Gnosis

Echoes of knowledge

 

The ancient Comma of Pythagoras

The celebrated author John Michell maintained within his thought-provoking and insightful book: The Dimensions of Paradise

“In the operations of simple arithmetic and throughout all the numerical manifestations of nature, such as the periods and intervals of the solar system, certain “nodal” numbers occur, providing a link between processes and phenomena which otherwise appear quite unconnected with each other” 

{The foregoing refers to a Numerical Canon that I will denote as NC}

Likewise as the celebrated author Robert Temple maintains within his stimulating book: The Sirius Mystery

"A value of the Comma of Pythagoras…appears in the form of an arithmetical fraction preserved in the ancient Greek Pythagorean treatise Katatome˜ Kanonos"

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The FP denotes the musical scale: Pythagorean Limma {256:243} that, as indicated, I denote as FP {Fraction of Plato} since within the Timaeus of Plato {Timaeus: 31-37…43-45} following the creation of the "World-Soul" there was a surplus in the ratio 256:243

Likewise I calculated the Plato “Whole” via which the "World-Soul" was created to be 46656, that in our day we identify as the cubic inches in one cubic yard and 46656 x 9216 = 429981696 as we will observe presently, the 35th PWS member is 9216 By means of Timaeus a list of numbers will be gleaned, my calculated list contains 36 numbers, commencing with 384, ending with 10368, that I denote as PWS {Plato's World Series} I fashioned my version re: PWS via thorough study of Timaeus, even though my version created via a dissimilar method than renowned individuals such as: J, Michell, J. Dupois, and A. E. Taylor etc nonetheless it gels agreeably

The general consideration that Plato gave no heed to the Comma of Pythagoras to me seems somewhat impractical, In view of the fact that within: the Dialogues of Plato: The Republic Book 1X… there is a paragraph wherein the number 729 is clearly referred to

“Yes the mathematicians will easily do the sum…the multiplication is complete, living 729 times more pleasantly…”

Accordingly it is no surprise, to me at least, that 729 is the square root of 531441, a Comma component: 531441:524288 Accordingly we examine the 729 in view of the fact that it is intentionally remarked upon in support of some purpose or other, moreover: 729 x 729 x 729 = 387420489 this multiplied twice by the FP {256:243} obtains 429981696 which divided twice by the PWS end number: 10368 = 4

Alternatively 429981696 ÷ 32768 = 13122 that divided by the first PWS number: 384 = 34.171875 which multiplied by the FP = 36. Alternatively 429981696 being the Plato-Timaeus “Whole” 46656 x 9216, which is the 35th PWS, number moreover 9216 ÷ 384 = 24 Alternatively the 429981696 equates as 4 x 2 x 9 x 9 x 8 x 1 x 6 x 9 x 6 = 1679616 which is 36 x 46656 Then again the square root of tother Comma component, namely: 524288 is 724.07734393502… which is exactly 512 x 2, the 4th PWS member is 512 and 512 is 486 times the FP {256:243} or 512 x 48.6 = 24883.2, which is the NC {Numerical Canon} Earth mean circumference

Therefore it is no shock that the 724.07734393502… is Pi x 0.631036… x 365.2422000269… a tolerable Earth year and this Earth year of 365.2422000269… x 360000 ÷ 5280 = 24902.877274…a tolerable Earth Equatorial circumference {miles}

Then again 12561.6161 x 1.9824580617506… = 24902.877228213… that multiplied by 5280 ÷ 360000 = 365.2421993471… additional versions with regard to an Earth circumference and Earth year The 12561.6161 x 1881 ÷ 6080 = 3886.25 which is the 1st PWS member: 384 x 1.125 x 8.995949074074 that multiplied by both FP {256:243} components, namely 243 x 256 = 559620, this is exactly: 44.55 x 12561.6161 The 44.55 x 42.222 = 1881, the 42.222 x 0.45 = 19 pertaining to the Metonic cycle, a prime number in addition to 19 x 99 = 1881 The 724.07734393502… divided by the employed 1.9824580617506…= 365.2422000269… exactly as prior

I will denote the Comma of Pythagoras {531441:524288} as Comma With reference to the musical scale: Pythagorean Limma {256:243} this, as indicated prior, I denote as FP {Fraction of Plato} given that it is the surplus ratio subsequent to the moulding of the World-Soul within the dialogues of Plato Upon the Rhind Papyrus circa 1650 BCE, the Egyptian scribe Ahmes indicates a “Pi” of {256:81} this obtains of 3.160493827 please note the Rhind component 81 x 3 = 243, an FP {256:243} component: hence the Limma x 3 =  Rhind

