gines, &c. manor. from him his due rent and service. Fizt. Cess. 60; 1 Inst. | GAZANA (Com.) a silver coin, and one of the roupees 142. current in the great Mogul's territories. GAVELGELD (Archæol.) payment of tribute or toll. GAZE (Her.) i e. at Gaze; a term in blazon signifying GAVELGI'DA (Archæol.) one that pays toll or tribute. that a beast of chase, as the hart, is looking full at you. GAVEL-KIND (Law) a tenure or custom annexed, or be- Gaze (Com.) a small copper money made and current in longing to lands in Kent, whereby the lands of the father Persia, worth two French liards. are equally divided at his death among all his sons; or the GAZE-HOUND (Sport.) a sort of hunting dog in the North land of the brother among all the brethren, if he have no of England, so called because it uses its sight more than issue of his own. F. N. B. 198; Co. Lit. 210, &c. its nose. GAVELMAN (Laro) or Gavelling-man, one who paid a re GAZELLE (Zool.) an Arabian antelope with tapering horns, served rent besides the customary duty. the Antilope Gazella of Linnæus. GAVELMED (Law) the duty of mowing meadow-land re- GAZETTE (Polit.) a newspaper, particularly the official quired by the lord of his customary tenant. paper published by order of the government; it is derived GAVELOCK (Mech.) an iron bar to enter stakes into from the Italian gazeta, an old Venetian half-penny, which the ground. Gavelocks are also javelins, warlike en was originally the price of the newspaper printed there. GAZONŠ (Fort.) sods, or pieces of fresh earth covered GAVELREP (Law) the duty of reaping for the lord of the with grass, cut in the form of a wedge to line the parapet and the traverses of the galleries. GAUGE-PENNY (Law) the fee paid to the King's gauger GAZUL (Bot.) a weed growing in Egypt, of which the for the gauging of wine. [vide Ganger] finest glass is made. GAUGE Line (Mech.) a line on the common gauging-rod GE (Com.) or Je, a long measure in the empire of the great used for the purpose of gauging liquids. Mogul. of a circle, whose area is equal to the solid content of the GEARS (Mar.) vide Jears. GEASTER (Bot.) a species of the Lycoperdon of Linnæus. GAUGER (Law) an officer appointed by the King to exa- GEAT (Mech.) the little spout or gutter made in the brim mine all tuns, pipes, hogsheads, barrels, &c. Stat. 27 Ed. 3. of casting ladles for the casting of ordnance, type, &c. c. 8, &c. GEBEYGIS (Mil.) a name for armourers among the Turks. GAUGE'TUM (Archæol.) a gauge, or the operation of GEBELUS (Mil.) Turkish horsemen, who are supported by gauging: the Tamariots during a campaign. GÅ'UĞING (Men.) the art or act of measuring the capa- GEDER (Com.) a measure of continence used by the In cities of all kinds of vessels, and thence ascertaining the dians for their grain, containing near four pounds of sixquantity of liquor they contain. teen ounces weight of pepper. GA'ULONITES (Theol.) a sect among the Jews who op- GEIR (Orn.) a vulture. posed the tribute raised by Cyrenius, in the time of Au- GEI'SON (Anat.) ysłcov, signifies properly the eaves of a gustus. Joseph. Antiq. I. 18, c. 1, &c. house, but metaphorically the prominent part of the GĂULTHERIA (Bot.) a genus of plants, so called from eyebrows. Gaulthier, the botanist of Canada, Class 10 Decandria, GELA'LA (Bot.) another name for the Erythrina of Lin- petalled.-STAM. filaments ten; anthers two-horned. epithet for the middle fore-teeth which are shown in GELATINA (Chem.) Gelatine, a clear gummy juice; a Species. The two species are the Gaultheria procumbens, gelly extracted from animal substances by solution in seu Anonyma, Trailing Gaultheria, native of Canada. water, but not in alcohol. Gaultheria antipoda, native of New Zealand. GELATIO (Med.) signifies literally freezing, but is applied GAUNTLET (Her.) an iron glove which co medicinally to that rigidity of body which happens in a vered the hand of a cavalier when armed cap catalepsy, as if the patient were frozen. nopee, as in the annexed example." He GELD (Law) geldum from the Teutonic geld, money, sigbeareth sable, a horse's head erased or, be nified a tribute, but particularly a compensation for any tween three gauntlets argent, name Guillim.” thing, as-Were-geld, the value or price of a man slain.Gauntlets were always borne with the casque -Orfgeld, the value of a beast slain. Angeld, the single in processions, and mostly thrown by way of value of a thing.