THE

ELEMENTS

OF

EUC L I. D.

BOOK I.

A

A

DEFINITION S.

I.

Point is that which hath no parts, or which hath no mag- See Notes. nitude.

II.

A straight line is that which lies evenly between its extreme

points.

V.

A fuperficies is that which hath only length and breadth.

VI.

A plane superficies is that in which any two points being taken, See Na

the straight line between them lies wholly in that superficies.

VIII.

"A plane angle is the inclination of two lines to one another Sce N

" in a plane, which meet together, but are not in the fame

"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.

Ν. Β.

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.'

Χ.

When a straight line standing on ano-
ther 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."

Χιν.

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

XV.

:

XV.

A circle is a plane figure contained by one line, which is cal-
led the circumference, and is such that all straight lines
drawn from a certain point within the figure to the circum-
ference, are equal to one another :

Book T.

XVI.

And this point is called the centre of the circle.

XVII.

A

A diameter of a circle is a straight line drawn through the Se Ni

centre, and terminated both ways by the circumference.

XVIII.

A femicircle is the figure contained by a diameter and the part

of the circumference cut off by the diameter.

XIX.

"A fegment 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.

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

XXIV.

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

XXV.

An isofceles triangle, is that which has only two fides equal.
XXVI,

Book 1.

XXVI.

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

XXVII.

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

XXVIII.

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

ΧΧΙΧ.

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

xxx.

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

XXXIII.

See N. A rhomboid, is that which has its opposite sides equal to one another, but all its fides are not equal, nor its angles right angles.

XXXIV.