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Toward the closing stages we will observe:

"Exactly 810.43961348005266835 x FP ÷ 1.269841 = 672.36471636863628781629629 that divided by exactly 415.544247552 = 1.61803398874989484820458683…which is Phi correct to 26 decimal places”

This occurs given that the 5 x 415.5445307872380677771641303555 = 929.1858185 that divided by the Pythagorean Minor Third {32:27} of 1.185185 = 784.000534375 this multiplied by the 29th PWS member: 6144 = 4816899.2832

Subsequently 118098 ÷ 729 = 162 the 729 as indicated prior, is the square root of 531441, a Comma of Pythagoras component {531441:524288} The 118098 is the Great Pyramid of Giza base side length of 9072 x 13.017857142 that multiplied by 0.7 = 9.1125 this is relevant to the ancient unit of measure: 1 Artaba = 3200 Egyptian Qedet of 9.1125 g = 3240 Egyptian Qedet of 3240 g

Then 4816899.2832 divided by the 162 = 29733.9461925925 this is 160 x 185.83716370370 that multiplied by the 5 = 415.5445307872380677771641303555 exactly as prior Accordingly I altered this 415.5445307872380677771641303555 to, as indicated, the exact 415.544247552, although it is practicable, furthermore advantageous; to employ additional digits, in view of the fact that William Flinders Petrie with reference to the 3rd Giza Pyramid indicates:

North: …

East: 4149.2

South: 4157.8

West: 4153.9

Mean: 4153.6

Petrie mentions: “The N. end of the W. side could not be reached, after several attempts; and hence the lack of knowing the length of the N. or azimuth of the W side”

Subsequently with the data we possess: 4149.2 + 4157.8 + 4153.9 = 12460.9 this divided by 3 = 4153.6333 whereas the Petrie mean indicates: 4153.6, hence I will employ the aforementioned exact 415.544247552 in view of the fact that 415.544247552 x 10 = 4155.44247552 that minus 4153.6333 = 1.80914218666 that minus 0.23414218666 = 1.575, which is the 1st Pyramid ratio {Great Pyramid}: 9072 ÷ 5760 = 1.575

A selection of the numerous options:

The employed 0.23414218666 x 106363.6363 = 24904.2144 a tolerable Earth Equatorial circumference, the 106363.6363 x 12.848 = 1366560 the Maya super number, the employed 12.848 divided by the longer value Greek foot of 1.01376 = 12.6736111 this multiplied by 115.2 = 1460, which is the Sothic Cycle Then again, the Comma component: 524288 ÷ 1460 = 359.101369863 this multiplied by exactly 16.93115234375 = 6080, the “Sea” mile

The employed 115.2 is 100 x 1.152 the longer value Egyptian foot, likewise the 115.2 x 78.75 = 9072, 1st Pyramid base side length, the 78.75 is 50 x 1.575 Likewise at the very last part we will divide the Comma of Pythagoras {531441:524288} component, namely 524288, by numerous units of measure, ancient and modern

The employed 16.93115234375 x 80712.7578947368421052631 =1366560 the Maya super number, the 80712.7578947368421052631 x 1881 = 151820697.6 that divided by the 359.101369863 = 422779.5 which is Gem: Simon Peter: 1925 x 219.62571428 This is the Schooldays Pi {22 ÷ 7} of 3.142857 x 69.880909 this is 61.00714285 Egyptian feet of 1.14545, the 61.00714285 is the Egyptian unit {12 ÷ 7} of 1.714285 x 35.5875 and this multiplied by 10.256410 = 365, Gem: Abraxas, Mithras

The Greek cubit of 1.52064 x 10.256410 x Gem: YHWH: 26 = 405.504 this is the Plato-Magnesia number: 5040 x 0.0804571428 one seventh of exactly 0.5632, hence the properties of 0.0804571428 are indeed plentiful given that it will obtain: 5068.8…101376…152064…608256…4561920000…etc

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Musical Scales and Comma of Pythagoras {531441:524288}

As a brief intro: whilst ascending from an initial {low} pitch by a cycle of justly tuned perfect fifths {3:2} leapfrogging 12 times, we arrive at a pitch of more or less 7 whole octaves above the opening pitch  The octave being: the interval of 8 diatonic degrees between 2 tones of the same name, the higher of which has twice as many vibrations per second as the lower Likewise, apart from the cyclic {underlined} digits that appear, please make a note of the amount of times a number will end with the number 5, given that whilst a number ends with a 5 or 0 it is divisible by 5. The Great Pyramid of Giza denoted as GP