-Twi-geld, double value, &c. challenge instead of the glove. GE'LDABLE (Law) liable to pay taxes. GAUNTLET (Mil.) vide Gantlet. GELDER-ROSE (Bot.) a well-known flowering shrub, the GAUNTREE (Mech.) a frame to set casks upon. Vibernum rosea of Linnæus. It derives its English name GAVOT (Mus.) a brisk and lively air. from Guelderland, whence it was first imported. GAU'RA (Bot.) a genus of plants, Class 8 Octandria, Order 1 GE'LIBACH (Mil.) a sort of superintendant or chief of Monogynia. the gebegis or armourers in Turkey. Generic Character. Cal. perianth one-leaved. - Cor.GELSE'MINUM (Bot.) a name for the jasmin. petals four.-Stam. filaments eight; anthers oblong.- GEM (Min.) a common name for every jewel, or precious Pist. germ oblong; style filiform; stigmas four.- Per. stone. Gems are distinguished generally into the pellucid drupe ovate ; seeds oblong. and the semipellucid. (vide Gemma ] Species. The single species is a biennial, namely, the Gaura GEME'LLES (Her.) vide Bar-Gemel. biennis, a native of Virginia. GEME'LLI (Anat.) vide Gemini. GAURA is also the Combretum secundum. GEMINI (Anat.) from geminus, twin; a name for a pair of GAUT (Geog.) an Indian term for a passage or road from muscles which move the thigh outward. the coast to the mountains. Gemini (Astron.) didepos, the twins ; a zodiacal constellation, GAUZE (Com.) a thin sort of silk. or one of the twelve signs of the zodiac, representing GA'YNAGE (Law) vide Gainage. Castor and Pollux, marked thus II. The stars in the næus. sign Gemini, according to Ptolemy, are 25; to Tycho, 25; || TO GENERATE (Mus.) the operation of that mechanical to Hevelius, 38 ; and in the Britannic catalogue, 85. Onę power in nature which every sound has of producing one star on the top of the left foot of Pollux, of the second or more general sounds. magnitude, is called by Proclus spórks. Arat. Phænom. GENERATED (Math.) an epithet for any quantity prov. 147; Eratosthen. Character. ; Hygir. Astron. Poet.; duced in arithmetic by the operation of multiplication, Proc. de Sphær. division, extraction of the roots, &c. or in geometry, for GE'MINOUS Arteries (Anat.) a name for two small arteries the figures produced by the revolution of lines, &c.; thus, passing down the joint of the knee. twenty is the product generated by four and five ; and a GÊMINUS (Bot.) double, an epithet for leaves and stipules. circle is generated by the supposed revolution of a line GEMMA (Min.) gem, a genus of Siliceous Earths, consist about one of its extremities, &c. ing of silica, and a large proportion of alumina, with some GENERATE'UR (Mus.) the name first given by Rameau times a small portion of lime and oxyde of iron. The gem to the fundamental note of the chord, so called because it is remarkable for its hardness and internal lustre. is the principal sound by which others are produced. Species. The principal species are as follow:- Gemma GENERATING line or figure (Geom.) is that which, by its adamas, the Diamond.-Gemma rubinus, the Ruby.- motion or revolution, produces any other figure, solid or plane. Gemma sapphirus, the Sapphire.—Gemma topazius, the GENERATION (Math.) the formation or production of Topaz. - Gemma hyacinthus, the Hyacinth. - Gemma figures and quantities. [vide Generated} aquamarina, the Beryll . — Gemma chrysoberyllus, the GENE’RIC character (Nat.) a term applied to the characters Chrysoberyl.—Gemma smaragdus, the Emerald.—Gemma in plants, animals, &c. by which the genera are distinchrysolithus, the Chrysolite. - Gemma garnatus, the guished from each other. Garnet.-Gemma scorlites, the shorlite. GENESIS (Geom.) yéveris, from yirouets, to be made; the Gemma (Bot.) vide Bud. forming of any plain or solid figure by the motion of some GEMMA'TIO (Bot.) Gemmation, or Budding, the con. point, line, or surface. The moving line, &c. is called the struction of the bud, as composed of leaves, stipules, and describent, and the line in which the motion is made petioles. is the dirigent. Thus, a right line moving parallel to GEMMI'PARUS (Bot.) an epithet for what produces buds. itself is said to generate a parallelogram; and a parallelGEMMOW-RING (Mech.) a double ring in links. ogram turned about one of its sides as an axis generates a