Pythagoras of Samos (c.600BC) very likely gleaned megalithic number science on his travels around the “Mysteries” of the ancient world. His father, operating from the island of Samos, became a rich merchant, trading by sea and naming his child Pythagoras; after the god of Delphi who had “killed” the Python snake beneath Delphi’s oracular chasm, now a place of Apollo. The eventual disciples of Pythagoras were reclusive and secretive, threatening death on anybody who would openly speak of mysteries, such as the square root of two, to the uninitiated. It can be seen from the previous post that many such “mysteries” were natural discoveries made by the megalithic astronomers, when learning how to manipulate number without arithmetic, through a metrological geometry unfamiliar to the romantic sacred geometry of “straight edge and compass”.

As previously stated, the vertex angles of right triangles whose longer sides are integer in length, are *angular invariants *belonging to the invariant ratio of their sides. To create a {11 14} angle one can use any multiple of 11 and the same multiple of 14 to obtain the invariant angle whereupon, the hypotenuse and base will shrink or grow together in that ratio: any length on the “14” line is 14/11 of any length below it on the “11” base line and visa versa.

If one enlarges the base line to being** 99** then the diagonal of the square side length 99 will be **140**, which is 99 times the square root of two. In choosing, as I did, to enlarge 91 (the quarter year) to 9 x 11 = 99, I encountered the cubit3/2 feet of any sort, such as 12/7 {1.714285}, 1.5 Royal feet of 8/7 feet, but sometimes a double foot, such as the Assyrian {9/10} of 1.8 feet. of the Samian (“of Samos”) foot of 33/35 feet, as follows. When Heraclitus, also of Samos, visited the Great Pyramid he gave its southerly side length as 800 “of our feet” and 756 English feet (the measured length) needs to be divided by 189 and multiplied by 200 to obtain such a measurement, giving a Samian foot of 189/200 (=**0.945** feet) which is 441/440 of the Samian root foot of 33/35 feet. 33/35 x 3/2 = **99/70 **(1.4143) feet but its inverse of** 35/33 **x 4/3 = 140/99 feet.

There is then no doubt about Samos as being a center in the Greek Mysteries since, the form of the Greek temple seems first to evolve there. For example, 10,000 feet of 0.945 feet equal **945 feet**, the number of days in **32 lunar months**. The *Heraion *of Samos (pictured above) has been shown to have had pillars around a platform (a *peristyle*), and an elongated rectangular room (a *cella*), involving megalithic yards and a 4-square geometry cunningly linking lunar and solar years, to alignmentsA name special to Carnac's three successive groups of parallel rows of stones, starting above Carnac called Le Menec, Kermario, and Kerlescan and another found near Erdevan. to the Moon’s minimum using the {5 12 13} second Pythagorean Triangle. (diagram at top is from f*igure 5.9 of *Sacred Geometry: Language of the Angels).

The reason for the Samian (*lit.* “of Samos”) foot being 33/35 feet appears to be that as a cubit of **99/70 **feet, or **√2** =1.4142, it is the twin of 140/99 as 1.41. In the geometrical world such foot ratios were exact, relative to the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000].; which is the root of the Greek module and of all other rational modules, such as the Royal of 8/7 feet. Such cubits could measure across the diagonal the same number as the side length in English feet. Such measures became essential for building of rectangular temple structures in Greece and further east, but when the metrological geometry, of square and circle in equal perimeter, was the focus, 140 in the diagonal can use 99 in the base (or side-length of the square).

If we remember that the 99 length must be rooted from the shared center of the square and equal circle then, the side length of the square must be twice that, or 198. This means that the perimeter of the square must be 4 times that, equal to **792**, at which point readers of John Michell’s books on *models of the world *will recall that the diameter of the mean earth can be presented, within an equal perimeter design, if each unit is multiplied by 720 units of 10 miles, my own summary being in my recent Sacred Geometry book , chapter 3 on measuring the Earth. This model Michell called **The Cosmological Prototype**, where the mean earth diameter is (quite accurately) 7920 miles.

If the square of 198 feet is rolled out into a single line, it “*becomes” *the mean diameter of the Earth in units of 10 miles. For this sort of reason, my 2020 book was called *Language of the Angels*, since this model looks like a first approximation of the mean earth size which a later Ancient Metrology would improve upon as to accuracy, by a couple of miles! That is, that the earth’s dimensions follow a design based upon metrological geometry and the properties of numbers.

John Michell finalized his Cosmological Model in an Appendix to** The Sacred Center**, and in his text on “sacred Geometry, Ancient Science, and the Heavenly Order on Earth” called

*, both published by Inner Traditions.*

**The Dimensions of Paradise**