Definitions
Definitions
Definitions
Postulates
Common Notions
100
That which has no part.

What is a point?

100
The extremities of a surface.

What are lines?

100

Breadthless length.

What is a line?

100

That all right angles...

...are equal to one another.

100

The whole is...

...greater than the part.

200

Figures which are contained by straight lines.

What are rectilineal figures?

200

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.

What is a circle?

200

That which has length and breadth only.

What is a surface?
200

To describe a circle...

...with any center and distance.

200

If equals be subtracted from equals...

...the remainders are equal.

300

A line which lies evenly with the points on itself.

What is a straight line?

300

That which is contained by any boundary or boundaries.

What is a figure?

300

A quadrilateral which is both equilateral and right-angled.

What is a square?

300

To draw a straight line...

...from any point to any point.

300

Things which are equal to the same thing...

...are also equal to one another.

400

Any straight line drawn through the center and terminated in both directions by the circumference of the circle.

What is a circumference?

400

The inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.

What is a plane angle?

400

A rectilineal figure contained by three lines.

What is a trilateral figure?

400

To produce a finite straight line...

...continuously in a straight line.

400

If equals be added to equals...

...the wholes are equal.

500

A quadrilateral figure which has its opposite sides and angles equal to one another, but is neither equilateral nor right-angled.

What is a rhomboid?

500

A quadrilateral figure which is equilateral but not right-angled.

What is a rhombus?

500

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

What are parallel lines?

500

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles...

...the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

500

Things which coincide with one another...

...are equal to one another.

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