GEMO'NIÆ (Ant.) Gemoniæ scalæ, or gradus ; a place in cylinder. Rome elevated by several steps, from which condemned | GENET (Man.) a particular kind of Turkish bit, the curb Genet (zool.) an animal of the weasel kind, the Viverra GEMU'RSA (Med.) from gemo, to groan, on account of the genetla of Linnæus, which resembles the civet cat in its pain which it was said to occasion in walking; the name musk smell. of an excrescence between the toes. GENETHLIA (Anat.) ysvédaise, a private festival observed GENA (Anat.) the cheek. on the day of a child's birth. Hesychius. ; Meurs. Græc. GENDARMERI'E (Mil.) a select body of cavalry in the Fer. apud Gronov. Thes. Antiq. Græc. tom. vii, old French service, that took precedence of every regiment || GENEVA. (Com.) from the French génièvre, juniper; a of horse, and ranked immediately after the King's house strong spirituous liquor distilled from juniper berries. hold. The Gens-d'armes are still a distinct body of men, || GENIANES (Min.) a precious stone said to bring punishbut are now particularly made to answer the purpose of a ment to a man's enemies. Plin. l. 37, c. 10. police. GENICULATUS (Bot.) kneed, or, according to Withering, GENDER (Gram.) in French gendre, from the Latin genus, knee-jointed; an epithet applied to a stem, peduncle, or a kind; the distinction of nouns in regard to sex. There awn, forming a very obtuse angle at the joints. are three genders in Latin and Greek Nouns; namely, the GENIOGLOSSI (Ant.) a pair of muscles, with which the masculine for the male sex, feminine for the female sex, tongue is thrown out.-Genio-hyoideus, a muscle which and the neuter for things of no sex. pulls the os hyoides upwards and forwards, and also assists GENEALOGY (Her.) gevodozic, from yéros, a race, or the geninglossi in thrusting the tongue out. family, and tóyos, a discourse ; a description of the stock, GENIO'STOMA (Bot.) a genus of plants, Class 5 Pentarlineage, or pedigree of any family or person. dria, Order 1 Monogynia. GENEIAS (Surg.) yetías, a bandage that comes under the Generic Character. Cal. perianth inferior.—Cor. onechin. Gal. de Fasc. petalled.-Stam. filaments five; anthers oblong.–Pist. GENEION (Anat.) vide Antherion. germ ovate; style filiform; stigma blunt.—Per. capsule GENERA (Mus.) vide Genus. oblong; seeds very many. GENERAL (Mil.) an officer in chief, to whom the com Species. The single species is the Geniostoma rupestris. mand of troops is entrusted. There are different ranks GENIPAT (Bot.) an Indian tree. of generals, as-Captain-General, who is the commander GE'NIPI (Bot.) the Artemisia rupestris of Linnæus. in chief, and answers to the naréchal of France.—Lieute-GENI'STÀ (Bot.) oruptior, a plant recommended by Diosnant-General, the next in dignity to the general. Major. corides and others for its medicinal virtues, particularly as General, next to the Lieutenant-General. - General officers, a purgative. Dioscor. I. 4, c. 158; Plin. l. 24, c. 9, &e.; all officers above the rank of lieutenant-colonel in the line. Gal. de Simpl. 1. 8; Oribas. Med. Collect. I. 15; Aet. General is also a particular beat of drum, early in the Tetrab. 1, serm. 1; Paul. Æginet. l. 7, c. 3. morning, to give notice to the men to be ready to march. Genista, in the Linnean system, a genus of plants, Class 17 GENERAL (Ecc.) the principal governor of a religious oriler. Diadelphia, Order 4 Decandria. -General Synod, a council in which bishops, priests, &c. Generic Character. Cal. perianth one-leaved.-Cor. paof all nations are assembled together. pilionaceous.--STAM. filaments ten; anthers simple.GENERALE (Ecc.) the single commons, or ordinary pro Pist. germ oblong; style simple; stigma sharp.--PER. visions of a convent. legume roundish ; seeds solitary. GENERALI'SSIMO (Mil.) the supreme general, or the Species. The species are shrubs, as the Genista canacommander in chief of an army. riensis, seu Cytisus, Canary Genista, or Cytisus, native VOL. II. of Spain.-Genista sagittalis, Genistella, seu Chame- || GENU'GRA (Med.) another word for gonogra. genista, native of France.