Book I.

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

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

X.
A figure is that which is inclosed by one or more boundaries.

XI.“
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 circuir-
ference, are equal to one another.

XII.
And this point is called the centre of the circle.

XIII.
A diameter of a circle is a straight line drawn through the

centre, and terminated both ways by the circumference.

XIV.

A femicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter,

XV.

B 2

Book I.

XV.
Re&ilineal figures are those which are contained by straight
lines.

XVI.
Trilateral figures, or triangles, by three straight lines.

XVII.
Quadrilateral, by four straight lines.

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

XIX.
Of three fided figures, an equilateral triangle is that which
has three equal sides.

XX.
An isosceles triangle is that which has only two fides equal.

АДА

XXI.
A scalene triangle, is that which has three unequal fides,

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

XXIII.
An obtuse angled triangle, is that which has an obtuse angle,

XXIV

Book I.

XXIV.
An acute angled triangle, is that which has three acute angles.

XXV.
Of four fided figures, a square is that which has all its-fides

equal, and all its angles right angles.

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

XXVII.
A rhombus, is that which has all its fides equal, but its angles

are not right angles.

XXVIII.
A rhomboid, is that which has its opposite fides equal to one

another, but all its sides are not equal, nor its angles right
angles.

XXIX.
All other four fided figures besides these, are called Tra-

peziums.

Book 1.

XXX.
Parallel straight lines, are such as are in the same planė, and

which, being produced ever so far both ways, do not meet.

POSTULATES.

L

I. 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 centre, at any distance from that centre.

A X I O M S.

M

N.

T

I.
HINGS 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.

VI.

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

VII. Things which are halves of the same thing, are equal to one another.

VIII. Magnitudes which coincide with one another, that is, which exa&ly fill the same space, are equal to one another.

IX.
The whole is greater than its part.

X.
All right angles are equal to one another.

“ Two straight lines, which interfect one another, cannot be

“ both parallel to the same straight line."