continent of Africa, appears to be their greatest hindrance to improvement. They make but little use of domestic animals for draught and agriculture. The women alone cultivate the land, carry the produce to market, range the forests to provide food and firing, and oftentimes, in their canoes, formed from the excavated trunks of the cotton-tree or bombax, skim the bosom of the most dangerous lakes to procure fish for their unnatural masters, while they supinely recline under the shade of the wide-spreading adansonia, the monarch of the forest wearing out the lazy hours stringing cowrie shells, or strumming on some musical instrument: or if they exert themselves at all, it is in dancing by moonlight, or indolently sauntering about their habitations. They are represented, however, as lively and good natured, hospitable, and at all times ready to share their miserable pittance with the stranger or passing sojourner. They are also said to be very honest; the rights of property are strictly observed, and the division is sometimes carried to so fine a point, that three, four, or six persons occasionally claim a right in a single fowl or pig. Every man in Congo has wives according to his degree or rank in society. The chenoo has as many as fifty, and some of the mafooks from ten to twenty. The females belonging to the highest dignitaries were offered to captain Tuckey's party on terms, and in language the most disgustingly obscene, for the most trifling consideration. The chenoo himself estimated the virtue of any of his wives or daughters, simply at the rate of a few beads or a glass of rum. The females, on their part, did not appear averse to these arrangements, but manifested much indignation when the offers of their husbands or fathers were despised or rejected by the Europeans. It is but justice to presume, however, that this disregard of modesty is unknown in those parts where the European slave merchant has not intruded; for, as captain Tuckey advanced farther up the river, he met with no recurrence of this offensive custom. Adultery amongst the natives is punished by the slavery of both the offenders;. and, if one of the parties be the wife of a chenoo, the paramour is liable to suffer death. An atrocious crime, singular from the simple form of their society, prevails amongst the Congoese; it is that of poisoning. Amongst a people so little enlightened, it is matter of no wonder that superstition should be so prevalent. The Portuguese missionary Carazzi, a Capuchin friar, stated the principal body of the natives to be good Catholics; but the English who have lately visited Congo, fourd but few or no vestiges of the benefits of that civilisation and conversion so much extolled by the Romish church.

At Loando, the natives exhibited their relics, rosaries or crosses and Agnus Deis, jumbled together with their domestic fetiches. The fetiche may, indeed, be said to form their only religion, and there is nothing so vile in nature or art, that is not regarded by the negroes as fit for this potent charm against evil. The horn-hoof, hair, teeth, or bones, of the most savage animal that prowls through the forest; the feathers, claws, beaks, skulls, and bones, of the meanest bird that flies in the air; the shells and fins of fishes; the

heads or skins of the filthiest snakes or reptiles that crawl on the earth; pieces of old copper, iron, wood, seeds of plants, are severally used to form a fetiche, and sometimes it consists of a mixture of them all. The priests are the usual artificers of these fetiches, and are said to derive considerable emolument from the sale of them. These charms are considered by the negroes as a protection against every danger flesh is heir to; and if it should so happen that the wearer perish, through the very means against which the fetiche had been adopted; it is not for want of protective potency in the charm, but for some offence, real or imaginary, of which the possessor has been guilty.

CONGRATULATE, v. a. & n.~
CONGRATULATION, n. s.
CONGRATULANT, adj.
CONGRATULATOR, n. s.
CONGRATULATORY, adj.

Fr. congratuler, Ital. con

gratulare; Span. con

gratular; Lat. congratulari. To express joy to another that he has experienced any thing which contributes to his welfare; to compliment on any fortunate event; to rejoice in conjunction with; to felicitate ones' self. It is the opposite of condole. Sometimes, says Johnson, it has the accusative case of the cause of joy, and to before the person. He might have added, that this usage is obsolete.

He sent Hadoram his son to king David, to congratulate him, because he had fought against Hadare

zer, and smitten him. 1 Chron. xviii. 10. Nothing more fortunately auspicious could happen to us, at our first entrance upon the government, than such a congratulator. Milton. Forth rushed in haste the great consulting peers, Raised from the dark divan, and with like joy Congratulant approached him.

Id. Paradise Lost.

I think the little I have enough, and do not desire to live higher, or die richer, than am ; and therefore you have reason rather to pity the folly, than congratulate the fortune, that engages me in the whirlpool. Locke. An ecclesiastical union within yourselves, I am rather ready to congratulate to you.