 FP x Comma x Rhind ÷ 1.125 = 3, the GP Tan: 480 ÷ 378 = 1.269841 The Rhind Papyrus “Pi” {256:81} of 3.160493827 is 3 x FP

The 1.125 x 1.777 = 2, the 1.777 is the square root of the Rhind {256:81} The FP x Comma = 1.06787109375 this multiplied by the GP Tan of 1.269841 = 1.3560267857142 this multiplied by 179.2 = 243 an FP component {256:243} The 179.2 multiplied by 8.888 = 20.16 the 8.888 x 72 = 640 the acres in one square mile

{A} FP x FP x Comma = 1.125, obviously: 9 ÷ 8

For this reason the Comma divided by the perfect fifth {3:2} of 1.5 = 0.675762176513671875 In that case 12 x 0.675762176513671875 = 8.1091461181640625 that multiplied by the FP {256:243} = 8.54296875 It follows that exactly 2187 ÷ 8.54296875 = 256, an FP component {256:243}

The square root of the Comma component 531441 being 729 that is one third of 2187 the 17th PWS member, and the FP {256:243} multiplied by 729 = 768, the 6th PWS member, accordingly it follows that 2187 ÷ Comma ÷ FP = 2048 which is the 16th PWS member, hence the options are myriad  Then again, tother Comma component: 524288 divided by the 768 = 682.666 that divided by the 1st PWS member: 384 = 1.777 which is the square root of 3.160493827 which is the Rhind Papyrus "Pi" {256:81} the 682.666 x 3 = 2048

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{B} the {A} above 8.1091461181640625 x 81 x FP x FP = 729

Then 1881 x 6080 x 30 subsequently divided by the 729 ÷ Pi ÷ 410.16186556… = 365.2421989187… a tolerable Earth year, which multiplied by 360000 then divided by 5280 = 24902.8771990053… a tolerable Earth Equatorial circumference, the employed 410.16186556… divided by the FP {256:243} obtains 389.333 that multiplied by 1.5 = 584, the Maya Synodic period of Venus

The above 682.666 divided by this 389.333 afterwards multiplied by exactly 303087.4453125 obtains the Comma component: 531441 and the employed 303087.4453125 x 256 = 77590386 which, for example, divided by the 729 will obtain exactly 106434 that divided by 2187 = 48.666 which multiplied by 30 = 1460 which is the Sothic Cycle

The Comma component: 531441 ÷ 243 = 2187 the 17th PWS member The Comma component:  524288 ÷ 256 = 2048 the 16th PWS member as a result obviously: 2187 ÷ 2048 = 1.06787109375, which is FP x Comma

{C} Therefore 1.06787109375 divided by the {A} above: 0.675762176513671875 = 1.580246913 which is the Eye of Horus fraction {63:64} reversed as: 1.015873 multiplied by 1.555, one ninth of 14, given that 63 ÷ 64 = 0.984375 x 1.015873 = 1

As stated prior, the 1st member of PWS being: 384, the end member being: 10368 the 384 x 1.06787109375 = 410.0625, the 2nd PWS member: 432 ÷ 410.0625 = FP {256:243}The 36th and last, member: 10368 ÷ 1.06787109375 = 9709.037037, which multiplied by 54 = 524288, obviously a Comma component, although ancient fractions, the FP {256:243} and Comma {531441:524288} numbers subsist in our day, such as within a PC, otherwise with regard to screen resolutions we often observe the numbers: 256, 512, 768, 1024 etc, similarly 262144.kb, however 262144 x 2 = 524288

Likewise the 524288 is a tad shy of 525000, therefore 525000 minus 524288 = 712 that divided by the 1st PWS member: 384 = 1.8541666, that multiplied by the FP {256:243} and "Rhind" {256:81} component, namely: 256 = 474.666 that multiplied by tother FP component: 243 = 115344 currently we perceive tother Comma component: 531441 rearranged as it were, for this reason 531441 minus 115344 = 416097  The square root of the 531441 is 729, the 416097 is 729 x 570.777 that is exactly 321.0625 x 1.777, which is the square root of the Rhind Papyrus "Pi" {256:81} of 3.160493827 The employed 321.0625 multiplied by Maya Tzolkins: 5256 = 1687504.5 that divided by the 416097 = 4.0555 that multiplied by 90 = 365, Gem: Abraxas, Mithras

