Euclid

Father of geometry

Ancient influential 90 sayings

Sayings by Euclid

If four magnitudes be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means.

c. 300 BCE — Theorem 16, Book VI of 'Elements'

Strange & Unusual Unverifiable

Similar triangles are to one another in the duplicate ratio of their corresponding sides.

c. 300 BCE — Theorem 19, Book VI of 'Elements'

Strange & Unusual Unverifiable

To construct a regular pentagon in a given circle.

c. 300 BCE — Proposition 11, Book IV of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

To inscribe a regular hexagon in a given circle.

c. 300 BCE — Proposition 15, Book IV of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

A number is a multitude composed of units.

c. 300 BCE — Definition 2, Book VII of 'Elements'

Strange & Unusual Unverifiable

A prime number is that which is measured by a unit alone.

c. 300 BCE — Definition 11, Book VII of 'Elements'

Strange & Unusual Unverifiable

If a number be the least that is measured by any prime numbers, it will not be measured by any other prime number except those originally measuring it.

c. 300 BCE — Theorem 33, Book IX of 'Elements'

Strange & Unusual Unverifiable

The elements of geometry are derived from a small set of axioms and postulates.

c. 300 BCE — Implied structure of 'Elements'

Strange & Unusual Unverifiable

A straight line is that which lies evenly between its extreme points.

300 BC — Definition in 'Elements'

Strange & Unusual Unverifiable

The extremities of a line are points.

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

The extremities of a surface are lines.

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

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.

300 BC — Definition in 'Elements'

Strange & Unusual Unverifiable

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.

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

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

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

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

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

A boundary is that which is an extremity of anything.

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

And the point is called the center of the circle.

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

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

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

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

300 BC — Definition in 'Elements'

Strange & Unusual Confirmed

Rectilinear 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.

300 BC — Definition in 'Elements'

Strange & Unusual Unverifiable