A Figure, is that which is inclofed 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 fuch 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.

XIX.

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.

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

14, 15, 16, 17.

XXI.

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

XXII.

Quadrilateral Figures, are thofe 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 fided 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

DEFINITIONS.

XXVI.

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

XXVII.

Likewife, among those fame trilateral figures:

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

XXVIII.

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

XXIX.

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.

1

7

AR

DEFINITIONS.
XXXIII.

Rhomboid, is that which has its oppofite fides equal to one another, but all its fides are not equal, nor its angles right angles. F.g. 25.

XXXIV.

All other four fided figures befides thefe, are called Trapefiums. F'g. 26.
XXXV.

Parallel ftraight Lines, are fuch as are in the fame plane, and which being produced ever so far both ways, do not meet. Fig. 27.

It is for this reafon that every quadrilateral figure whofe appofite fides are parallel, is called a Parallelogram. Fig. 25.

LET it

ET it be granted, that a straight line may be drawn from any one point to any other point.

II.

That a terminated straight line may be produced to any length in a straight line.

III.

And that a circle may be described from any center, at any distance from that center.

Two

W O magnitudes, which are equal to the fame third, are equal to one another.

If the line A is equal to the line B, and the line C equal to the fame line B, the line A will be equal to the line C. Fig. 1.

II.

If to equal magnitudes be added equal magnitudes, the wholes will be equal. If to the line AD be added the part DE, and to the line BF, which is equal to the line AD, be added the part FG, equal to the part DE, the wholes AE, BG, will be equal to one another.