---
book: 1
part: "definitions"
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:1"
license: "CC-BY-SA-4.0"
---

# Book I Definitions

## Definition 1

A *point* is that which has no part.

## Definition 2

A *line* is breadthless length.

## Definition 3

The extremities of a line are points.

## Definition 4

A *straight line* is a line which lies evenly with the points on itself.

## Definition 5

A *surface* is that which has length and breadth only.

## Definition 6

The extremities of a surface are lines.

## Definition 7

A *plane surface* is a surface which lies evenly with the straight lines on itself.

## Definition 8

A *plane angle* is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.

## Definition 9

And when the lines containing the angle are straight, the angle is called *rectilineal*.

## Definition 10

When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is *right*, and the straight line standing on the other is called a *perpendicular* to that on which it stands.

## Definition 11

An *obtuse angle* is an angle greater than a right angle.

## Definition 12

An *acute angle* is an angle less than a right angle.

## Definition 13

A *boundary* is that which is an extremity of anything.

## Definition 14

A *figure* is that which is contained by any boundary or boundaries.

## Definition 15

A *circle* is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another;

## Definition 16

And the point is called the *centre* of the circle.

## Definition 17

A *diameter* of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle.

## Definition 18

A *semicircle* is the figure contained by the diameter and the circumference cut off by it. And the centre of the semicircle is the same as that of the circle.

## Definition 19

Rectilineal figures are those which are contained by straight lines, trilateral figures being those contained by three, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.

## Definition 20

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

## Definition 21

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acuteangled triangle that which has its three angles acute.

## Definition 22

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

## Definition 23

Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.