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VIII.

A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

A plane rectilineal A

angle is the in

clination of two

straight lines to B

IX.

D

CE

one another, which meet together, but are not in the same straight line.

N.B. When several angles are at one point B, any one of them is expressed 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: Thus, the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA; and that which is contained by DB, CB, is called the angle DBC or CBD; but if there be only one angle at a point, it may be expressed by a letter placed at that point, as the angle at E.

X.

When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right

angle; and the straight line which stands on the other, is called a perpendicular to it. XI.

An obtuse angle is that which is greater than a right angle.

XII.

An acute angle is that which is less than a right angle.

XIII.

کے

A term or boundary is the extremity of any thing.

XIV.

A figure is that which is enclosed by one or more boundaries.

XV.

Acircle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

XVI.

And this point is called the centre of the circle.

XVII.

A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

XVIII.

A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter.

XIX.

A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.

XX.

Rectilineal figures are those which are contained by straight lines.

XXI.

Trilateral figures, or triangles, by three straight lines.

XXII.

Quadrilateral, by four straight lines.

XXIII.

Multilateral figures, or polygons, by more than four straight lines.

XXIV.

Of three-sided figures, an equilateral triangle is that which has three equal sides.

XXV.

An isosceles triangle is that which has

only two sides equal.

XXVI.

A scalene triangle is that which has three unequal sides.

XXVII.

A right-angled triangle is that which has a right angle; and the side opposite the right angle is called the hypothenuse.

XXVIII.

An obtuse-angled triangle is that which has an obtuse angle.

XXIX.

An acute-angled triangle is that which has three acute angles.

XXX.

Of four-sided figures, a square is that which has all its angles right angles, and all its sides equal.

XXXI.

An oblong is that which has all its angles right angles, but has not all its sides equal.

XXXII.

A rhombus is that which has all its sides equal, but its angles are not right angles.

XXXIII.

A rhomboid is that which has its opposite sides equal to one another, but all its sides are

not equal, nor its angles right angles. XXXIV.

All other four-sided figures, besides these, are called trapeziums.

XXXV.

Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

POSTULATES.

I.

Let 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 duced to any length in a straight line.

III.

pro

That a circle may be described from any centre, at any distance from that centre.

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