Spratt's Sermons. The subjects of England may congratulate to them. selves, that the nature of our government, and the clemency of our king, secure us.

Dryden's Preface to Aurengzebe.

I cannot but congratulate with my country, which hath outdone all Europe in advancing conversation. Swift.

I congratulate our English tongue, that it has been enriched with words from all our neighbours.

With all my follies of youth, and, I fear, a few vices of manhood, still I congratulate myself on having had, in early days, religion strongly impressed on Burns. my mind.

All the cities you have taken, all the armies which retreated before your leaders, are but paltry subjects of self-congratulation, if your land divides against itself, and your dragoons and executioners must be let loose against your fellow citizens.

Byron. Speech on the Frame-breaking Bill.
CONGRE'E. Fr. gre. To agree together;
to unite harmoniously. Not in use.
For government,

Put into parts, doth keep in one consent,
Congreeing in a full and natural close.

Shakspeare. Henry V. To CONGRE'ET, v. n. From con and greet. To salute reciprocally. Not in use.

My office hath so far prevailed,
That face to face, and royal eye to eye,
You have congreeted.

Shakspeare. Henry V.
French

CONGREGATE, v. a.,v.n.& adj. CONGREGATION, n. s. CONGREGATIONAL, adj.

congreger; Ital. congregare;

CONGREGATIONISTS, n. 8. Span. congregar; Lat. congregare, from con and grer, a flock. To collect into one spot; to assemble in numbers; to meet. Congregation signifies the act of collecting together; a collected mass of persons or things; an assemblage of persons who are met for the public worship of God. Congregate is collected; compact; closely pressed together. Congregational is public; general; and, more commonly, appertaining to an assembly of such Christians as hold every congregation to be a separate and independent church.

Take ye the sum of all the congregation of the children of Israel, after their families, by the house of their fathers, with the number of their names, every male by their polls. Numbers i. 2. Than by conseil of his wife Prudence, this Meli

beus let

The means of reduction by the fire, is but by congregation of homogeneal parts. Bacon. Where the matter is most congregate, the cold is the greater. Id. Natural History. The dry land, earth; and the great receptacle Of congregated waters, he called seas;

And saw that it was good. Milton's Paradise Lost. 'Tis true (as the old proverb doth relate) Equals with equals often congregate.

Denham.

The practice of those that prefer houses before churches, and a conventicle before the congregation. South.

Heat congregates homogeneal bodies, and separates Newton's Opticks. heterogeneal ones.

If those preachers who abound in epiphonemas would look about them, they would find part of their congregation out of countenance, and the other asleep. Swift.

Every parish has a congregational or parochial presbytery for the affairs of its own circle. Warton. My subject is only general congregational psalmody. Mason.

Ill fares the traveller now, and he that stalks
In ponderous boots beside his reeking team.
The wain goes heavily, impeded sore
By congregated loads adhering close

To the clogged wheels; and in its sluggish pace
Noiseless appears a moving hill of snow.

Compared with this, how poor religion's pride,

In all the pomp of method, and of art,
When men display to congregations wide
Devotion's every grace, except the heart.
Explore the caverns dark and drear
Mantled around with deadly dew,

Where congregated vapours blue,
Fired by the taper glimmering near,
Bid dire explosion the deep realms invade.

Cowper.

Burns.

Huddisford.

CONGREGATION, in the Romish church, is principally used for assemblies of cardinals, appointed by the pope, and distributed into chambers, for the discharge of certain functions and jurisdiction.

CONGREGATION is also used for a society of religious cantoned out of an order; and making a subdivision of it. Such are the congregations of the oratory of Cluny, &c. among the Benedictines.

CONGREGATIONALISTS, in ecclesiastical history, is a name sometimes given to those Protestants who reject all church government, except that of a single congregation, under the direction of one pastor, with deacons, assistants, or managers. It is equivalent to the modern term independents.

CONGRESBURY, an ancient town of Somersetshire, situated under the Mendip Hills, six miles from Axbridge, and 134 from London. It is said to derive its name from St. Conger, the son of an eastern emperor, who founded in It was forthis place a cell for twelve canons. merly a market town, but now ranks only as a village.

CO'NGRESS, n. s. CONGRESSION, n. s. CONGRESSIVE, adj.

A

Lat. congressus. coming together; shock; conflict; a meeting of diplomatists, to settle affairs between different nations; the legislature of the North American states. Congression is synonymous with congress, in the first of the foregoing senses. Congressive denotes coming together,

If it be understood of sexes conjoined, all plants are female; and if of disjoined and congressive generation, there is no male or female in them. Browne's Vulgar Errours. Here Pallas urges on, and Lausus there; Their congress in the field great Jove withstands, Both doomed to fall, but fall by greater hands.

