history, one of the fifty daughters of Danaus, king of Argos. She alone refused to obey the cruel order Danaus had given to all his daughters, to murder their husbands the first night of their marriage; and therefore saved the life of Lyncens, after she had made him promise not to violate her virginity. Danaus, enraged at her disobedience, confined her closely in prison, whence Lynceus delivered her some time after.

HYPERO'STOSIS. (Hyperostosis, is, f. neproTwais; from itp, upon, and coreo, a bone.) See ExoSTOSIS.

HYPEROXYMURIATIC ACID. MURIATIC ACID.

See

HYPEROXYMURIATS. See MURIATS. HYPERSARCO'SIS. 8. (¿ñepoapwors.) The growth of fungous or proud flesh (W ́isem.).

HYPHEN, 're, in grammar, an accent or character, which implies, that two words are to be joined, or connected into one com pound word. As, mal-administration, &c.