Euclidian Geometry Glossary

A Euclid-based Glossary of Terms for Book 13

*Definition derived from both Euclid and the Webster's New World Dictionary.

(Plane) Angle
The inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Bisect*
To divide into equal parts.
Circle
A plane figure contained by one curved line such that all the straight lines falling up it from one point among those lying within the figure are equal. And the point is called the center on the circle.
Circumference*
The outer boundary of a circular area.
Cube
A solid figure contained by 6 equal squares.
Decagon*
A polygon having 10 angles and 10 sides.
Diameter
Any straight line drawn through the center and terminated by the circumference of the circle and the straight line bisects the circle.
Equilateral Triangle
That which has its three sides equal.
Equiangular*
Having all angles equal.
Dodecahedron
A solid figure contained by 12 equal and equilateral triangles.
Figure
That which is contained by any boundary or boundaries.
Hexagon*
A polygon with 6 angles and 6 sides.
Icosahedron
A solid figure contained by 20 equal and equilateral triangles.
Irrational*
Not capable of being expressed exactly as the ratio of two integers.
Lemma*
A proposition proved, or sometimes assumed, to be true and used in proving a theorem.
Line
Breadthless length. A line will have length, but it will not have width or breadth.
Octahedron
A solid figure contained by 8 equal and equilateral triangles.
Parallel
Straight lines (in the same plane) going indefinitely in both directions and do not meet in either direction.
Pentagon*
A polygon with 5 angles and 5 sides.
Perpendicular
When a straight line stands on a straight line and makes the adjacent angles equal to one another and at right angles, the straight line standing on the other is called the perpendicular to the other.
Plane Surface
A surface which lies evenly with the straight lines on itself.
Point
That which has no part. A point has no width, length, or breadth, but has an indivisible location.
Polygon*
A closed plane figure, especially with more than four sides and angles.
Proportional
Magnitudes that have the same ratio.
Pyramid
A solid figure, contained by planes, which is constructed from one plane to one point.
Radius*
a straight line extending from the center of a circle/sphere to the circumference of the circle/sphere.
Ratio
A sort-of relation in respect of size between two magnitudes of the same kind.
Rectangle*
Any four-sided figure with 4 right angles.
Right Angle
When a straight line standing on a straight line makes the adjacent angles equal to one another.
Square
That which is both equilateral and right-angled.
Segment (of a circle)
The figure contained by a straight line and a circumference of a circle.
Semicircle
a figure contained by the diameter and the circumference cut off by it. And the center is the same as that of the circle.
Sphere
A figure resulting from state when there is a fixed diameter of a semi-circle and the semi-circle is carried around and restored to the same position.
Straight Line
A line which lies evenly with the points on itself.
Surface
That which has length and breadth only.
Triangle*
A plane having 3 sides and 3 angles.
Vertex*
The intersection of 2 sides of a plane figure.