I. A Point is that which hath no parts, or which hath no See Notes. magnitude.

II.
A line is length without breadth.

III.

The extremities of a line are points.

IV.

A straight line is that which lies evenly between its ex-
treme points.

V.
A superficies is that which hath only length and breadth.

VI.
The extremities of a superficies are lines.

VII.
A plane superficies is that in which any two points be- See N.

ing taken, the straight line between them lies wholly in that superficies.

B

See N.

VIII. 66 A plane angle is the inclination of two lines to one

“another in a plane, which meet together, but are 66 not in the same direction.”

IX.

A plane rectilineal angle is the inclination of two

straight lines to 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 6 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;

that which is contained by AB, DB, is named the angle ABD, or DBA; and that which is contained by (DB, CB, is called the angle DBC, or CBD; but, if 6 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. “ A term or boundary is the extremity of any thing."

XIV.
A figure is that which is enclosed by one or more boun-
daries.

XV.
A circle 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 See N.

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.

B 2

XXV.
An isosceles triangle is that which has only two sides

equal.

ΔΔΔ

XXVI.
A scalene triangle, is that which has three unequal sides.

XXVII.
A right angled triangle, is that which has a right angle.

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

sides equal, and all its angles right angles.

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.

See N.

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 produced to any length in a straight line.

III. And that a circle may be described from any centre, at

any distance from that centre.

AXIOMS.

I. Things which are equal to the same thing, are equal to one another.

II.
If equals be added to equals, the wholes are equal.

III.
If equals be taken from equals, the remainders are equal.

IV. If equals be added to unequals, the wholes are unequal.

V.

If equals be taken from unequals, the remainders are

unequal.