DEMONSTRATION. s. (demonstratio, Lat.) 1. The highest degree of deducible or argumental evidence (Hooker). 2. Indubitable evidence of the senses or reason.

DEMONSTRATION, in logic, a syllogism in form containing a clear and irrefragable proof of the truth of a proposition.

A demonstration is a convincing argument, the two first propositions whereof are certain, clear and evident; whence of necessity arises an infallible conclusion.

The method of demonstrating things in mathematics is the same with that of drawing conclusions from principles in logic. In effect, the demonstrations of mathematicians are no other than series of enthymemes; every thing is concluded by force of syllogism, only omitting the premises, which either occur of their own accord, or are recollected by means of quotations. To have the demonstration perfect, the premises of the syllogisms should be proved by new syllogisms, till at length you arrive at a syllogism, wherein the premises are either definitions, or identic propositions.

Indeed it might be demonstrated, that there cannot be a genuine demonstration, i. e. such a one as shall give full conviction, unless the thoughts be directed therein according to the rules of syllogism. Clavius, it is well known, resolved the demonstration of the first proposition of Euclid into syllogism; Herlinus and Dasipodius, demonstrated the whole six first books of Euclid, and Henischus, all arithmetic, in the syllogistic form.

Yet many persons, and even mathematicians, usually imagine, that mathematical demonstrations are conducted in a manner far remote from the laws of syllogism; so far are they from allow ing that those derive all their force and conviction from these. But we have men of the first rank on our side the question. M. Leibnitz, for instance, declares that demonstration to be firm and valid which is in the form prescribed by logic; and Dr. Wallis confesses, that what is proposed to be proved in mathematics is deduced by means of one or more syllogisms: the great Huygens, too, observes, that para logisms frequently happen in mathematics, through want of observing the syllogistic form. See SYLLOGISM.

Problems consist of three parts: a proposition, resolution, and demonstration.

In the proposition is indicated the thing to

be done.

In the resolution, the several steps are orderly rehearsed, whereby the thing proposed is performed.

Lastly, in the demonstration it is shewed, that the things enjoined by the resolution being done, that which was required in the proposition is effected. As often, therefore, as a problem is to be demonstrated, it is converted into a theorem; the resolution being the hypothesis, and the proposition the thesis: for the general tenor of all problems to be demonstrated is this; that the thing prescribed in the resoJution being performed, the thing required is

done.

The schoolmen make two kinds of demonstration: the one dion, or propter quod; wherein an effect is proved by the next cause. As when it is proved, that the moon is eclipsed, because the earth is then between the sun and moon. The second T OTI, or quia; wherein the cause is proved from a remote effect: as when it is proved, that fire is hot, because it burns; or that plants do not breathe, because they are not animals; or that there is a God from the works of creation. The former is called demonstration à priori, and the latter demonstration à posteriori.

DEMONSTRATION (Affirmative), is that which, proceeding by affirmative and evident propositions, dependent on each other, ends in the thing to be demonstrated.

DEMONSTRATION (Apagogical). See APA

GOGICAL.

DEMONSTRATION (Geometrical), is that framed of reasonings drawn from the element of geometry.

DEMONSTRATION (Mechanical), is that, the reasonings whereof are drawn from the rules of mechanics.

DEMONSTRATION A PRIORI, is that whereby an effect is proved from a cause, either a next, or remote one; or a conclusion proved by something previous, whether it be a cause, or only an antecedent.

DEMONSTRATION A POSTERIORI, is that whereby either a cause is proved from an effect, or a conclusion is proved by something pos terior; whether it be au effect, or only a cunsequent.

DEMONSTRATIVE. u. (demonstrativus, Latin.) 1. Having the power of demonstration; invincibly conclusive; certain (Hooker). 2. Having the power of expressing clearly (Dryden). 3. That which shows as demonstrative pronouns.

DEMONSTRATIVELY. ad. 1. With evidence not to be opposed or doubted (South). 2. Clearly; plainly; with certain knowledge (Brown).

DEMONSTRATOR. s. (from demontrate.) One that proves; one that teaches. DEMONSTRATORY. a. (from demonstrate.) Having the tendency to demonstrate.

