manor.

GAUGE-PENNY (Law) the fee paid to the King's gauger for the gauging of wine. [vide Gauger]

GAUGE Line (Mech.) a line on the common gauging-rod used for the purpose of gauging liquids. GAUGE-POINT of solid measure (Geom.) is the diameter of a circle, whose area is equal to the solid content of the

same measure.

GAUGER (Law) an officer appointed by the King to examine all tuns, pipes, hogsheads, barrels, &c. Stat. 27 Ed. 3. c. 8, &c.

GAUGE TUM (Archeol.) a gauge, or the operation of gauging.

GAUGING (Men.) the art or act of measuring the capacities of all kinds of vessels, and thence ascertaining the quantity of liquor they contain.

GA'ULONITES (Theol.) a sect among the Jews who opposed the tribute raised by Cyrenius, in the time of Augustus. Joseph. Antiq. 1. 18, c. 1, &c.

GAULTHE'RÍA (Bot.) a genus of plants, so called from Gaulthier, the botanist of Canada, Class 10 Decandria, Order 1 Monogynia.

Generic Character. CAL. perianth double.-COR. onepetalled.-STAM. filaments ten; anthers two-horned.PIST. germ roundish; style cylindric; stigma obtuse.PER. capsule roundish; seeds many.

Species. The two species are the Gaultheria procumbens, seu Anonyma, Trailing Gaultheria, native of Canada.Gaultheria antipoda, native of New Zealand. GAUNTLET (Her.) an iron glove which covered the hand of a cavalier when armed capa-pee, as in the annexed example." He beareth sable, a horse's head erased or, between three gauntlets argent, name Guillim." Gauntlets were always borne with the casque in processions, and mostly thrown by way of challenge instead of the glove.

GAUNTLET (Mil.) vide Gantlet.

GAUNTREE (Mech.) a frame to set casks upon.
GA'VOT (Mus.) a brisk and lively air.

GAURA (Bot.) a genus of plants, Class 8 Octandria, Order 1
Monogynia.

Generic Character.

CAL. perianth one-leaved. COR. petals four.-STAM. filaments eight; anthers oblong.PIST. germ oblong; style filiform; stigmas four.-Per. drupe ovate; seeds oblong.

Species. The single species is a biennial, namely, the Gaura biennis, a native of Virginia.

GAURA is also the Combretum secundum.

GAUT (Geog.) an Indian term for a passage or road from the coast to the mountains.

GAUZE (Com.) a thin sort of silk.
GA'YNAGE (Law) vide Gainage.

current in the great Mogul's territories. GAZE (Her.) i e. at Gaze; a term in blazon signifying that a beast of chase, as the hart, is looking full at you. GAZE (Com.) a small copper money made and current in Persia, worth two French liards.

GAZE-HOUND (Sport.) a sort of hunting dog in the North of England, so called because it uses its sight more than its nose. GAZELLE (Zool.) an Arabian antelope with tapering horns, the Antilope Gazella of Linnæus. GAZETTE (Polit.) a newspaper, particularly the official paper published by order of the government; it is derived from the Italian gazeta, an old Venetian half-penny, which was originally the price of the newspaper printed there. GA'ZONS (Fort.) sods, or pieces of fresh earth covered with grass, cut in the form of a wedge to line the parapet and the traverses of the galleries.

GAZUL (Bot.) a weed growing in Egypt, of which the finest glass is made.

GE (Com.) or Je, a long measure in the empire of the great
Mogul.
GEAR (Husband.) harness for draught horses.
GEARS (Mar.) vide Jears.
GEA'STER (Bot.) a species of the Lycoperdon of Linnæus.
GEAT (Mech.) the little spout or gutter made in the brim
of casting ladles for the casting of ordnance, type, &c.
GEBE GIS (Mil.) a name for armourers among the Turks.
GEBELUS (Mil.) Turkish horsemen, who are supported by
the Tamariots during a campaign.

GE'DER (Com.) a measure of continence used by the In-
dians for their grain, containing near four pounds of six-
teen ounces weight of pepper.
GEIR (Orn.) a vulture.

GEI'SON (Anat.) yue, signifies properly the eaves of a house, but metaphorically the prominent part of the eyebrows.

GELA'LA (Bot.) another name for the Erythrina of Lin

næus.

GELA'SINOS (Anat.) yehands, from yeaάw, to laugh; an epithet for the middle fore-teeth which are shown in laughter.

