getable, or mineral kingdoms. All the species of a genus agree in certain characteristics. GEOCENTRIC pluce of a planet, is the place in which it appears to us from the earth, supposing the eye to be fixed there, or it is a point in the ecliptic to which a planet seen from the earth is referred, GEOGRAPHY, the description of the surface of the earth, its natural divisions, and local characteristics. The fundamental principles of geography are the spberical figure of the earth, its rotation on its axis, its revolution round the sun, and the position of the axis or line round which it revolves, with regard to the celestial luminary; whence it follows that astronomy is the key of all geographical knowledge. See EARTH. In general terms, the earth is termed a perfect sphere, in which case, the diameter from north to "south would be precisely equal to the diameter from east to west; but it having been found that the latter exceeds the former by thirty-six miles, the shape of the earth is more truly denominated an oblate spheroid : by which is to be understood a globe, the upper and lower parts of which are flattened. When any portions of the heavens are called the right or left, the expression is to be understood according to the profession of the person by whom it is used; because, according to that, bis face is supposed to be turned toward a certain quarter. A geographer is conceived to stand with his face to the north, because the northern part of the earth is best known ; an astronomer looks toward the south, to observe the celestial bodies as they ap : proach the meridian ; the antient augurs, in ob serving the flight of birds, looked toward the east, while the poets turned to the Fortunate Isles : in books of geography, therefore, by the right hand we must understand the east: in those of astronomy, the west ; in such as relate to augury, the south ; and, in the writings of the poets, the north. Agreeably with these observations, the upper part of a map is the north ; the lower, the south; the right-band the east ; and the left the west. See GLOBE. GEOLOGY, bas for its object the structure and for: mation of this globe: it, of course, embraces the consideration of the materials of which it is com posed, and the circumstances peculiar to its original formation, as well as the different states under which it has existed, and the various changes which it has undergone. GEOMETRY, the art of measuring quantity of every kind; whether length, breadth, heighth, or depth. The parts of geometry are, 1. “Longimetry," or the art of measuring lines; Planimetry," or the art of measuring sura 3. Stereometry,” or the art of measuring so 2. 56 faces; lids; 4. “ Trigonometry," or the art of measuring not only surfaces, but heights and unknown distances. The instruments used in geometry are the scale and the compass: the scale to draw and measure lines ; the compass to describe circles, of which the ܪܐ use is the measurement of angles. The scale is usually divided into feet, inches, and lines; the circle is divided into 360 parts or degrees; and when' an angle of 10, 20, or any other number of degrees are mentioned, 10, 20, or the specific number of parts of a circle divided into 360 degrees is intended. The origin of this science is always attributed to Egypt, where it is said to have been produced by the necessity of ascertaining the boundaries of landed property, which are every year effaced by the inundations of the Nile. From the time of Euclid, who died three hun. dred years before the Christian era, to that of Purback and Müller, who died in the fifteenth century, geometry was neglected. Since its revival, it has benefited by the illustrious labours of Neper, Descartes, Newton, and Leibnitz. Geometry is of the utmost value as a branch of general knowledge, since it induces precision of thinking by admitting nothing but evident and indubitable demonstration. Geometry is distinguished into theoretical and practical. Theoretical or speculative geometry treats of the various properties and relations in magnitudes, demonstrating theorems : and practical geometry is that which applies those speculations to the uses of life in the solution of problems. The science of geometry depends wholly on definitions and axioms. The definitions in geometry are clear, plain and universal, such as these': “A point has neither parts nor magnitude :" "" A line is length without breadth or thickness." " A surface has length and a breadth only." "A solid is any thing that bas length, breadth and thickness," “ An angle is the opening or inclination of two lines meeting in one point. “ If one line standing on another makes the angles on both sides equal, those angles are right angles, and the line standing on the other is a perpendicular to that on which it stands." 6 A triangle is a plain figure, bounded by three lines or sides." “ A circle is a plane figure, bounded by a curve line called the circumference, every part of wbich is equally distant from a point within called the centre." An axiom is a manifest truth not requiring a demonstration: The following are examples of axioms, “ Things equal to the same thing are equal to one another :" “ The whole is greater than any of its parts, and equal to all its parts.” “ If equal things , ” “ be taken from equal things the remainders will be equal." “ Magnitudes which coincide with one another, or which exactly fill the same space, are equal to one another." A proposition is something proposed either to be done or to be demonstrated, and is either a problem or a theorem. A problem is something proposed to be done, of which the following are examples. Ex. 1. To divide a given line, as A B, into two equal parts : Plate GEOMETRY, Fig. 1. From the points A and B as centres, and with any opening of the compasses greater than half the given line A B, describe the ares cutting each other in cc, and draw the line cc: the point x, where the kine cc cuts A B, is the middle point required. Ex. 2. To raise a perpendicular to a given line CD, fig. 2, at A. Takeany two equal distances Ab, A d, and from the points b and d with any opening of the compasses greater than b A, describe the arcs cutting each other in c, and draw the line A c, which is perpendicular to C D. Ex. 3. To bisect the angle B, or to divide it into two equal angles. Fig. 3. From the point B, with any radius, describe the arc A C, and from the points A and C with the same radius describe the arcs cutting one another at b, and draw 6 B, which will bisect the angle, ABC. Ex. 4. To describe an equilateral triangle, A B C, that is, a triangle whose three sides are each equal to a given line. Fig. 4. Let A B be the given line: from the points A and B, with an opening of the compasses equal to A B, describe the arcs, cutting each other in C, and from the point of intersection draw. A C and C B, and the thing is done. Ex. 5. To describe a triangle whose sides shall be equal to three given lines, fig. 5. Let the lines be A, B, C. Take B as the base A B, then from A, with an opening of the compasses equal to C, and from B, with an opening of the compasses equal to A, describe the arcs cutting one another in C; draw the lines C A and C B, and the thing is done. |