Euclid

What has been affirmed without proof can also be denied without proof.

c. 300 BCE (attributed much later) — Widely attributed, but a direct primary source from Euclid's time is elusive.

Strange & Unusual Confirmed

The laws of nature are but the mathematical thoughts of God.

Uncertain (misattributed) — Often attributed, but widely considered misattributed, possibly originating from Kepler or Plato.

Strange & Unusual Confirmed

What do I gain by learning these things?

c. 300 BCE — Reported response to a student who, after learning the first theorem, asked what he would get by lea…

Strange & Unusual Unverifiable

A point is that which has no part.

c. 300 BCE — Definition 1, Book I of 'Elements'

Strange & Unusual Confirmed

A line is breadthless length.

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

Strange & Unusual Confirmed

A surface is that which has length and breadth only.

c. 300 BCE — Definition 5, Book I of 'Elements'

Strange & Unusual Confirmed

The postulates are not self-evident, but they are necessary for the development of geometry.

c. 300 BCE — Implied understanding from the structure of 'Elements', though not a direct quote.

Strange & Unusual Unverifiable

If equals be added to equals, the wholes are equal.

c. 300 BCE — Common Notion 2, from 'Elements'

Strange & Unusual Confirmed

If equals be subtracted from equals, the remainders are equal.

c. 300 BCE — Common Notion 3, from 'Elements'

Strange & Unusual Confirmed

Things which coincide with one another are equal to one another.

c. 300 BCE — Common Notion 4, from 'Elements'

Strange & Unusual Confirmed

Let it be granted that a straight line may be drawn from any one point to any other point.

c. 300 BCE — Postulate 1, from 'Elements'

Strange & Unusual Confirmed

Let it be granted that a finite straight line may be produced to any length in a straight line.

c. 300 BCE — Postulate 2, from 'Elements'

Strange & Unusual Confirmed

Let it be granted that a circle may be described with any center and any radius.

c. 300 BCE — Postulate 3, from 'Elements'

Strange & Unusual Confirmed

Let it be granted that all right angles are equal to one another.

c. 300 BCE — Postulate 4, from 'Elements'

Strange & Unusual Confirmed

And that, if a straight line falling on two straight lines make 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.

c. 300 BCE — Postulate 5 (Parallel Postulate), from 'Elements'

Strange & Unusual Unverifiable

If a straight line be drawn from the ends of a straight line, it will be a triangle.

c. 300 BCE — Paraphrased from implications within 'Elements', not a direct definition.

Strange & Unusual Unverifiable

Magnitudes which can be made to coincide are equal.

c. 300 BCE — Implied from Common Notion 4, 'Elements'

Strange & Unusual Unverifiable

The properties of figures are derived from their definitions and postulates.

c. 300 BCE — Implied methodology of 'Elements'

Strange & Unusual Unverifiable

There are infinitely many prime numbers.

c. 300 BCE — Theorem 20, Book IX of 'Elements'

Strange & Unusual Unverifiable

The greatest common divisor of two numbers can be found by successive division.

c. 300 BCE — Euclidean Algorithm, Book VII of 'Elements'

Strange & Unusual Unverifiable

Sayings by Euclid