Dryden's Æneid.

We sent out a solemn embassy across the Atlantic Ocean, to lay the crown, the peerage, the commons of Great Britain, at the feet of the American congress. That our disgrace might want no sort of brightening and burnishing, observe who they were that composed this famous embassy. Burke. SIR BENJ. In short, her face resembles a table d'hote at Spa-where no two guests are of a nation.

CRABT. Or, a congress at the close of a general war-wherein all the members, even to her eyes, appear to have a different interest, and her nose and chin are the only parties like to join issue.

Sheridan. School for Scandal. There is, therefore, no absurdity in believing that the most simple animals and vegetables may be produced by the congress of the parts of decomposing organic matter. Darwin,

CONGRESS, AMERICAN, the legislative power of the United States, consisting of a senate and house of representatives. See AMERICA.

CONGREVE (William), a younger brother of an ancient family in Staffordshire. His father was steward of the earl of Burlington's estate in Ireland, where our author was born in 1672. When he first came to England he began to study the law, but his bias was towards polite literature and poetry. His first performance was a novel, entitled Incognita, or Love and Duty Reconciled. He soon afterwards began his comedy of the Old Bachelor, the composition of which had been his amusement during a slow recovery from a fit of illness. When brought on the stage, in 1693, it met with such universal approbation, that Congreve, though only nineteen years of age, was hailed as the support of the declining stage, and obtained the decided patronage of lord Halifax. In 1694 he produced the Double Dealer; which, however, did not meet with so much success as his former play. In 1695, when Betterton opened the theatre in Lincoln's InnFields, Congreve, joining with him, gave him his comedy of Loye for Love, which was so well received, that Betterton immediately offered the author a share in the management of the house, on condition of his furnishing to it one play yearly. This offer he accepted; but, whether through indolence or fastidiousness, his Mourning Bride did not come out till 1697, nor his Way of the World till 1699. The indifferent success this last met with, completed that disgust to the theatre, which a long contest with Jeremy Collier, who had attacked the immoralities of some of his pieces, had begun, and he determined never more to write for the stage. It is probable, however, that he might not so soon have given way to this disgust, had not the easiness of his circumstances rendered him totally independent of the caprice of the town. The earl of Halifax had made him one of the commissioners for licensing hackney-coaches; and soon after, bestowed on him a post in the customs worth £600 per annum. În 1718 he was appointed

secretary of Jamaica; so that his income, at this period, was upwards of £1200 a-year, and the last twenty years of his life were spent in ease and retirement. When Voltaire was in England, he waited upon Mr. Congreve, and passed some compliments upon the merit of his works. Congreve thanked him; but said that he did not choose to be considered as an author, but only as a private gentleman. Voltaire, with the readiness so peculiar to him, replied, that if he had never been anything but a private gentleman, in all probability he had never been troubled with that visit. He died January 19th, 1729, aged fifty-seven; and, on the 26th following, was bu ried in Westminster Abbey. CONGRUE, v. n. & adj. CONGRUENCE, n.s. CONGRUENCY, n. s. CONGRUENT, adj. CONGRU'ITY, n. s. COʻNGRUOUS, adj. CO'NGRUOUSLY, adv.

CO'NGRUMENT, n. s.

Lat. congruere. 'Tepavoç, grus; a crane; unde congruo; à gruibus tractum; quæ se nonsegregant, sive cum volent, sive cum pascantur; to

Christ?

Hooker.

Locke

Id.

Motives that address themselves to our reason, are fittest to be employed upon reasonable creatures: it is no ways congruous, that God should be always frightening men into an acknowledgement of the truth.

Atterbury. The faculty is infinite, the object infinite, and they infinitely congruous to one another.

Cheyne's Philosophical Principles. These planes were so separated as to move upon a common side of the congruent squares, as an axis. Id. It is an act of reasoning of which we are unconscious, except by its effects in preserving the congruity of our ideas. Darwin.

