47th Problem of Euclid

In this article, I would like to tell you what is the 47th problem of Euclid and how it is related to Freemasonry. So, if you are interested to know it then go through the whole article because it will be so informatics and interesting.

One of the oldest surviving fragments of Euclid’s Elements, circa AD 100

How to square your own square?

Here we are going to tell you that how can you square your own square with the help of this theory. 

The 47th problem of Euclid, also referred to as the 47th proposition of Euclid, or even the Pythagorean Theorem, is represented by what appears to be 3 squares.  

First of all we are going to understand what 47th problem of Euclid is. And how it works:

47th problem of Euclid 

47th problem of Euclid
47th problem of Euclid

To non-Freemasons, the 47th problem of Euclid may be rather mysterious. Most wonder in the significance of this odd-looking, 3-box emblem on a sheet of Masonic jewelry. 

Most Masonic books, only describe it as” A general romance of their Arts and Sciences”. However, to leave its explanation at that would be to omit a topic that’s extremely important… not just in Pythagoras’s Theory, but of those Masonic Square.

Masonic Symbol
Square and Compasses

What Are All These 3 Black Boxes and Why Are They Important To Freemasons?  

As we mentioned that Euclid, the Father of Geometry, that lived a few hundred years following Pythagoras, worked hard and long to address the 3:4:5: ratio puzzle. It’s said by some that he then sacrificed a hecatomb (a sacrificial offering to God of up to 100 oxen or cows).

However, historically, it’s believed that the Egyptians and Babylonians understood that the mathematical utility of the 3:4:5 ratio extended before Euclid.  The mathematics is the trick to understanding this emblem’s broader and universal meaning.  

The Pythagorean Theorem and The 47th problem of Euclid

Let me tell you one thing that the Pythagorean Theorem, too called the 47th problem of Euclid or even 3:4:5:

In any Perfect triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse! 

The hypotenuse of an ideal triangle which is the best “leg” or the side of this triangle are 3, 5, and 4, respectfully.

The angle made between the 3 (side) along with also the 4 (side) will be the perfect angle of the square. 

Somewhat later, when we begin to construct it, (with sticks and string), you will place your rods at the 3 corners of the Right triangle.  

According to the 47th problem of Euclid;

  • The square of 3 is 9. 
  • The square of 4 is 16.  
  • The sum of 9 and 16 is 25.
  • The square root of 25 is 5. 

Hence, the ratio is, 3:4:5:

Measuring steps in Masonry Lodge

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

Ok, let us try it.1, 4, 9, 164-1 =39-4 = 516-9 = 73:5:7:  

All these are the steps in Masonry. They are the measures in the Winding Stair which contributes into the Middle Chamber and they are the number of brethren which kind the amount of Master Masons required to start a lodge of:

Master Mason: 3Fellow Craft: 5Entered Apprentice: 7

These are the sacred numbers. OK, stick with me now the significant math is finished.  

The essence of the Pythagorean Theorem (also referred to as the 47th problem of Euclid) is about the significance of establishing an architecturally true (correct) base based on usage of this square.  

Why is this significant to speculative Masons who merely have a representational square and not the true square (the tool) of a surgical Mason?  

The 47th problem of Euclid will be the mathematical ratio (the knowledge) that allows a Master Mason to:

“Square his square after it gets from the square.”   

I learned that!  

You’re saying to yourself: “What’s this so important to ME in today’s world unless I am a carpenter? Home Depot is only a few miles apart.”  

How to Make a Fantastic Square

Now we are going to discuss that how can make a fantastic square using the 47th problem of Euclid.

The knowledge of how to form a perfect square minus the slightest possibility of error was accounted of the highest importance in the art of construction from the time of the Harped on a pate, (and before). 

Harped on a pate, literally interpreted, means “rope stretchers” or “rope attachments” of early Egypt (long until Solomon’s Temple was built).   

The Harped on a pate were architectural specialists that were called in to lay out the baselines of buildings. They have been highly proficient and relied on astronomy (the celebrities) as well as mathematical calculations to form perfect square angles for every building.  

Historical preview of 47th problem of Euclid and Freemasonry

In the Berlin memorial is a deed, composed on leather, dating back to 2000 B.C. (long until Solomon’s period), that informs the job of these rope stretchers.  

Historically, a building’s cornerstone was placed in the northeast corner of this building. Why from the northeast?  

The ancient builders first laid outside the south and north lines by observation of the stars and the sun, especially the North Star, (Polaris), they believed at the time to be fixed in the skies.  

Only after putting out an ideal North and South line would they use the square to set up perfect East and West lines due to their foundations.  

The 47th problem of Euclid established those authentic East and West lines, so the rope stretchers can ascertain a perfect 90-degree angle to the North/South line that they had established using the celebrities.   

If you are interested 

If you want to perform this yourself, it’s truly quite simple and once you get the necessary bits together, are an excellent “Show-and-Tell” educational schooling piece within your lodge. 


