OF CURVATURE OF LENGTH. 333 53 A Curvature is a portion of a line past operations of the mind, or upon or oblong body which is curved. past events. To Incurvate is to turn from a right line or from a straight form by : curving. Incurvate, (adj.) curved inward or upward. To Bow is to bend downward. A Bow (bou) is an inclination or downward bending of the head in token of respect. A Bow (bo) is, 1. An instrument of Recurvate, curved downward. war made of wood or other elastic To BEND is to change the direc-substances, and having been forcibly tion of a line or the form of an ob- bent, is kept in that position by a long body by curving it. To WIND is to bend irregularly, as a road that adapts itself to the diversities of the surface. string attached to each end. 2. TO MEANDER is to wind after the bow. manner of a crooked stream. NOTE.-Meander was the ancient name of a Arch, 1. A curved structure of stone or brick supporting its own very crooked river in Asia Minor, and hence the weight. 2. A curvature in the form English verb to meander. A SPIRAL is a curve that either makes a succession of widening circuits on a plane around a fixed point, or which rises as it winds, as when we commence winding a thread at the bottom of a cylinder or cone, and pass it round in successive turns till it reaches the top. A Waving line consists of a succession of alternating waves. A Serpentine line or path, winds like a serpent. Sinuous, winding in and out after the manner of a coast indented with small bays. (L. sinus, a bay.) FLECTO [flexum], to bend. Hence, Flexion, the act of bending. Flexure, a bending turn. Flexible, that may be bent, flexible rod. Flexile, easily bent. An twig is flexile. of an arch. To PRODUCE a straight line is to lengthen it out at one end. (L. pro, forward; and duco, to draw.) To EXTEND is to lengthen at one (L.) or both ends. (L. ex, out; and tendo, to stretch.) as a osier To Inflect is to turn from a direct line or course. to To Deflect a moving body is turn it aside from its proper or regular course. (de, from.) To Reflect a ray of light is turn it back from the surface on which t falls. (re, back.) To Reflect, as a mental act, is to turn the thoughts back upon the SHORT, having but little length. To Curtail is to shorten by cutting off. A name may be curtailed by cutting off some of the final letters. Persons may be curtailed of their privileges by the exercise of superior authority. (L. curtus, short, and Fr. tailler, to cut.) BREVIS, short. (L.) Hence, Brevity, 1. Shortness, applied to time; as the brevity of human life. 2. Shortness in discourses or writings; or the expression of thoughts in few words. Brief, 1. Short in duration; as a 54 OF SURFACES OF BREADTH-OF ANGLES. brief period. 2. Short in discourse from which a person is unable to or writing. extricate himself; or, in other words, Abbreviate, to shorten by omitting a strait is a tight place. viate a word. or retrenching a part; as, to abbre-8. Accidental Properties of Surfaces. ROUGH, abounding in inequalities of surface. ABREGER, to shorten. (Fr.) Hence, Abridge, to make shorter; as, to abridge a literary work. 6. Of Surfaces. A SURFACE is that which has length and breadth without thickness. (L. superficies, from super, over; and facies, the face.) A PLANE surface is such, that if two points assumed at pleasure be connected by a straight line, that line will be wholly in the surface. A PLANE is a plane surface. (L. planus, level.) A CONVEX Surface is such that if any two points of the surface be joined by a straight line, that line will lie wholly beneath the surface. The surface of a globe is convex. ROUND, having a convex surface. any two points be joined by a straight line, that line will lie wholly above the surface. The inner surface of a hollow sphere is concave. The sky has the appearance of being concave. (L. concavus, hollow.) 7. Of Breadth. BREADTH is the less of the two dimensions of a surface. Broad, having great breadth. WIDE, affording abundant room; as a wide passage; a wide garment. Narrow, having but little breadth. Strait, narrow in the sense of not being sufficiently wide to afford a free passage, or to be comfortably roomy; as, a strait gate, a straitjacket. NOTE.