CONI, a considerable town of Italy, in Piedmont, and a bishop's see; seated at the confluence of the Gesso and the Stura. It is said to have been first founded in 1520, during the pontificate of Celistus II. The inhabitants being divided into two factions, it surrendered to the French in 1641, but restored to Savoy soon after. It was again besieged by them in 1744, without being taken; but, on the 26th April,

1796, it surrendered to the republican troops under Buonaparte, previous to the peace with the king of Sardinia. It is strong by nature and art, and its trade is considerable, being the repository for all the traffic between Turin and Nice, and Lombardy, Switzerland, and Germany, Its principal articles of commerce are corn and hemp; but silk is the only manufacture. It lies thirty-five miles south of Turin, and thirty-four north of Nice, and has a strong citadel. Population about 10,000.

CONICA SCABRITIES. See BOTANY. CONICHTHYODONTES, or PLECTRONITE, in natural history, the fossile teeth of fishes, so called from their resembling a cock's spur. They are of an oblong conic figure, broad at the base, narrow at the point, and a little crooked, and from one-tenth of an inch to two inches long. They are often found in England, in strata of stone or clay, with part of the jaw-bones; but it is not certain to what fish they belong.

INTRODUCTION.

CONIC SECTIONS are the figures formed by cutting a cone by a plane. They are five in number, corresponding to the different positions of the cutting plane; viz. a triangle, a circle, an ellipse, a parabola, and an hyperbola. The last three of these only are peculiarly called conic sections.

The more ancient mathematicians, before the time of Apollonius Pergaus, admitted only the right cone into their geometry, and they supposed a section made of it by a plane perpendicular to one of its sides; and as the vertical angle of a right cone may be either right, acute, or obtuse, this method of cutting these several cones produced all the three conic sections. The parabola was called the section of a right angled cone, the ellipse the section of the acute angled cone, and the hyperbola, the section of the obtuse angled But Apollonius, who, on account of his writings on this subject, obtained the title of the Great Geometrician, observed that these sections might be obtained in every cone, both oblique and right, and that they depended on the different inclinations of the section to the cone itself.

cone.

There have been two methods employed in treating of the conic sections: by the one they are considered as cut out of the solid cone, which is the method of the ancients, and of some of the most elegant writers of the moderns; and by the other method certain curves are defined, either from some property by which any number of points may be found in them, or else by which they may be described mechanically upon a plane; or they are defined by means of an algebraical equation, and in either case these curves are shown to have the very same properties as those which are formed by the intersections of a plane and cone. Each of these methods has its

advantage; although some of the demonstrations of writers who have treated the subject geometrically, by the latter, be short and perspicuous, yet there are others, upon which depend some of the principal properties, that are tedious and difficult. The demonstrations of writers who have pursued the first method are free from this objection, being generally plain and concise; but they have been obliged to introduce so many previous propositions concerning the properties of lines touching and cutting conical surfaces, in order to arrive at the principal properties of the three sections, that it requires a considerable portion of time and resolution for a beginner in mathematical studies to go through them.

Some writers, who have treated the subject algebraically, have reduced the whole into a narrower compass; but, in their eagerness to avoid prolixity, they have fallen into another more exceptionable fault. The method in which they have deduced some of the properties, particularly the relations of the abscisse and ordinates, is extremely operose and inelegant; each step in the process is so little connected with the preceding one, that it is scarcely possible to retain them in the memory.

The conic sections are of great use in physical, and plane, astronomy, as well as in all the physico-mathematical sciences, and, therefore, they have been much cultivated ever since their great importance in these sciences was known. The abbe Boscovich has deduced the properties of the conic sections in a very elegant manner from a property common to them all, and the same method has also been followed by the Rev. T. Newton, of Jesus College, Cambridge, in a very neat treatise upon the subject, published in 1794. We shall now proceed to demonstrate some of the most material properties of these figures, availing ourselves chiefly of the work of the last mentioned ingenious writer.

THE

SECT. 1.-OF THE RELATION BETWEEN ABSCISSE AND ORDINATES IN ALL THE SECTIONS. PROPERTIES OF TANGENTS DRAWN TO THE CURVES, &c.

DEFINITIONS. See plate I. fig. 1, 2.

I. Let a point, S, be assumed anywhere without a straight line DX, given by position, and let a point P be supposed to move always in such a manner, that PS, its distance from the given point, may be to PE, its distance from the line DX, in a given ratio, the curve described by the point P is called a conic section; which will be a parabola, an ellipse, or an hyperbola, according as PS is equal to, less, or greater than PE. II. The indefinite straight line, DX, is called the directrix.

III. The point S is called the focus. IV. The given ratio of SP to PE, is called the determining ratio.

V. If a line SD be drawn through the focus, perpendicular to the directrix, which is produced indefinitely, it is called the axis of the conic section.