-Genista tinctoria, seu Tinc- || GENUS (Log.) yios, one of the five predicables, or that torius, Common Dyer's Genista, or Broom. - Genista which is common to a great number of individual things. lusitanica, seu Scorpius, Portugal Genista, or Broom, This is distinguished according to the different degrees of native of Portugal, &c. – Clus. Hist. ; Dod. Pempt. ; generality, into-Genus summum, or generalissimum, that Bauh. Hist.; Bauh. Pin.; Ger. Herb. ; Park. Theat.; which appertains to the greatest number of individuals, as Raii Hist.; Tourn. Inst. substance, which belongs to all material things. This is Genista is also the Aspalanthus indica, chenopoda, spinosa; never a species.—Genus subalternum, subaltern genus, that the Anthyllis citysoides ; the Psoralea pinnata ; and the which is sometimes a genus and sometimes a species; thus, Hedysarum alhagi. animal, in respect to substance, is a species ; and in GENITIVE (Grum.) in Latin genitivus, from gigno, to respect to man, brute, dog, &c. is a genus. The subaltern beget ; a name for the second case in Latin and Greek, genera may also, in a series, be proximate or remote; which implies property and possession. thus, man is the proximate genus to animal, body is a GENITU'RA (Anat.) youn, the seed which has been emitted remote genus. Porphyr. Isagog. c. 1, &c. recently into the uterus, and is contained within the vessels. Genus (Mus.) a distribution of the Tetrachord, or the four It is the first stage of gestation, in distinction from the principal sounds, according to their quality. The Genera embryo and the fætus, which are the two other stages. were formerly three, namely, the diatonic, Catonixón; chroHippocrat. de Nat. Puer. &c. matic, xpwpatixòv; and enharmonic, zrceppiórcov. [vide DiatoGENOVI'LLIER (Her.) a piece of armour that covers nic, &c.] the knees. Genus (Nat.) one part of the systematic division of plants, GENOVILLIE'RE (Fort.) French for that part of the pa animals, or minerals, which is contained under the Order, rapet of a battery which lies under the embrasure. and contains the Species. GE'NTIAN (Bot.) vide Gentiana. GENUS (Med.) a division of any order of diseases which GENTIA'NA (Bot.) yetir, a plant so called, according contains the species. to Dioscorides and Pliny, because its medicinal virtues Genus (Gram.) vide Gender. were first discovered by Gentius, King of the Illyrians. It | Genus (Law) the general stock, extraction, &c. as the word was reckoned very efficacious against the bites of serpents. office, in law, is the genus, or general term; but sheriff is Dioscor. l. 3, c. 3; Plin. l. 25, c. 7; Gal. de Simplic. ; the species. Oribas. Med. Collect. I. 11; Aet. Tetrab. 1, serm. 1 ; Paul. | Genus (Rhet.) is distributed into the demonstrative, delibeÆginet. 1. 7, c. 3. rative, and judiciary. [vide Rhetoric] GENTIANA, in the Linnean system, a genus of plants, Class 5 | GEOCENTRIC (Astron.) an epithet applied to a planet, or Pentandria, Order 2 Digynia. its orbit, to denote its being concentric with the earth, or Generic Character. CAL. perianth five-parted. — Cor. . having the earth for its centre.-Geocentric place of a petal one.-STAM. filaments five; anthers simple.-Pist. planet is the place in which it appears to an observer from germ oblong; styles none; stigmas two.-Per. capsule the earth.-Geocentric longitude of a planet is the distance oblong; seeds numerous. measured on the ecliptic between the geocentric place, Species. The species are mostly perennials, as the-Gen and the first point of Aries. (vide Astronomy] tiana viscosa, seu Exacum, Clammy Gentian.-Gentiana | GEODESIA (Mens.) the art of measuring or surveying purpurea, seu Coilantha, Purple Gentian. - Gentiana land or surfaces, and finding the contents of all plain asclepiadea, Swallow Wort-leaved Gentian.— Gentiana figures. pneumonanthi, seu Pneumonanthi, Marsh Gentian, or Cala- GEODES LAPIS (Min.) dobos ysádne, a stone so called, thian Violet. But the Gentiana verna, seu Gentianella, and from yñ, the earth which it contains. It is of an astringent the-Gentiana campestris, seu Gentianella, are annuals. and drying quality. Dioscor. l. 5, c. 169. Clus. Hist.; Dod. Pempt. ; Bauh. Hist.; Bauh. Pin.; GEOFFROYA (Bot.) a genus of plants, so called from Mon Ger. Herb.; Park. Theat.; Raii Hist.; Tourn. Inst. sieur Geoffroy, Class 17 Diadelphia, Order 4 Decandria. Gentiana is also the Orobanche uniflora, et Chlora per Generic Character. Cal. perianth one-leaved.--Cor. pafoliata. pilionaceous. -STAM. filaments diadelphous; anthers GENTIANE'LLA (Bot.) the Gentiana campestris of Lin roundish.