-A strait-jacket is an apparatus for confining the arms of a madman. A Strait is, 1. A narrow passage either on land or in the ocean; as the Straits of Thermopyla; the Straits of Gibraltar. 2. A difficult situation in which a person is at a loss as to the course proper to be pursued. 3. A distressing situation NOTE. The idea of roughness is figuratively applied to the temper, to the manners, to certain flavors, sounds, etc. ASPER, rough. (L.) Hence, Asperity, roughness; as, asperity of temper. 2. Exasperate, 1. To roughen the temper; that is, to make angry. To increase in severity; as, to exasperate a disease. SMOOTH, free from inequalities of surface. NOTE.-Smoothness is predicated, figuratively, of sounds and tastes, of the manners, of language, etc. TO POLISH is to impart a glossy smoothness by friction." POLITE, polished in manners. (L. polio [politum], to polish.) TO BURNISH is to polish metals. An EVEN surface is one that is free from eminences and depressions, (or hights and hollows.) A LEVEL surface is one that coincides with, or is parallel to, the plane of the horizon." The ALTITUDE (Hight) of a triangle is the perpendicular drawn from the B vertex to the base. An OBLIQUE ANGLE is one that is either acute or obtuse. (L., obliquus, nclined.) 10. Of Plane Figures. Plane Figures are of two classes: 1st. RECTILINEAR FIGURES, which are bounded by straight lines. 2d. CURVILINEAR FIGURES, which are bounded by curve lines. 11. Of Rectilinear Figures. A TRIANGLE is a figure which has three angles, and, consequently, has also three sides. (L., tri, three; and angulum, an angle.) A QUADRILATERAL has four sides. (L., quadri, four; and latus [lateris], a side.) A PENTAGON has five angles, and is, consequently, a five-sided figure. Gr., TETE [pente], five; and [gonia], an angle.) A HEXAGON has six angles and sides. (Gr., [her], six.) A HEPTAGON has seven angles and sides. (Gr., ira [hepta], seven.) An OCTAGON has eight angles and sides. (Gr., TO (Gr., xTo [octo], eight.) A NONAGON has nine angles and sides. (L., non for novem, nine.) A DECAGON is a figure which has ten angles and sides. Gr., Sexx [deca], ten.) A DODECAGON is a figure which has twelve angles and sides. (Gr., dodexx [dodeca], twelve.) A POLYGON is a figure which has many angles and sides. (Gr., Texus [polys], many.) 12. Of Plane Triangles. The BASE of a triangle is the side on which it stands. The LEGS of a triangle are the two sides besides the base. The HYPOTENUSE is the side opposite to the right angle of a right-angled triangle. (Gr., o [hypo], under; and Tavura [teinousa], stretching, be cause it is stretched under or opposite to the right angle.) An OBTUSE-ANGLED TRIANGLE has one obtuse angle. An ACUTE-ANGLED TRIANGLE has all its angles acute. TRIGONOMETRY is the science of the measurement of triangles. (Gr., gyvas [trigonos], a triangle; and urge [metreo], to measure.) 13. Of Quadrilaterals. A TRAPEZIUM is a four-sided figure which has neither pair of its opposite sides parallel. (Gr., Tganov [trapezion], a little table.) A TRAPEZOID has one pair of its opposite sides parallel and" the other not. (Gr., рasov [trapezion], a trapezium; and ados [eidos], à resem|blance.) OF QUADRILATERALS-OF THE CIRCLE. A PARALLELOGRAM is a four-sided | A HYPERBOLA is a cu figure which has both pairs of its opposite sides parallel. (Gr., прямих with two opposite. branches, and may be formed by cutting, with a plane, two equal cones which are placed opposite to each other, ver NOTE 1.-The ellipse, the parab hyperbola are called the three Coni cause they are formed by the sectio of a cone by a plane. NOTE 2.-The planets all revolv orbits. NOTE 3.-A stone projected obliq describes a parabola. NOTE 4.-If a planet should rec projectile impulse as would be bare to prevent its return toward the su would be a parabola. NOTE 5.