VI. The point A, where the axis meets the curve, is called the vertex.

VII. A straight line LST, drawn through the focus parallel to the directrix, and terminated by the curve in the points L and T, is called the principal parameter, or the latus rectum.

COROLLARY 1. Fig. 2. SP being greater than PE in the hyperbola, two curves will be described, one on each side of the directrix; which are called opposite hyperbolas.

COR. 2. When the line SP comes into the position SAD, SP PE will be equal to SA, AD; therefore SA is to AD in the determining ratio.

COR. 3. When SP comes into the position SL, or ST, the distance of P from the directrix will be equal to SD, and SL or ST will be to SD in the determining ratio, therefore LS ST. COR. 4. The latus rectum in the parabola is equal to twice the distance of the focus from the directrix, or to four times its distance from the vertex. For SLSD, and SAAD, therefore LT 2SD=4SA.

PROPOSITION I. Fig. 3, 4, 5.

If two straight lines, DQ, Dq, be drawn from the point D, where the axis meets the directrix, through L and T, the extremities of the latus rectum, which are produced both ways in the hyperbola; and through any point P in the conic section, a line QPp be drawn parallel to the directrix, meeting DL and DT in Q and q; the segment QN, which is intercepted between either of the lines and the axis, will be equal to S P, the distance of P from the focus.

The triangles DNQ, DSL, are similar, therefore NQ ND: SL: SD, (that is Cor. 3. Def.): SP: ND. Hence NQ SP, and in the same manner it may be proved that Ng = Sp.

COR. 1. If KAG be drawn through the vertex, parallel to the directrix, SA will be equal to A K or AG.

COR. 2. The lines DQ, Dq, touch the conic section in the points L and T. For the triangle SNP being right angled, SP or QN is always

greater than PN, except when P is at L, where they coincide, therefore DQ meets the curve only in one point L. In like manner it may be shown that Dq touches the curve at T.

PROP. II. Fig. 3, 4, 5.

If from the point G, where the straight line KG, which is drawn through the vertex, parallel to the directrix, meets either of the tangents DQ, Dq, a line GR be drawn through the focus S, and produced both ways in the hyperbola, it will be parallel to the other tangent D in the parabola; it will meet it somewhere in g in the direction GS g in the ellipse, and in the opposite direction in the hyperbola.

Let SG meet the directrix in X. The triangles SAG, SDX, are similar, now SAAG, Cor. 1. Prop. 1, therefore S D DX, but in the parabola, fig. 3, SL DS, therefore S L is equal and parallel to DX; and consequently XS is equal and parallel to DL. In the ellipse, fig. 4, SL is less than SD or DX, and therefore the lines DL, XS, must meet when produced in the direction X GS. In the hyperbola, fig. 5, SL is greater than SD or DX, and therefore the lines must meet when reduced in the direction SGX.

COR. 1. Because the triangles GAS, SNR, are similar, SN will be equal to NR.

COR. 2. Fig. 4, 5. Hence where Q coincides with g, in the ellipse or opposite hyperbola, QN will be equal to g M or SM; therefore SP will be equal to SN; and therefore SP will coincide with S N, and the curve will meet the axis in the point M.

COR. 3. Hence the whole ellipse, fig. 4, is contained between the lines GK, gk, on one side of the directrix.

COR. 4. In the parabola, fig. 3, NQ being always greater than NR, except at the vertex, SP is greater than SN; therefore the curve will meet the axis only in one point A, and it will extend without limit on one side of the directrix.

COR. 5. In the hyperbola, fig. 5, NQ being greater than NR, except at A and M, SP is greater than S N, and the two curves will be extended without limit, on opposite sides of the directrix.

DEFINITIONS. Fig. 4, 5.

VIII. The tangents DLQ, DTq, which are drawn through the extremities of the latus rectum, are called focal tangents.

IX. The straight line A M, in the ellipse and hyperbola, is called the transverse axis, or the axis major.

X. If the transverse axis be bisected in C, the point C is called the centre of the ellipse or hyperbola.

XI. If a line BC b, which is bisected in C, be drawn perpendicular to the transverse axis, and CB, Cb, be each a mean proportional between SA, SM, the segments of the axis between the focus and the vertices, BCb is called the conjugate axis, or axis minor.

XII. A line PNp, drawn through any point N, in the axis parallel to the tangent KG, or perpendicular to the axis, and terminated by the curve at P and p, is called an ordinate to the axis.