--Pist. germ roundish; style subulate ; stigma obtuse.- Per. drupe ovate ; seeds nut, subovate. GENTIANO'IDES (Bot.) the Gentiana sessilis of Lin Species. The species are trees, as the-Geoffroya spinosa, seu Umari, Thorny Geoffroya, native of Carthagena.GENTILES (Ant.) those who were not Roman subjects. Geoffroya inermis, Smooth Geoffroya, native of Jamaica, Theodos. A. l.fin. C.de Offic. milit.; Panciroll. Notit. Dign. &c. Raii Hist. Plant. imp. occid. c. 88. GEOG NOSY (Min.) from y, the earth, and yodoxw, to Gentiles (Theo!.) from gens, a nation; the general name know; a name given by Werner to his system of mineralogy. given by the Jews to all who were not of the twelve tribes. | GEOGRAPHICAL MILE (Math.) the 60th part of a The term is now applied by Christians to all heathens. degree, in distinction from an English mile, of which 691 Gentiles (Gram.) nouns betokening the country of the form a degree. person. GEOGRAPHY, yarpa Pice, from yñ, the earth, and spécow, to GENTILI'TIUS (Med.) another word for hereditary as ap describe; a description of the earth, or the habitable world, plied to diseases. by which it is distinguished from the description of the earth, GENTLEMAN (Law) in French gentilhomme, from gentil, as one of the planetary system, which falls under the head i. e. è bonâ gente, a man born of a good country or family; of Astronomy. This science constitutes a branch of the a term originally applied to all who were above the estate mixed mathematics, as far as the relative positions of of a yeoman; it is now used for all such as are honour places, the different circles and lines imagined to be able by their birth, education, or profession. drawn upon the earth, their measure, distance, &c. are deGENTLEWOMAN (Law) a good addition for the estate termined by astronomical computation, or deduced from and degree of a woman, as generosus is for a man. mathematical principles. GENTRY (Law) the order and rank of gentlemen, descended Geography is distinguished from Cosmography, as a part of ancient families, which have always borne coat armour. from the whole, the latter comprehending the whole dæus. næus. universe within its description; it is distinguished from Chorography, or the description of countries ; and Topography, or the description of particular places, as a whole from the part. The natural divisions of the Earth are Land and Water. The Land is divided into Continents, Islands, Peninsulas, Isthmuses, Promontories, Mountains, Volcanoes, Champaign, Coasts, Cliffs, Archipelagoes, &c. (vide Continent, Island, &c.) The Water is divided into Oceans, Seas, Gulfs, Bays, Havens, Straits, Lakes, Rivers, Creeks, Cataracts, &c. [vide Ocean, Sea, &c.] The political division of the earth is into Countries, Empires, Kingdoms, States, Circles, Provinces, Counties, Towns, Cities, Villages, &c. The principal writers on geography among the ancients are Ptolemy, Strabo, Pomponius Mela, Pausanias, Arrian, Dicæarchus, Dionysius, Stephanus, &c. Among the moderns, Johannes de Sacrobosco, Sebastian Mun ster, Clavius, Cluverius, Cellarius, Wolfius, &c. GEO'LOGY (Nat.) from yñ, the earth, and nonos, a dis course ; that branch of Natural History which treats of the structure of the earth in regard to the origin, constitu tion, and composition of its solid contents. GEOMANCY (Ant.) Epific, from yñ, the earth, and parteia, divination; a kind of divination performed by making circles on the earth, or by opening the earth. GEOMETRA (Ent.) a rame given by Fabricius to a divi sion of the genus Phalæna, comprehending those insects of this tribe which have the antenna pectinate. GEOMETRICAL (Geom.) an epithet for what appertains to the science and principles of geometry, as a-Geometrical place, a certain bound or extent wherein any point may serve for the solution of a local or undetermined problem. - Geometrical solution of a problem, a solution according to the rules of geometry, &c. GEOMETRY, the science which teaches the dimensions of lines, surfaces, and solids. The word is derived from the Greek yempestpice, signifying, literally, a measuring of land, because the study of geometry first took its rise from the measuring of lands. The invention of it is generally ascribed to the Egyptians, who, in consequence of the periodical inundations of the Nile, which destroyed all their landmarks, had recourse to mathematical admeasurement to determine the boundaries of each man's possessions. Geometry is distinguished into theoretical and practical. Theoretical Geometry treats of the various properties and relations of magnitudes and the different propositions which flow out of these.