Demonstrative Math800 - 336 BC

Thales A circle is bisected by any diameter The base angles of an isosceles triangle are

equal Two triangles are congruent if they have two

angles and one side in each respectfully equal.

Thales (continued)

The vertical angles formed by two intersecting lies are equal.

Any angle inscribed in a semicircle is a right angle.

Thales Anecdote 1

Olive oil press

Thales Anecdote 2

Mule with salt

Thales anecdote 3

Marriage

Pythagoras ( 570-500 BC)

Pythagoras ( 570-500 BC)

Pythagorean TheoremFounded Pythagorean School

Brotherhood Whole number is the cause of various

qualities of man and matter Exaltation and study of numbers

Pythagorean Arithmetic

Amicable numbers Two numbers such that each is the sum of

the proper divisors of the other 284,220

Pythagorean Arithmetic

Perfect numbers Number is equal to the sum of its proper

divisors 6,28,496

Pythagorean Arithmetic

Deficient numbers Number exceeds the sum of its divisors 8

Pythagorean Arithmetic

Abundant numbers Number is less than the sum of its proper

divisors 12

Figurate numbers

Triangular numbers

Figurate numbers

Square numbers

Figurate numbers

Pentagonal numbers

Irrational Magnitudes

Rational numbersNumber lineIrrational numbersSquare root of 2Mortal blow to Pythagorean philosophy