I.
Point is that which hath no parts, or which hath no magnitude. Set Motes,

II.
A line is length without breadth.

III.
The extremities of a line are points.

IV.
A straight line is that which lies evenly betwecn its extreme 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 being taken, the

See Y. straight line between them lies wholly in that superficies.

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.”

IX. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the fame straight line.

А

Set N.

'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; 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 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 an-
gles 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 inclosed by one or more boundaries.

XV.

Book 1. 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 cer. tain point within the figure to the circumference, are equal to one another.

XVI.
And this point is called the center of the circle.

XVII. A diameter of a circle is a straight line drawn thro' the center, atid See Ni terminated both ways by the circumference.

XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cót 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 fided figures, an equilateral triangle is that which has three
equal sides.

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

Book I.

ΔΔΔ

XXVI.
A scalene triangle, is that which has three unequallides.

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

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

AAA

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 fides equal.

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

not right angles.

Ses N.

XXXIII.
A rhomboid is that which has its opposite sides equal to one ano.

ther, but all its sides are not equal, nor its angles right angles,

XXXIV.

Book 1. All other four fided 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.

L

POSTULAT E S.

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 center, at any distance

from that center,

A X I 0 MS.

I
HINGS which are equal to the same are equal to one an.
other.

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 unequat.

VI.
Things which are double of the same, are equal to one another.

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

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