The instructions are below, but it is simpler to adhere to the directions in a step-by-step fashion (with string and sticks in hand) than it is to only read them for a whole comprehension.   

Better yet, print numbers 1 through 4, below, and then get your sticks and your string prepared. 

The 47th problem of Euclid contrary to the Harped on a pate, you haven’t any way to set up true North and South, unless you use a compass. But a compass is not necessary for this demonstration.  

After understanding, however, you will be able to create a perfect square with just sticks and string, as our ancestors did.  

You may need 4 thin sticks that are strong enough to stick into soft dirt, 40 inches of series along with a black magic marker. In fact, any period will work, but this size is very manageable.   

The larger the foundation which the Mason wished to construct, obviously, the longer his rope (string) would need to be.  

Place your 1st stick flat on the floor so that its ends point north and south.  

Then Have a series (it’s much more laborious if you use rope) and tie knots inside, 3 inches apart. 

This will split the series into 12 equal divisions. Tie the two ends of this string together again remember that from knot-to-knot it has to be 3 inches apart. The divisions between knots must be appropriate and equal or it won’t work.  

Your string’s total duration is 36″. After you have tied the finished knot, then you may cut off the surplus 4″ of series.  

If you’ve got more than 4″ of string left or less than 4″ of series left, you have to re-measure the spans between your knots.  

Your string is currently circular and has 12 knots and 12 branches between the knots. 

Euclid’s 47th Issue Note: 

The Operative Masons of older, used rope, however, as much of the period of the rope are within the knot, if you use rope, you need to use an extended piece, quantify each branch, tie your knot, and then measure your next 3-inch branch before you reduce the length of rope, instead of marking the whole rope when it’s lying flat then linking your knots.  

Stab your own 2nd stick from the ground near either end of the North/South stick and organize a knot in the stick.   

Stretch 3 divisions away from it in almost any way (9 inches) and add the 3rd rod in the floor, then put the 4th rod so that it falls on the knot between the 4-part and the 5-part division (12 inches).   

This forces the creation of a 3:4:5: proper triangle. The angle between the 3 units and the 4 units is also of necessity, a square, or a proper angle.  

Now, go your 3rd and 4th sticks until they become an ideal angle (90 degrees) for your North/South stick.  

You currently have not only the ability to square your own square but to put a geometrically correct basis for your new foundation!  

Here’s the rest of the story Euclid’s 47th proposition, the Forty-Seventh Problem of Euclid

In the modern world with this easy geometric 3:4:5 ratio of how to create a 90 degree, Proper Angle:

  • Man can reach out into space and measure the distance of these stars in lighting years! 
  • He can questionnaire land, mark off boundaries, and construct everything on Earth. 
  • He can construct houses, churches, and buildings, and with the understanding of the easy ratio. 
  • He can begin digging on other sides of a mountain and dig a straight tunnel through the middle of it, which meets exactly at the center! 
47th Problem of Euclid 3

The 47th problem of Euclid as a symbol of Freemasonry

The 47th problem of Euclid represents such a perfect symbol of Freemasonry encompassing both science and art that the easy knowledge of it involves breathtaking awe to which we may simply bow our heads in reverence at the perfection, the universality, and the infinite wisdom of what is given to us by God.  

With the understanding of the simple geometric ratio, (provided from the 47th problem of Euclid), the word “Eureka!” Nearly palls in expressing the basic powers that our creator has bestowed upon us!  

And it all begins by simply learning how to square your own Square!

Oh! …, and one last thing you have also learned but maybe it quite difficult to recognize it.

This Is the Reason the old classic, wooden carpenter squares that you have observed or have heard about having a longer leg.  

  • Their “thighs” were created using the”3″ and”4″ section of the 3:4:5 ratio, the 5 will be the hypotenuse with the 47th problem of Euclid.  
  • Equal length “thighs” on modern-day (carpenter) squares are comparatively “new” tech.

Masonic Symbol for the 47th Issue of Euclid

Now, take another look at the Masonic symbol for the 47th problem of Euclid, above. You are going to understand that the square on the top-left steps 3 units on every one of its sides; the square on the top-right measures 4 components on each of its sides and the base square steps 5 units on each of its sides.  

Now you can see the right triangle (white space in the center) that is encompassed with the 3″ poles”.  

From that day forward, after you see this picture image denoting the 47th problem of Euclid. This Masonic symbol, it will not only look like 3 odd-shaped black boxes for you. 

You will see the 3:4:5 ratio along with the square (right angle) in them and understand that you have the capability to square your square in your Middle Chamber.


In this article, I tried to mention all about the 47th problem of Euclid. I think this post is enough to understand what the 47th problem of Euclid is and how it works. But if you are still confused about it and want to learn more about it then you can comment below and ask whatever you want. We will try to give you the best information about it. 

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