GELATINA (Chem.) Gelatine, a clear gummy juice; a gelly extracted from animal substances by solution in water, but not in alcohol.

GELATIO (Med.) signifies literally freezing, but is applied medicinally to that rigidity of body which happens in a catalepsy, as if the patient were frozen.

GELD (Law) geldum from the Teutonic geld, money, signified a tribute, but particularly a compensation for any thing, as-Were-geld, the value or price of a man slain.-Orfgeld, the value of a beast slain.-Angeld, the single value of a thing.-Twi-geld, double value, &c. GE'LDABLE (Law) liable to pay taxes. GELDER-ROSE (Bot.) a well-known flowering shrub, the Vibernum rosea of Linnæus. It derives its English name from Guelderland, whence it was first imported. GELIBACH (Mil.) a sort of superintendant or chief of the gebegis or armourers in Turkey. GELSE'MINUM (Bot.) a name for the jasmin. GEM (Min.) a common name for every jewel, or precious stone. Gems are distinguished generally into the pellucid and the semipellucid. [vide Gemma] GEMELLES (Her.) vide Bar-Gemel. GEMELLI (Anat.) vide Gemini.

GEMINI (Anat.) from geminus, twin; a name for a pair of muscles which move the thigh outward.

GEMINI (Astron.) diduo, the twins; a zodiacal constellation, or one of the twelve signs of the zodiac, representing Castor and Pollux, marked thus II. The stars in the

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 Munster, Clavius, Cluverius, Cellarius, Wolfius, &c. GEO'LOGY (Nat.) from y, the earth, and yo, a discourse; that branch of Natural History which treats of the structure of the earth in regard to the origin, constitution, and composition of its solid contents.

GEOMANCY (Ant.) yewpάvrsia, from y, the earth, and parsia, divination; a kind of divination performed by making circles on the earth, or by opening the earth. GEOMETRA (Ent.) a name given by Fabricius to a division of the genus Phalana, comprehending those insects of this tribe which have the antennæ 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 yewμsrpść, 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 A C B.-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, CDB and C DA, 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 OP 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 TO and UQ, fig. 4.-Divergent lines are those whose distance from each other becomes always greater, as O N and R S, 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, DBC. The sides which contain the angle are called the legs, as A B, B C, or D B, B C. 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 CD B, and C D A, 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 DBC, fig. 5, AEB, 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 FDE and FED, are equal to each other.- Scalene triangle, which has three unequal sides, as CA B, fig. 10.-Right-angled triangle, that which has a right angle, as M KL, 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 47th 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 perimeter consists of four sides. The principal of these figures are as follow: nainely-The square, i. e. a foursided figure, which has all its sides equal, and all its angles right angles, as A B C D, fig. 13.—An oblong square, a figure having all its angles right angles, but not all its sides equal, as ABC D, fig. 15.- A rhombus is a figure which has all its sides equal, but its angles are not all right angles, as EFGH, fig. 14.-A rhomboid is a figure which has its opposite sides equal to each other, but all its sides are not equal, and its angles are not right angles, as OPQ N, fig. 16.-A rectangle is any quadrilateral figure whose angles are right angles, such as fig. 15.-Parellelogram is any quadrilateral figure whose opposite sides are parallel, and consequently equal, as fig. 13, 14, 15, and 16.-The diagonal is the line which divides any parallelogram into two equal parts, as DB, fig. 15, and PN, fig. 16; and if any two lines, as EG and HK, be drawn parallel to A B and B C, then four parallelograms will be formed; namely, two, which are called parallelograms about the diameter, as H G and EK, fig. 15; and two which are complements, namely, AF and FC. Any one of the parallelograms about the diameter, together with the two complements, is called a gnomon, as the parallelogram HG, together with the complements À F, FC, is the gnomon, which is briefly expressed by the letters A G K or EHC. Every rightangled parallelogram or rectangle is said to be contained by the two lines which contain one of the right angles : thus, the rectangle A B C D is said to be contained by the lines B A and A D. Trapeziums are all other foursided figures, as fig. 17.

Multilateral Figures. Multilateral figures or polygons are those figures which consist of more than four sides, which are called pentagons, if they consist of five sides, as in fig. 18; hexagons, if of six sides, as fig. 19; octagons, if of eight sides, &c.

