The Areas, or imaginary Planes, of the Top and Bottom of the Mortise, are parallel to each other, but not equal.
Its Two opposite Sides are equal, but not parallel, by reason of their Inclination to each other upwards, which is the Bevel hereafter to be described.
The Two Ends are neither parallel nor equal, because the Hinder-end D is perpendicular to the Top and Bottom, and the Fore-end oblique, and therefore longer.
When Two opposite Sides, or Surfaces, are inclined to each other upwards, I call that Inclination a Bevel; but when they are inclined downwards, I call it a Bevel revers’d.
The Line a e, being the Bottom, or Base, of the Hinder-end D, by being longer than the Line l m, shews that the Mortise is bevel.
The Two prick’d Lines m n and l o, with the Line l m, and Part of the Line a e, make a rectangled Parallelogram, which shews the exact Depth of the Mortise, and forms on each Side of it a rectangled Triangle, the one m e n, and the other l o a; which Triangles being similar and equal, and their acute Angles at l and m being each of Four Degrees, make the whole Bevel, or Inclination of the Sides of the Mortise, to be of Eight Degrees, their Hypothenuses being the same with the Sides of the Mortise.
This End D, being raised up to its Place, will be at right Angles with the Plane of the Top and of the Bottom of the Mortise; which, being both rectangled Parallelograms, prove that Bevel, or Angle of Inclination, to be the same from one End to the other of the Sides, which Sides are the Hypothenuses of those Two Triangles: But this could not be proved by the Triangles in the opposite End C; because the Bases being the same with the other, and having their Legs longer, the vertical Angles at k and i are more acute. The Legs are longer; because the End C, when in its Place, is not at right Angles with the Top and Bottom of the Mortise, as the End D is.
The next thing to be described in the Mortise, is the Bore, great Hole, or Perforation; which is best shewn in the Side of a Mortise of a Wheat-drill, being larger, as in [Fig. 3.] wherein c e b d is the great Hole, and is a Section of an hollow Cylinder, that passes through the Mortise, with its Axis parallel to the Edges of the Ends of the Mortise: This Cylinder, being cut by the Side of the Mortise obliquely, and not parallel to its Base, is an Ellipse.
The prick’d curve Line is a Circle parallel to the Base of the Cylinder, and the curve Line b d c e is the Ellipsis; and this Curve is more or less elliptical (or oval) in proportion to the Angle of Inclination, or Bevel, of the Sides of the Mortise.