-Practical Geometry is the application of these general principles to the various purposes of admeasurement in the concerns of life. Speculative geometry may again be divided into the elementary and the sublime geometry.-Elementary or Common Geometry is employed in the consideration of lines, superficies, angles, planes, figures, and solids.-Sublime or Higher Geometry enters into the consideration of curve lines, conic sections, and the bodies formed of them. Line. A Line, according to Euclid, is length without breadth, the extremities of which are points that have no parts or magnitude.— A straight line is that which lies evenly between the points, as A B, fig. 1, Plate 37. This being the shortest line between any two points, is denominated their distance from each other. -A curve line is that whose parts lie unevenly between their points or tend different ways, as ACB.-A perpendicular is a line which is normal or perpendicular to another, as CD perpendicular to A B. This makes the adjacent angles equal, namely, CD B and C D A, fig. 2, and each of them is called a right angle.-- An oblique line is that which is oblique to another, and makes the angles oblique, as A B to A C, fig. 3.-Parallel lines are those which preserve the same distance from each other, as O P and Q R, fig. 7. These lines if infinitely produced will never meet.-Convergent lines are those whose distance from each other becomes always less, as T O and UQ, fig. 4.—Divergent lines are those whose distance from each other becomes always greater, as ( N and RS, fig. 4. Superficies. The Superficies is that which has only length and breadth; the terms and boundaries of which are lines, and the measure or quantity is called the area. Superficies are either plane, rectilinear, curvilinear, convex, or concave.-A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.- A rectilinear superficies is that which is bounded by right lines.--A curvilinear superficies is bounded by curved lines.-A convex superficies is that which is curved, and rises outwards.-A concave superficies is curved, and sinks inwards. Angles. An angle is the mutual inclination of two lines or two planes meeting in a point, called the vertex, or angular point, as B, fig. 5. Angles are mostly denoted by three letters, the middle of which stands for the vertex or angular point, as A B C, D BC. The sides which contain the angle are called the legs, as A B, B C, or D B, BC. Angles are distinguished in respect to the form of their legs, their magnitude, and their relative situation, into-Rectilinear angles, whose legs are both right angles.-Curvilinear angles, which are contained by curves.--Mixt, or mixtilinear angles, which have one leg rectilinear and the other curvilinear.Right angles are formed by one line standing perpendicularly on another, as Č D B, and C DA, fig. 2.Oblique angles are those which are not right; these may be either acute or obtuse.-An acute angle is less than a right one, as D B C, fig. 5, A E B, fig. 6.-An obtuse angle is greater than a right angle, as FDB, fig. 2.Vertical angles are such as have their legs mutually continuations of each other, as A and b,c and d, fig. 7: these are also called opposite angles.-Alternate angles are · those made on the opposite sides of a line cutting two parallel lines, A y, fig. 7.-External angles are the angles of a figure made without it by producing the sides, as c, fig. 7.-Internal angles are those within the figure, as b, y, fig. 7. [vide Angle] Figure. A Figure is that which is included within one or more boundaries, called sides. Figures are, as to their form, either rectilinear, curvilinear, or mixtilinear. Rectilinear Figures. Rectilinear Figures are those figures which are contained by right lines: the ambit or limit of such a figure is called the perimeter. Rectilinear figures are distinguished, according to the number of their sides, into trilateral figures, or triangles; quadrilateral figures, or squares; and multilateral figures, or trapeziums. Triangles. Trilateral figures, or Triangles, are figures contained by three straight lines; of these there is the -Equilateral triangle, which has all its sides equal, as fig. 8.