Figures are moreover distinguished into-equiangular, which have their angles equal; equilateral, when they have their sides equal each to each; regular, when they are both equiangular and equilateral; irregular, when they are not equiangular and equilateral.-Similar rectilinear figures are those which have their several angles equal each to each, and the sides about the equal angles proportional.-Reciprocal figures, i. e. triangles and parallelograms, are such as have their sides about two of their angles proportionals in such manner, that a side of the one is to a side of the other, as the remaining side of the second is to the remaining side of the other.

The Base of a figure is the lowest part of the perimeter, as KL, fig. 11. The vertex of a figure is the extreme point opposite to the base, as M. The altitude of a figure is the distance from the vertex to the base, as M K. A rectilinear figure is said to be inscribed in another rectilinear figure, when all the angles of the inscribed figure are upon the sides of that in which it is inscribed, each upon each, as ABDC, fig. 27. In like manner, a figure is said to be described about another figure, when all the sides of the circumscribed figure pass through the angular points of the figure, about which it is described, each to each.

Turvilinear Figures. Of curvilinear figures the most important is the circle.

Circle. A circle is a plane figure contained by one line, called the circumference or periphery, as BAD, fig. 20, which is at an equal distance from a certain point, called the centre, as C. All the lines drawn from this point to the circumference are equal, as CA, CE, CD.-The chord of a circle is the right line drawn from one point of a circumference to another, as A B, fig. 20.-The

diameter is a chord which passes through the centre, as A E: the semi-diameter, or the half of the diameter, is otherwise called a radius, as AC or CD.-The arc is any part of the circumference cut off by the chord, as AFB, fig. 20.-The arc of a circle is the measure of an angle: thus the angle BA C, in fig. 3, is measured by the arc D E.-The segment of a circle is that part which is bounded by an arc and its chord, as the segment AFBA, comprehended within the arc FB A, and the chord A B. It is called the greater segment when it is greater than a semicircle; and the lesser segment when it is less. The sector of a circle is the part, ACD, comprehended within the two radii, A C and CD, fig. 20. -The tangent to a circle is that line which touches a circle; but if produced, falls wholly without the circle, as HI, fig. 21, which touches the circle M L, in the point L. A circle is a tangent to another circle within if it lies wholly within the other circle, as L M touches the circle L N within, as in fig. 23. A circle touches another circle without, if, meeting the other circle, it falls wholly without it, as L M and L N touch each other in the point L, fig. 22.-Straight lines are said to be equally distant from the centre of a circle, when perpendiculars, drawn to them from the centre, are equal, as DE and FG, which have the equal lines C A and C B drawn perpendicularly to them, as in fig. 24.-An angle at the centre of a circle is that which forms the vertex of a triangle at the centre, as B G C, E HF, fig. 25, 26.-The angle at the circumference is that which forms the vertex of a triangle at the circumference, as B AC, EDF. The angle at the centre is double that at the circumference, as proved by Prop. 26, Book III, of Euclid's Elements. An angle is said to insist or stand upon the circumference, intercepted between the straight lines that contain the angle: thus the angles BA C, BG C, EDF, and EH F, stand on the circumferences B K C, ELF. A rectilinear figure is said to be inscribed in a circle when all the angles of the inscribed figure are upon the circumference of the circle, as A BDC, fig. 28. -A rectilinear figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle, as A B DC, fig. 29.-A circle is said to be inscribed in a rectilinear figure when the circumference touches each side of the figure, as A B D C, fig. 29.-A circle is said to be described about a rectilinear figure when the circumference of the circle passes through all the angular points of the figure, about which it is described, as ABDC, fig. 30.

Solid Figures. A solid is that which has length, breadth, and thickness. That which bounds a solid is a plane, or a plane superficies.-A straight line is perpendicular, or at right angles to a plane when it makes right angles with every straight line meeting it in that plane, as A B in fig. 36. A plane is perpendicular to a plane when the straight lines drawn in one of the planes perpendicularly to the common section of the two planes are perpendicular to the other, as A B C, fig. 37.—The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which a perpendicular to the plane drawn from any point of the first line above the plane, meets the same plane, as AC B, fig. 38.-The inclination of a plane to a plane is the acute angle contained by two straight lines drawn from any the same point of their common section at right angles to it, one upon one plane, as A B, and the other upon the other, as BC, fig. 39. Two planes are said to have the same or like inclination to one another, which two other planes have, when the said angles of inclination are equal to one another.-A