2

A ftraight Line, is that which lies evenly between its extreme points (A, F,). Fig. 3.

This definition is imperfect, since it presents no essential character of a Straight line; for which reason, Euclid could make no use of it: it is no more quoted in the body of the work. He is obliged to bave recourse to other primi. ples (for example, to the 12th axiom) as often as be bas occasion of employing truths, which depend on a perfect definition of a straight line.

V.

A Superficies, is that which hath only length and breadth. Fig. 4.

VI.

The Extremities of a Superficies, are lines (AB, CD, AC, BD,). Fig. 4.

VII.

A Plave Superfices, or fimply a Plane, (AD) is that which lies evenly between i's extremities (AB, CD, AC, BD,). Fig. 5.

This definition is liable to the same exceptions as the fourth.

1

A

DEFINITIONS.

VIII.

Plane Angle, is the incliratior of two lines (AB, BC,) to one another, which meet together, and which are situated in the same plane. Fig. 6.

IX.

A Plane Rectilineal Angle, is the inclination of two straight lines to one another. Fig. 6.

N. B. When feveral angles are at one point B, any one of them is expreffed by three letters, of which the letter that is at the vertex of the angle, that is at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of those straight lines, and the other upon the other line.

Χ.

When a straight line (AB) standing on another stright line (CD) makes the adjacent angles (ABD, ABC,) equal to one another, each of the angles is called a right angle; and the straight line (AB) which stands on the other (CD) is called a perpendicular. Fig. 7.

ΧΙ.

An Obtufe Angle, (ABC) is that which is greater than a right angle (EBC). Fig. 8.

XII.

An Acute Angle, (ABC) is that which is less than a right angle(EBC). Fig. 9.

XIII.

A Term or Boundary, is the extremity of any magnitude.

A2

DEFINITIONS.
XIV.

is that which is inclosed by one or more boundaries. Fig. 10.

XV.

A Circle, is a plane figure contained by one line, which is called the circumference, and is such that all straight lines (CB, CD,) drawn from a certain point (C) within the figure to the circumference, are equal to one another. Fig. 11.

XVI.

This point (C) is called the center of the circle, and the straight lines (CB, CD,) drawn from the center to the circumference, are called the Rays. Fig. 11.

XVII.

A Diameter of a Circle, is a straight line (DB) drawn thro' the center, and terminated both ways by the circumference. Fig. 12.

XVIII.

A Semicircle, is the plane figure (DEB) contained by a diameter (BD) and the part of the circumference (DEB) cut off by the diameter (DB). Fig. 12.

ΧΙΧ.

A Segment of a Circle, is a figure contained by a straight line (AF) called a Chord, and the part of the circumference it cuts off (AGF, or AEF) called an Arc, Fig. 12.

Rectilineal Figures, are those which are contained by straight lines. Fig. 13,

14, 15, 16, 17.

ΧΧΙ.

Trilateral Figures, or triangles, are those which are contained by three straight lines. Fig. 13, 16, 17.

XXII.

Quadrilateral Figures, are those which are contained by four straight lines.

Fig. 14.

XXIII.

Multilateral Figures, or polygons, are those which are contained by more than four straight lines. Fig. 15.

XIV.

As to three sided figures in particular:

An Equilateral Triangle, is that which has three equal fides. Fig. 16.

XXV.

An Ifofceles Triangle, is that which has only two fides equal. Fig. 17.

A

DEFINITION S.

XXVI.

Scalene Triangle, is that which has three unequal fides. Fig. 18.

XXVII.

Likewife, amorg those same trilateral figures :

A Right angled Triangle, is that which has a right angle. Fig. 19.

XXVIII.

An Obtuse angled Triangle, is that which has an obtuse angle, (A). Fig. 20.

ΧΧΙΧ.

An Acute angled Triangle, is that which has three acute angles, (A, B, C,). Fig. 21.

XXX.

After the fame manner in the species of four sided figures:

A Square, is that which has all its fides equal, and all its angles right angles. Fig. 22.

XXXI.

An Oblong, is that which has all its angles right angles, but has not all its fides equal. Fig. 23.

XXXII.

A Rhombus, is that which has all its fides equal, but its angles are not right angles. Fig. 24.