DEMOSTHENES, the celebrated orator of Athens, was son of a rich blacksmith, called Demosthenes, and of Cleobule. He was but seven years of age when his father died, and his guardians having embezzled the greatest part of his possessions, his education was totally neglected; and for whatever advances he made in learning, he was indebted to his own industry and application. He became the pupil of Isæus and Plato, and applied himself to study the orations of Isocrates. At the age of 17, he gave an early proof of his eloquence and abili ties against his guardians, from whom he obtained the retribution of the greatest part of his estate. His rising talents were, however, impeded by weak lungs, and a difficulty of pronunciation, especially of the letter g, but thesa obstacles were soon conquered by unwearied application. To correct the stammering of his

voice, he spoke with pebbles in his mouth; and removed the distortion of his features, which accompanied his utterance, by watching the motions of his countenance in a looking-glass. That his pronunciation might be loud, and full of emphasis, he frequently ran up the steepest and most uneven walks, where his voice acquired force and energy; and on the sea-shore, when the waves were uncommonly agitated, he declaimed aloud, to accustom himself to the noise and tumults of a public assembly. He also confined himself in a subterraneous cave, to devote himself more closely to studious pursuits; and to eradicate all curiosity of appearing in public, he shaved one half of his head. His abilities, as an orator, raised him to consequence at Athens, and he was soon placed at the head of government. In this public capacity he roused his countrymen from their indolence, and animated them against the encroachment of Philip of Macedonia. In the battle of Cheronæa, however, Demosthenes betrayed his pusillanimity, and saved his life by flight. After the death of Philip, he declared himself warmly against his son and successor, Alexander. Though he had boasted that all the gold of Macedonia could not tempt him, yet he suffered himself to be bribed by a small golden cup from Harpalus. This forced him to retire to Egina, whence, when Antipater made war against Greece, he was recalled and received with much splendor at Athens. His triumph and popularity were but of short duration. Antipater and Craterus were near Athens, and demanded all the orators to be given up. Demosthenes, with all his adherents, fled to the temple of Neptune in Caluria; and when he saw that all hopes of safety were vanished, he took a dose of poison, which he always carried in a quill, and expired in the 60th year of his age. B.C. 322.

Demosthenes has been deservedly called the prince of orators. Indeed no orator had ever a finer field than Demosthenes in his Olynthiacs and Philippics, which are his capital orations; and undoubtedly to the greatness of the subject, and to that integrity and public spirit which breathe in them, they owe a large portion of their merit. Cicero calls him a perfect model, and such as he himself wished to be. These two great orators have been often compared together; but the judgment hesitates to which to give the preference. The archbishop of Cambray, however, seems to have stated their merits with great justice and perspicuity in his Reflections on Rhetoric and Poetry. The passage, translated, is as follows: "I do not hesitate to declare that I think Demosthenes superior to Cicero. I am persuaded no one can admire Cicero more than I do. He adorns whatever he attempts. He does honour to language. He disposes of words in a manner peculiar to himself. His style has great variety of character. Whenever he pleases, he is even concise and vehement: for instance, against Catiline, against Verres, against Antony. But ornament is too visible in his writings. His art is wonderful, but it is perceived. When

the orator is providing for the safety of the republic, he forgets not himself, nor permits others to forget him. Demosthenes seems to escape from himself, and to see nothing but his country. He seeks not elegance of expression; unsought for he possesses it. He is superior to admiration. He makes use of language, as a modest man does of dress, only to cover him. He thunders, he lightens. He is a torrent which carries every thing before it. We cannot criticise, because we are not ourselves. His subject enchains our attention, and makes us forget his language. We lose him from our sight: Philip alone occupies our minds. I am delighted with both these orators; but I confess that I am less affected by the infinite art and magnificent eloquence of Cicero, than by the rapid simplicity of Demosthenes." La Harpe, also, has some fine remarks on the dif ferent kinds of eloquence of Cicero and Demosthenes, and their comparative fitness for the audiences they had respectively to address: but they are too long to be transcribed into this place.

