The science of geometry is founded on certain axioms, or self-evident truths; it is introduced by definitions of the various objects which it contemplates, and the properties of which it investigates and demonstrates, such as point:, lines, angles, figures, surfaces and solids :—lines again are con sidered as straight or curved ; and in their relation to one another, either as inclined or parallel, or as perpendicular : angles, as right, oblique, acute, obtuse, external, vertical, &c. : —figures, with regard to their various boundarie:, as triangles, which are in respect to their sides equilateral, isosceles, and scalene, and in reference to their angles. right-angled, obtuse angled, and acute-angled; as quadrilaterals, which compre __ hend the parallelogram, including the rectangle and square, the On un bus and rhomboid, and the trapezium and trapezoid; as multilateral: or polygons, comprehending the pentagon, hexagon, heptagon, &e.; and as circles ;—also as solids, in cluding a prism, parallelopipedon, cube, pyramid, cylinder, cone, sphere, and the frustum of either of the latter.
For practioal ge•anet•y, the fullest and most complete treatises are those of Mallet, written in French, but without the demonstrations; and of Sch \venter and Cantzlerus, both in high Dutch. In this class are likewise to be ranked
Clavius's, Tacquet's, and Ozanain's Practical Geometries; De la _Hire's Ecole des Arpenteurs ; Geodwsia ; Hartman Beyers's Stercometria ; \'oigtel's Geometria Sub terranea ; all in high Dutch : ilulsius, Galilens,Goldmannus, Schenck, and Ozanam, on the Sector, &e. &e. An excellent treatise on practical geometry, particularly with reference to the study of architecture and perspective, was published some years ago by i1 r. Peter Nicholson, and still holds its ground in public estimation, notwithstanding the numerous works on the subject which have appeared front time to time. The following short essay on Practical Geometry, containing the formation of plain figures arising from straight lines and circles, will also be found exceedingly useful in the study of architectural construction. Curves of variable curvature, as those arising from the sections of a cone by a plane, will be found under their respective heads; as, Cosic SECTIONS, ELLIPSIS, &C.