— Isosceles triangle, which has only two sides equal, as fig. 9. It is proved in the fifth proposition of the first Book of Euclid, that the angles at the base of an isosceles triangle, as F D E and FED, are equal to each other.- Scalene triangle, which has three unequal sides, as C AB, fig. 10.–Right-angled triangle, that which has a right angle, as MKL, fig. 11.- An obtuse angled triangle, that which has an obtuse angle, as PNO, fig. 12.- Acute angled triangle, that which has all three acute angles, as A CB, fig. 8. To the right-angled triangle belongs the hypothenuse, i. e. the side which subtends, or is opposite to the right angle, as ML. In the 17th Proposition of the first Book of Euclid, it is proved that the square of the hypothenuse is equal to the squares of the other two sides, Quadrilateral Figures. A quadrilateral figure is that whose diameter is a chord which passes through the centre, as perimeter consists of four sides. The principal of these AE: the semi-diameter, or the half of the diameter, is figures are as follow : namely– The square, i. e. a four otherwise called a radius, as A C or CD.-The arc is sided figure, which has all its sides equal, and all its an any part of the circumference cut off by the chord, as gles right angles, as A B C D, fig. 13.-An oblong square, A FB, fig. 20.— The arc of a circle is the measure of an a figure having all its angles right angles, but not all its angle: thus the angle B AC, in fig. 3, is measured by sides equal, as A B C D, fig. 15.— A rhombus is a figure the arc D E.-The segment of a circle is that part which which has all its sides equal, but its angles are not all is bounded by an arc and its chord, as the segment right angles, as E F G H, fig. 14.- A rhomboid is a A FB A, comprehended within the arc FB A, and the figure which has its opposite sides equal to each other, chord A B. It is called the greater segment when it is but all its sides are not equal, and its angles are not right greater than a semicircle ; and the lesser segment when it angles, as O PQ N, fig. 16.-A rectangle is any quadri. is less.—The sector of a circle is the part, ACD, comlateral figure whose angles are right angles, such as prehended within the two radii, AC and CD, fig. 20. fig. 15.- Parellelogram is any quadrilateral figure whose -The tangent to a circle is that line which touches à ciropposite sides are parallel, and consequently equal, as cle; but it produced, falls wholly without the circle, as fig. 13, 14, 15, and 16.—The diagonal is the line which HI, fig. 21, which touches the circle ML, in the point divides any parallelogram into two equal parts, as D B, L. A circle is a tangent to another circle within if it fig. 15, and PN, fig. 16; and if any two lines, as EG lies wholly within the other circle, as L M touches the and HK, be drawn parallel to A B and B C, then four circle L N within, as in fig. 23. A circle touches another parallelograms will be formed; namely, two, which are circle without, if, meeting the other circle, it falls called parallelograms about the diameter, as H G and EK, wholly without it, as L M and L N touch each other in fig. 15; and two which are complements, namely, AF and the point L, fig. 22.–Straight lines are said to be FC. Any one of the parallelograms about the diameter, equally distant from the centre of a circle, when perpentogether with the two complements, is called a gnomon, diculars, drawn to them from the centre, are equal, as as the parallelogram HG, together with the comple D E and FG, which have the equal lines C A and CB inents À F, FC, is the gnomon, which is briefly ex. drawn perpendicularly to them, as in fig. 24.