The 47th Problem of Euclid

Who was Euclid? Of the 465 mathematical and scientific problems proposed by Euclid, why is the 47th problem so important? What should the 47th problem of Euclid remind us of in our Masonic journey?

Euclid was a Greek mathematician and generally recognized as the “Father of Geometry.” Very little information can be found regarding Euclid’s background but according to some Arabic authors, he is said to have been born in Tyre circa 330 B.C. It is also claimed that he came from a very wealthy family. Euclid contributed greatly to the field of mathematics. He is known to have taught in the Great Schools of Ancient Egypt during the reign of Ptolemy I, successor of Alexander IV, son of Alexander the Great. Euclid’s book Elements, is a collection of 13 books on the subjects of mathematics and geometrics. It offers definitions, theorems, and proofs and includes the first known source of geometric algebra and finding the square root of a number. His works were heavily influenced by Pythagoras, Aristotle, Eudoxus, and Thales.

In order to understand the meaning behind the problem you must first understand the problem. It simply states that the square of the sides of right angled triangles (legs) is equal to the square of the side containing the right angle (hypotenuse). This is also referred to as The Pythagorean Theorem, due to its discovery by our ancient friend and brother, Pythagoras.

The 47th problem of Euclid serves as a basis of common measurements for architects. Since a time of antiquity, builders have used this theorem, sometimes called the Rule of 3:4:5, in squaring a room. Engineers use the theorem to tunnel through mountainsides so that both tunnel shafts would meet in the center. By the study of this theorem, astronomers are provided with a mathematical equation whereby study the distances of the sun, moon and celestial bodies, thereby fixing the durations of times, seasons and cycles. Even the sailors used this theorem to study the longitude and latitude as well as true time.

In the study of Masonic emblems, we learn that 47th problem of Euclid helps us to define and measure the universe around us, all framed by the Supreme Architect of the Universe. The square, as an emblem for masonry, is the base needed for any solution. As a mason serves his position in lodge (3:4), he becomes more complete (3:4:5). Further research into the 47th problem of Euclid will reveal to a well-studied mason many of the ancient mysteries of the fraternity.