Of LINE S. A Line is a Length without Breadth. Fig. 2. The Line is nothing more than the Paffage Plate 1. made by a Point from one Place to another, and would be imperceptible, were it not defcribed by the natural Point, which by its Course represents it to us, as AB. CD. EF. There are as many Sorts of Lines, as the Point is fufceptible of different Movements. A Right Line, is that which is equally comprized between its two Extremities: Or, it is that which a Point defcribes in its Paffage directly from one Place to another, without any Turnings, as AB. A Curve Line, is that which departs from a direct Oppofition to its Extremities, by one or more Turnings or Windings, as CD. When this Line is described by the Compaffes, it is called Circular, as E. A Mix'd Line, is that which is both Right and Curve, as the Line V. Fig. 4. The Line receives feveral other Denominations according to its various Pofitions and Properties. A Perpendicular, is a right Line, which falls upon or is raised from another, making the Angles on each Side of it equal; AB. Plate 1. A Plummet Line, is that which defcends directly downwards, without inclining either to the Right or Left, and which, were it infinitely prolonged, would pafs through the Center of the World; C. The Horizontal, is a Line in equilibrium, or that inclines equally in all its Parts; DE. Parallel Lines, are those which are oppofite each other, and at equal Distances; H. An Oblique, is a Line which is neither horizontal nor a Plummet, but flanting or acrofs; FG. The Bafe, is the Line upon which any Figure refts; IL. Sides, are the Lines which enclofe any Figure; I. N. L. M. A Diagonal, is a Right Line which crofles any Fig. 5. Figure to two oppofite Angles of the fame Figure; AB. Plate 1. A Diameter, is a Right Line which croffes any Figure through its Center, and is terminated by its Circumference CD. A A Spiral Line, is a Curve Line which departs from its Center, and the farther, in Proportion as it turns round itfelf; EF. A Chord or Subtenfe, is a Right Line extended from one End of an Arch to the other End thereof; G. H. An Arch, is Part of a Circle or Circumference; GIH. A Tangent Line, is that which touches fome Figure without paffing into it, and without being able to pass into it or cross it, even though it were prolonged; LM. A Secant, is a Line drawn from the Center of a Circle, cutting it, and meeting with a Tangent without; L O. M ́O. If two Lines meet at their Extremities, they either meet directly or indirectly. If directly, they then make but one Line; if indirectly, they constitute an Angle. Geom. Plate 1. Fig. 6. A Of ANGLES. N Angle is the indirect Course of two Lines to the fame Point; or rather, it is the Space contained between the indirect Courfe of two Lines to the fame Point; as A. B. C. When this Courfe is defcribed by two Right Lines, the Angle is called Rectilinear, and when it is defcribed by two Curve Lines, it is called Curvilinear; but when it is defcribed by two Lines, one of which is a Right and the other a Curve, it is called Mixtilinear. A. Rectilinear, or Right-lin'd Angle. The Rectilinear Ángle, according as it is more or lefs open, receives particular Denominations, as Right, Acute, Obtufe; therefore the Terms Rectilinear, Curvilinear, and Mixtilinear, have regard only to the Nature of the Lines; and those of Right, Acute, and Obtufe, refpect only the Quantity of Space contained between the faid Lines. A Right-Angle, is when one of its Lines is perpendicular upon the other; EDF. An Acute Angle, is that which is less open than the Right; EDG. An Obtufe Angle, is that which is more open than the Right; FDG. The Letter D. in the middle fhews the Angle. Definition Definition of a SUPERFICIES. A Geom. Plate Superficies, is that which has Length and Breadth, without Thickness. 1. Fig. 7. According to Geometricians, as the Line is a Production of the Point, fo the Superficies is a Production of the Line. Thus, fuppofing the Line E F was from each of its Extremities drawn to G H, it constitutes the Superficies E F, G H, which is an Extent between Lines, that has Length and Breadth, but not Depth or Thickness; and this is frequently called a Surface; or if it is confidered with regard to its Extremities, which are the Lines by which it is encompassed, it is then called a Figure. If a Superficies is raised, it is called convex; if it is hollow, it is called concave; and if it is flat and even, it is called a Plane. B. Convex Superficies. C. Concave Superficies. D. Convex, Concave, and Plane Superficies. So far we have only fhewn the Conftruction of the Plane Superficies. The Termination is the Bounds or Limits of any thing. The Point is the Termination of the Line: the Line is the Termination of the Superficies: and the Superficies is the Termination of a Body. S Of Rectilinear Superficies or Figures. Uperficies have particular Names according to A. is a Trigon or Triangle, Fig. of three Sides. Geom. Plate 1. Fig. 8. All All these Figures are alfo called by the general Name of Polygons. Of TRIANGLES. Nature of their Angles, and the Difpofition of their Sides: thus, L is a right angled Triangle Plate 1. Fig. 9. A that is, it has One right Angle Of FIGURES of four Sides. Is a Square, a Figure of four equal Sides, . and four right Angles. B. a Long-Square, a rectangled Superficies, which has its Angles Right, but not its Sides equal. C. a Rhumbus, or a quadrilateral Figure, whofe four Sides are equal, but not its four Angles. D. a Rhomboides, whofe oppofite Sides and Angles are equal, tho' the Figure is neither equiangular nor equilateral. B. D. are alfo Parallelograms, which are quadrilateral Figures, whofe oppofite Sides are parallel. E. a Trapezium, two of whofe Sides only are parallel, the two others equal. F. a Trapezoid, whofe Sides and Angles are unequal. All other Figures of more than four Sides, are called by the general Name of Multilaterals. Plate 1. 10. Fig. Of CURVES, or Curvilinear Figures. A Is a Circle, which is a Superficies or Figure perfectly round, defcribed from a Center whofe Circumference is equally distant from it. The Circumference is the Extremity of the Circle, or the Line which inclofes it. B. an Oval, which is a curvilinear Figure defcribed from feveral Centers, and all whofe Diameters divide equally in two. C. an Ellipfis, which is alfo a curvilinear Figure defcribed from feveral Centers, but in form of an Egg, and of |