Demosthenes is said to have composed 65 orations, of which only a few have reached our times. Among the best editions of these, are that of Frankfort, 1604, folio, with Wolfius's Latin version; of Reiske, 12 vols. 8vo. Leips. 1770; of Auger, 4to. Paris, 1790. Of the select orations the best edition is by Mountenoy. Cant. 1731. Lond. Oct. 1785. The curious in bibliography are very eager to obtain the genuine editio princeps of Demosthenes, which is by Aldus, Venet. fol. 1504.

DEMULCENT. a. (demulcens, Latin.) Softening; mollifying; assuasive (Arbuthnot). DEMULCENTS. (demulcentia, medicamenta; from demulceo, to soften.) Medicines are thus called, which possess a power of di minishing the effects of stimuli on the sensible solids of the body. There are two orders of demulcents. 1. Lenient demulcents, as starch, gum arabic, and olive oil: these are best adapted to irritable constitutions, and persons with a remarkable disposition to have their secretions morbidly augmented. 2. Diluent demulcents, as water and watery substances: these are calculated for such as have a diminution of the secretions, and whose habits are naturally torpid.

To DEMUR. v. n. (demeurer, French.) 1. To delay a process in law by doubts and objec. tions (Walton). 2. To pause in uncertainty; to suspend determination (Hayward). 3. To doubt; to have scruples (Bentley).

To Demu'r. v. à. To doubt of (Milton).

DEMUR. S. (from the verb.) Doubt; hesitation; suspense of opinion (South).

DEMU'RE. a. (des mœurs, French.) 1. Sober; decent (Spenser). 2. Grave; affectedly modest (Swift).

1.

To DEMU'RE. v. n. (from the noun.) To look with an affected modesty (Shakspeare). DEMU'RELY. ad. (from demure.) With affected modesty; solemuly (Bacou). 2. Solemnly (Shakspeare).

DEMURENESS. s. (from demure.) 1.

Modesty, soberness; gravity of aspect. 2. Affected modesty; pretended gravity. DEMURRAGE. s. (from demur.) An allowance made to masters of ships, for their stay in a port beyond the time appointed.

DEMURRER, in law, a stop put to any action upon some point of difficulty which must be determined by the court, before any further proceedings can be had in the suit.

DEMURRER TO EVIDENCE, is where a question of law arises thereon; as if the plaintiff in a suit gives in evidence any records, deeds, writings, &c. upon which a law-question arises, and the defendant offers to demur upon it, then the plaintiff must join in such demurrer, or wave his evidence.

DEMURRER TO INDICTMENTS, is when a criminal joins issue upon a point of law in an indictment or appeal, allowing the fact as laid

to be true.

DEN. s. (den, Saxon.) 1. A cavern or hollow running with a small obliquity under ground (Hooker). 2. The cave of a wild beast (Dryden). 3. Den, in a local name, may signify either a valley or a woody place (Gibson).

DENARIUS, in Roman antiquity, the chief silver coin among the Romans, worth in our money about sevenpence three farthings. As a weight, it was the seventh part of a Roman In our law-books an English penny is

onnce.

often called Denarius. DENA'Y. ». Denial; refusal (Shakspeare). DENBIGH, a town of North Wales, the capital of the county of the same name. lt stands on the side of a rocky hill, on a branch of the river Clwyd; and is called by the Welsh Cledvyrn yn Rhos, i. e. The craggy hill in Ross. Denbigh contains 552 houses, and 2391 inhabitants; it sends one member to the British parliament, and has a market on Wednesdays. Lnt. 53. 11 N. Lon. 3. 35 W.

DENBIGHSHIRE, a county of Wales, bounded on the south by Merioneth and Montgomery shires, on the north by Flintshire and the Irish sea, on the west by Caernarvon and part of Merionethshire. It is about 40 miles long and 21 broad. The air is wholesome, but sharp, the country being pretty hilly, and the snow lying long on the tops of the mountains. The soil in general is barren; but the vale of Clwyd, so called, from its being watered by that river, is a very fertile pleasant spot of great extent, and well inhabited. The county contains about 410,000 acres of land, 13,048 houses, and 60,352 inhabitants. They send one meniber to parliament, besides one for the county town.

