# 546 BCE

## Thales’ theorem

## The book of science

Tom Sharp

Tom Sharp

Thales of Miletus geometry |

- Take the ends of the diameter of a circle, A and C,
- and consider any other point on the circle, B.
- then the triangle ABC is a right triangle.
- Consider the two isosceles triangles OAB and OBC.
- The base angles of an isosceles triangle are equal,
- and the three angles of a triangle add up to 180 degrees.
- Therefore, two α plus two β equals 180 degrees,
- so it is clear that α plus β equals 90 degrees,
- which is a right angle.

- Solomon chose wisdom
- so he could be an adequate king,
- not knowledge of the number
- of moving spirits in heaven,
- nor whether a prime mover exists,
- nor whether a necessary conclusion
- can be drawn from a necessary premise
- and a contingent premise,
- nor whether a triangle
- can be constructed in a semicircle
- that does not have a right angle.

- A point has no diameter,
- a line no width.
- A straight line has no deviation,
- a circle only one curvature.
- We do not assume these ideals;
- we do not pretend them.
- We say that any point, line, or circle
- drawn on wax or clay
- is only an approximation,
- only a crude representation.
- When our loved ones are with us,
- they can never be perfect.
- But true love is true,
- and can never deviate.

Like the Pythagorean theorem, Thales’ theorem was known by Indian and Babylonian mathematicians before Thales learned of it.

Dante’s theorem is a paraphrase of

ParadisoCanto 13, lines 94-102.See also in

The book of science:Proof of the Pythagorean theorem—PythagorasReadings on wikipedia: