Pythagorean Tetraktys and Masonic Delta by Arturo Reghini: “Every whole, or sum of four things, is called tetractys, after a Pythagorean word, and there are several tetractys.
But that we now have dealt with is the tetractis par excellence, which Pythagoreans took their oath under. A Speusippus fragment notes that ten contains within itself the linear variety, plane and solid number, because one is a point, 2 a line, 3 a triangle and 4 a pyramid (1).
We are continuing our translation from Arturo Reghini “ Sacred numbers in masonic Pythagorean Tradition” 1947. First chapter.
Jew Philo (2), repeating Pythagoreans concepts said that four are the limits of things: point, line, surface and solid, and Geminus says that arithmetic is divided into the linear theory of numbers, the numbers theory, the plane numbers theory, and the solid numbers theory.
Perfection, or the completion of universal manifestation, is achieved with ten which is the sum of the numbers up to four. The decade has it all, like the unit, which contains all potentially. The name δεκάς is just for that receptive property δεχάς.
This finding is the result of the limit set for the development of numbers from the three-dimensional quality of space, and would lead to the recognition of the same properties of four and ten even if the spoken numbering, instead of being a decimal numbering, was for example a duodecimal based or based ternary numbering.
As a matter of fact we note the coincidence. The reason why Greek, Latin, Italian spoken numbers and so on is decimal, is that human kind has ten fingers, which are of great help in the account (with your finger), so that in writing Latin and ancient Greek unit was represented by a finger identified by the letter I. The last finger is the tenth, and then 10 is perfect. Five has special representation in the two writings, in greek by the initial word of pente, in latin by the palm or open hand span later identified with the letter V, as in latin world the writing of number had been ahead of the knowledge and use of the alphabet; and 10 is represented in greek by the letter Δ, decade initial, and which has the shape of an equilateral triangle. While in Latin is represented by two open and opposite hands, that’s to say by the sign later identified with the letter X. These signs are enough in the greek and latin writing of numbers to writing or representation of numbers up to one hundred, which is carried in H of the original greek word Hecaton, and in Latin a sign then identifiable with the initial of centum.
Both Pythagorean tetractys and spoken numbering highlight the importance of the number ten in completely independent ways. And this is not the only correlation between four and ten because greek language forms the names of the numbers from ten to 99 using the names of the first ten numbers, introduces a new name to indicate 100, and then a new name to indicate the thousand, finally a new and final name for the tens of thousands. This very word μύριοι, μυρίοι if differently marked, indicates an indefinitely great number. In short, greek language has only four names, after nine, to designate the first four powers of ten and stops to the fourth power, as the sum of the integers ends with four in tetractys.