-If a planet should recei impulse than in the foregoing case, scribe a hyperbola. A CYCLOID is a curve desc a point P in the circumference of a circle which rolls/A along an ex tended straight line A B unt completed a revolution. (Gr [cyclos], a circle; and des a resemblance.) NOTE.-The number of regular ge curves is unlimited; but the foregoing most simple, and are, at the same time, useful. 15. Of the Circle. figure through; and TP [metreo], to A PARABOLA is a section of a cone straight line drawn from the ce to the circumference. (L., rad the spoke of a wheel. Plural ra A CHORD is a straight line than a diameter, having its extre ties in the circumference, as D (Gr. xpdn [chorde], a string.) OF THE CENTER-OF THE CIRCUMFERENCE-OF SOLIDS. An ARC is a portion of the circumference, as DF E. (L., arcus, a bow.) A SEGMENT is a portion of a circle intercepted between an arc and a chord, as DE F. (L., segmentum, a piece cut off.) A SECTOR is a portion of a circle included between two radii, as CDF E. (L., seco [sectum], to cut; be cause the sector is a portion cut out.) A QUADRANT is the fourth part of a circle. (L., quadrans, a fourth.) 16. Of the Center. CENTER, the middle point of any thing. (Gr., Tsw [centeo], to prick.) Concentrate, to bring to a common center. (con, together.) Concentric, having a center; as, concentric circles. 18. Of Solids. 57 A SOLID is a figure which has length, breadth, and thickness. A CUBE is a solid bounded by six equal square sides. A PRISM is a solid whose ends or opposite bases are parallel, similar, and equal figures, and whose sides are parallellograms. A CYLINDER is a long, round body of uniform diameter, whose bases are equal and parallel circles. (Gr., por [cylindros], a roller.) A PYRAMID is a solid whose base may be any rectilineal figure, the other sides being triangles whose called the apex. vertices meet at a common point A CONE is a solid having a circular base, and tapering gradually to the common top like a sugar loaf. A SPHERE is a solid, every point of a point within called the center. ECCENTRIC, deviating or departing whose surface is equally distant from from the center. Fig. Departing from the usual course; as, eccentric conduct; an eccentric genius. NOTE. The orbits of the planets are, more or less eccentric, because they have not the sun in the center; and the orbits of the comets are exceedingly so, since in one part of their orbits they approach very near to the sun, and in another part recede to an immense distance. An eccentric person is one who, in his conduct, does not move, planet-like, in a nearly circular orbit around the center of strict propriety, but, comet-like, at one time he approaches too near to that center, and, at another time, flies off to too great a distance from it. 17. Of the Circumference. A CIRCUMFERENCE is a curve described by a movable point carried in a plane around a fixed point in the same plane, in such a manner that the movable point is always at the same distance from the fixed point. (L., circum, around; and fero, to carry.) A PERIPHERY is any curve described in a plane by a movable point carried around a fixed point, whether the distance between the points continues the same, or varies; as, the periphery of a circle, ellipse, et (Gr., T [peri], around; and Lphero], to carry.) 19. Of the Platonic Bodies. The PLATONIC BODIES are five regular geometrical solids, first described by Plato. They are the tetrahedron, hexahedron, octohedron, dodecahedron, and icosahedron. A REGULAR TETRAHEDRON is a solid bounded by four equilateral and equal triangles. (Gr., TT2 [tetra], four; and ipa [hedra], a base or side.) A REGULAR HEXAHEDRON is a solid bounded by six equal squares. (Gr., [hex], six.) NOTE. The regular hexahedron is the same with the cube. A REGULAR OCTAHEDRON is a solid bounded by eight equilateral and equal triangles. (Gr., TO [octo], eight.) A REGULAR DODECAHEDRON is a solid bounded by twelve regular and equal pentagons. (Gr., Sud [dodeca], twelve.) A REGULAR ICOSAHEDRON is a solid bounded by twenty equilateral and equal triangles. (Gr., xoa [icosvi], twenty.) NOTE.-No other regular solids bounded by plane surfaces, than the foregoing, are possible. |