DENDERA, the ancient Tentyris or Tentyra, a town or large village of Egypt, built near the ruins of the ancient city at a short distance from the west bank of the Nile, about 242 miles S. of Cairo. Some of the ruins uear this place are very magnificent. Lat. 26. 10 N. Lon. 31. 40 E.

DENDERMOND, a strong town of Flan ders, in the Austrian Netherlands. Lat. 51.3 N. Lon, 4. 10 E.

DENDRITES, ог ARBORIZATIOSS. This appellation is given to figures of vegetables which are frequently observed in fossil substances. They are of two kinds; the one su perficial, the other internal. The first are chiefly found on the surface of stones, and between the strata and in the fissures of those of a calcareous nature. Stones of a similar kind, when very compact, sometimes also exhibit internal arborizations; such are the marbles of Hesse, of Angersburg in Prussia, and of Baden-Dourlach on the left bank of the Rhine.

DENDROBIUM, in botany, a genus of the class gynandria, order monandria. Calyx (in some species reversed) three-leaved, oblong, somewhat spreading; the two lowermost leaves extending at the base, on their underside, and cohering so as to form a pouch, bearing some resemblance to a spur; petals two, oblong, lateral; nectary a lip of various shapes in dit ferent species, its base included in and often connected with the pouch of the calyx, deștitute of a spur; capsule oblong or ovate, with three or six angles or ribs, one cell and three valves, bursting between the rib-; seeds numerous, minute, each clothed with a chaffy tunic. Thirty-two species; natives of the East or West Indies; resembling the orchis tribe, and growing parasitically for the most part on the trunks or branches of old trees.

DENDROLOGY. s. (deydfov and sys.) The natural history of trees. DENDROMETER, (from devdgov, a tree, and μετρέω, I measure), an instrument for measuring trees. The same name has also been applied, though with no propriety, to instruments contrived to measure distances and magnitudes from a single station.

DENDROPHORIA, in antiquity, the carrying of one, or more, trees, in ceremony, through a city, at certain feasts, and in honou of certain deities. The persons who performed the office of carrying the trees were called dendrophori, i. e. tree-bearers.

DENEB, an Arabic term, signifying tall, used by astronomers as a name to some of the fixed stars: as Deneb Alesed, Lion's-tail; Deneb Kaitos, the Whale's-tail. See CAUDA.

DENEHIA, in botany, a genus of the class syngenesia, order polygamia superflua. Receptacle naked; downless; calyx imbriate; florets of the ray two lipped. One species only; a Cape plant, with striate, downy branched stem; leaves half clasping, oblong lanceolate, obtuse with a point undulate; downy under neath, entire; flowers terminal in a close pani

cle.

DENHAM (Sir John), an eminent English poet, the only son of sir John Denham, chief baron of the exchequer in Ireland, and one of the lords commissioners there, was born in Dublin in 1615; but his father, in 1617, being made a baron of the Exchequer in Eng.

land, he received his education in this country, In his youth he followed gaming more than any thing else; but, in 1641, published a tragedy called the Sophy, which was much ad

times spirited and harmonious, and his subjects dated and judicious; and at others, flat, harsh, and puerile.-As a dramatic author, he deserves not to be held in any consideration. It was justly said of him by a wit, that he was the most complete instructor for a dramatic roet, since he could teach him to distinguish good plays by his precepts, and bad ones by his examples.

DENOMINABLE. a. (denomino, Latin.) That may be named or denoted (Brown).

To DENOMINATE. v. a. (denomino, Latin.) To name; to give a name to (Hamrond)

DENOMINATION.

S. (denominatio, Latin.) A name given to a thing (Rogers). DENOMINATIVE. a. (from denominate.) 1. That gives a name; that confers a distinct appellation. 2. That obtains a distinct appellation (Cocker).

DENOMINATOR. s. (from denominate.) The giver of a name (Brown).

DENOMINATOR OF A FRACTION, is the number below the line, shewing the nature and quality of the parts which any integer is supposed to be divided into. Thus, in the fraction, the denominator is 8; and shews that the integer is divided into 8 parts, of which the fraction contains 7.

DENOMINATOR OF A RATIO, is sometimes used in the sense of the exponent of a ratio.

