El Problema 47 de Euclides

The Symbolism of the 47th Problem of Euclid also called the 47th Proposition of Euclid.

Most Masonic books, simply describe it as "A general love of the Arts and Sciences". However, to leave its explanation at that would be to omit a subject which is very important... not only of Pythagoras's Theory, but of the Masonic Square.

We are told that Euclid, (the Father of Geometry), who lived several hundred years after Pythagoras, worked long and hard to solve the 3:4:5: ratio puzzle. It is said by some that he then sacrificed a hecatomb (a sacrificial offering to God of up to 100 oxen or cattle). However, historically, it is believed that the Egyptians and Babylonians understood the mathematical usefulness of the 3:4:5 ratio long before Euclid.

The math is the key to understanding this symbol's broader and universal meaning.

The Pythagorean Theorem, also known as the
47th Problem of Euclid or 3:4:5:

"In any right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse." (the hypotenuse of a right triangle...which is the longest "leg"...or the 5 side of the 3:4:5:).

The Right Triangle, below, shows the sides of 3, 4 and 5. The angle created between the 3 (side) and the 4 (side) is the Right angle of the square.

A little later, when we begin to build it, (with sticks and string), you will place your sticks at the 3 corners of this Right triangle.

47th Problem of Euclid

The square of 3 is 9. 

The square of 4 is 16. The sum of 9 and 16 is 25. (25 represents the hypotenuse). 

The square root of 25 is 5. 

Therefore, the ratio is written: 3:4:5:

When we write down the square of the 1st four numbers (1, 4, 9 and 16), we see that by subtracting each square from the next one, we get 3, 5 and 7. 

Ok, let's try it.

1, 4, 9, 16

4-1 =3

9-4 = 5

16-9 = 7


3:5:7: These are the steps in Masonry. They are the steps in the Winding Stair which leads to the Middle Chamber and they are the number of brethren which form the number of Master Masons necessary to open a lodge of:

Master Mason: 3

Fellow Craft: 5

Entered Apprentice: 7

These are the sacred numbers.

OK, stay with me now...the major math is over.

Learn more: 
http://www.masonic-lodge-of-education.com/47th-problem-of-euclid.html

http://en.wikipedia.org/wiki/Pythagorean_theorem

http://burningtaper.blogspot.com/2006/04/new-masonic-interpretation-of-euclids.html