-An angle pressed by the letters A G K or EHC. Every right at the centre of a circle is that which forms the vertex of angled parallelogram or rectangle is said to be contained a triangle at the centre, as B G C, EHF, fig. 25, 26.by the two lines which contain one of the right angles : The angle at the circumference is that which forms the verthus, the rectangle A B C D is said to be contained by tex of a triangle at the circumference, as B A C, E D F. the lines B A and A D. Trapeziums are all other four The angle at the centre is double that at the circumsided figures, as fig. 17. ference, as proved by Prop. 26, Book III, of Euclid's Multilateral Figures. Multilateral figures or polygons are Elements. An angle is said to insist or stand upon the those figures which consist of more than four sides, circumference, intercepted between the straight lines which are called pentagons, if they consist of five sides, that contain the angle: thus the angles B AC, BGC, as in fig. 18; hexagons, if of six sides, as fig. 19; oc EDF, and E H F, stand on the circumferences B KC, tagons, if of eight sides, &c. EL F.-A rectilinear figure is said to be inscribed in a Figures are moreover distinguished into-equiangular, circle when all the angles of the inscribed figure are which have their angles equal ; equilateral, when they upon the circumference of the circle, as ABDC, fig. 28. have their sides equal each to each ; regular, when they - A rectilinear figure is said to be described about a are both equiangular and equilateral ; irregular, when circle, when each side of the circumscribed figure they are not equiangular and equilateral.-- Similar rec touches the circumference of the circle, as A B Ď C, tilinear figures are those which have their several angles fig. 29.— A circle is said to be inscribed in a rectilinear equal each to each, and the sides about the equal angles figure when the circumference touches each side of the proportional.—Reciprocal figures, i. e. triangles and pa figure, as A B D C, fig. 29.- A circle is said to be derallelograms, are such as have their sides about two of scribed about a rectilinear figure when the circumference their angles proportionals in such manner, that a side of of the circle passes through all the angular points of the the one is to a side of the other, as the remaining figure, about which it is described, as A BDC, side of the second is to the remaining side of the fig. 30. other. Solid Figures. A solid is that which has length, breadth, The Base of a figure is the lowest part of the perimeter, as and thickness. That which bounds a solid is a plane, KL, fig. 11. The vertex of a figure is the extreme or a plane superficies.-A straight line is perpendicular, point opposite to the base, as M. The altitude of a or at right angles to a plane when it makes right angles figure is the distance from the vertex to the base, as with every straight line meeting it in that plane, as A B MK. A rectilinear figure is said to be inscribed in an in fig. 36.- A plane is perpendicular to a plane when the other rectilinear figure, when all the angles of the in straight lines drawn in one of the planes perpendicularly scribed figure are upon the sides of that in which it is to the common section of the two planes are perpendiinscribed, each upon each, as ABDC, fig. 27. In cular to the other, as A B C, fig. 37.- The inclination of like manner, a figure is said to be described about an a straight line to a plane is the acute angle contained by other figure, when all the sides of the circumscribed that straight line, and another drawn from the point in figure pass through the angular points of the figure, which the first line meets the plane, to the point in about which it is described, each to each. which a perpendicular to the plane drawn from any 1 'urvilinear Figures. Of curvilinear figures the most im point of the first line above the plane, meets the same portant is the circle. plane, as ACB, fig. 38.-The inclination of a plane Circle. A circle is a plane figure contained by one line, to a plane is the acute angle contained by two straight called the circumference or periphery, as B AD), fig. 20, lines drawn from any the same point of their common which is at an equal distance from a certain point, called section at right angles to it, one upon one plane, as the centre, as C. All the lines drawn from this point to A B, and the other upon the other, as BC, fig. 39. the circumference are equal, as CA, CE, CD.-The Two planes are said to liave the same or like inclination chord of a circle is the right line drawn from one point to one another, which two other planes have, when the of a circumference to another, as A B, fig. 20.—The said angles of inclination are equal to one another.-A |