DENOTATION. s. (denotatio, Lat.) The act of denoting.

To DENOTE. v. a. (denoto, Latin.) To mark; to be a sigu of; to betoken; to show by signs.

To DENOUNCE. v. a. (denuncio, Latin.) 1. To threaten by proclamation (Milton). 2. To threaten by some outward sign or expres sion (Dryden). 3. To give information against (Ayliffe).

DENOUNCEMENT. s. (from denounce.) The act of proclaiming any menace (Brown). DENOUNCER. s. (from denounce.) One that declares some menace (Dryden).

DENS. (dens, quasi edens; from edo, to eat, or from odas, odorlog.) A tooth. Many herbs have this specific name, from their fancied resemblance to the tooth of some animal; as dens leonis, the dandelion; dens canis, dog's tooth, &c.

DENS LEONIS. See TARAXACUM. DENSE. a. (densus, Lat.) Close; compact; approaching to solidity (Locke).

DENSE PANICLE, in botany. Densa panicula. Having abundance of flowers very close. A greater degree of congesta, heaped.

DENSITY, (from the Latin densitas), strictly speaking, denotes vicinity or closeness of particles. But in mechanical science it is used as a term of comparison, expressing the proportion of the number of equal moleculæ, Ar the quantity of matter in one body, to the number of equal molecule in the same bulk of another body: density, therefore, is directly as the quantity of matter, and inversely as the magnitude of the body.

Since it may be shewn experimentally that the quantity of matter in different bodies is proportional to their weight, of consequence, the density of any body is directly as its weight, and inversely as its magnitude: or, the inverse ratio of the magnitudes of two bodies, having experimentally equal weights (in the same place) constitutes the ratio of their densities. DENSITY OF THE AIR. MOSPHERE, and PNEUMATICS. DENSITY OF THE PLANETS. See AsTRONOMY, § viii.

See AIR, AT

DENTAGRA. (dentagra.) The tooth-achi? also an instrument for drawing the teeth.

DENTAL. a. (dentalis, Latin.) 1. Belonging or relating to the teeth. 2. (In grammar.) Pronounced principally by the agency of the teeth (Holder).

DENTALIUM. Tooth-shell. In zoology, a genus of the class vermes, order testacea. Animal a terebella; sheil univalve, tubular, straight or slightly curved, with an undivided cavity open at both ends. Twenty-two species; mostly inhabiting the seas of Europe and India; two of them found on our own coasts; and about five or six known only from fossile specimens. The shell is commonly white or green; and either ribbed, striated, or dotted:

those on our own coast are:

1. D. Entalis, with a white shell, reddish or pale yellow, polished with striæ so very minute as scarcely to be visible without a glass.

2. D. imperforatum. Found at Sandwich. Minute; shell white; opake, transversely striate, imperforate. Still inferior in size, how

ever, is

3. D. minutum, with a round straitish smooth cell; inhabiting the Mediterranean but so diminutive as not to be discerned by the naked eve; and resembling a small bristle on one of the spines of the echines. See Nat. Hist. Pl. LXXVII.

DENTARIA. Tooth-wort. In botany, a genus of the class tetradynamia, order siliquosa; silique bursting elastically, with the valves revolute and shorter than the partition; stizma notched at the end; calyx leaves meeting longitudinally. Seven species; all European plants, and one, d. bullifera, found in the retired shady parts of our own fields, with its lower leaves pinnate, its upper simple. This plant is to be distinguished from the pellitory of Spain, which is also called dentaria. It is the plumbago europæa; foliis amplexicaulbus, lanceolatis scabris, of Linnéus. The root was formerly esteemed, prepared in a variety of ways, as a cure for the tooth-ache, arising from caries.

DENTATE LEAF. In botany. A toothed leaf. Quod acumina horizontalia, folii consis tentia, spatio remota habet. Having horizontal points of the same consistence with the leaf, with a space between each. Dr. Berkenhout observes, that if, instead of horizontal, Linnéus had written, in the plane of the disk, it would have been more intelligible. In Delin. Pl. it is; margine acuminibus patentibus remous; having spreading points (or teeth), remote