Or the Maya Synodic period of Venus: 584 this is 4.0555 x 144 Or Gem: Son of man: 2190 is the 4.0555 x 540, otherwise the Sothic Cycle: 1460 is the 4.0555 x 360


As we observe prior: "Then again, tother Comma component: 524288 divided by the 768 = 682.666…" As a result the 682.666 minus the above procured: 474.666 = 208 which is 13 x 16, in addition to 474.666 multiplied by exactly 778.47802734375 = 369517.5703125, that divided by the prior 115344 obtains exactly 3.20361328125 that multiplied by the 531441 obtains exactly 1702531.44580078125 this being the 525000 divided by 3.24291703962053571428

This 3.24291703962053571428 minus the Schooldays Pi {22:7} of 3.142857 = 0.10005989676339285714 that multiplied by 3584 will obtain exactly 358.61467, at this time we are a tad shy of 360

Consequently 360 minus 358.61467 = 1.38533 exactly, the 3584 divided by the1st PWS member: 384 = 9.333 that multiplied by 0.75 = 7

The 778.47802734375 is the 768 x 1.0136432647705078125 which is the Comma

We find that: a reduced and reversed 115344 of 4.43511 minus the 1.38533 = 3.04978 that, for example, multiplied by 200 = 609.956, and this minus the Roman furlong of 608.256 = 1.7, that multiplied by 90 = 153, the "fishes" landed via Simon Peter upon the Sea of Galilee, therefore Gem {Gematria Value} Divine Circle, and the Net: 1224 divided by the 1.7 = 720, in that case Simon Peter: 1925 is 1.7 x 1132.3529411764705882  The cyclic 3529411764705882 contains Gem: 882: City of god……Gem: 294: Church……Gem: 1176: Only-begotten son, and 294 x 3 = 882 moreover 294 x 4 = 1176, hence whichever will suffice, we employ 882

Hence: 882 divided by 1132.3529411764705882 = 0.77890909 that multiplied by 1.4705882352941176 = 1.14545, the Egyptian foot, moreover please note that the cyclic has merely "shifted" As a result 1.4705882352941176 multiplied by exactly 1309 = 1925, Simon Peter, the 1309 being the above 1.7 x 770 that is the modern-day mile of 5280 divided by 6.857142 which is one seventh of 48, therefore 6.857142 will obtain numerous additional "numbers"

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The Comma of Pythagoras {531441:524288} multiplied twice by the Pythagorean Limma {256:243} will obtain exactly 1.125, {9 ÷ 8}

As indicated prior, the square root of the 531441 is 729 otherwise 531441 is 243 x 2187 that divided by the “Limma” obtains 2304, already there are additional than ample “numbers” to obtain numerous units of measure, nevertheless although the 524288 is 256 x 2048 yet another “number” to employ, there is much more As indicated prior, the square root of the 524288 is 724.07734393502466… which is exactly 512 x 2; as a result there are options aplenty at this point, the 4th PWS member is 512, given that the 3 x 724.07734393502466… = 1254.1387483049871

The prior 2187 x 1254.1387483049871… ÷ 524288 = 5.23147858151055712… this is the square root of exactly 27.3683681488037109375

The prior 2048 x 27.3683681488037109375 = 56050.41796875 exactly, this divided by 6.320987654 = 8867.35128021240234375 exactly the 6.320987654… x 81 = 512

This 8867.35128021240234375 x 65536 = 581130733.5 this is the Platonic Precession cycle of 25920 x 22420.1671875 that divided by the 27.3683681488037109375 = 819.2, the 33rd PWS member is 8192 the 65536 is 10.7789473684210526315 Sea miles of 6080, a prime number pertaining to the Metonic cycle, namely: 19 x 10.7789473684210526315 x 10 = 2048

The 5 x 27.3683681488037109375 x 324 ÷ 8867.35128021240234375 = 2.236067977499789…obviously the 5

Final examples

The Arabian Hashimi foot: 1.064448 x “Comma” = 1.0789705458984375 this multiplied twice by the “Limma” = 1.197504

The 1.197504 is: 0.504 x 2.376, the1.197504 is: 1.01376 x 1.18125, the 1.197504 is: 1.14048 x 1.05 and so forth The 1.197504 is the “Limma” x 1.13669325, this 1.13669325 multiplied by the prior 10.7789473684210526315 x 1881 = 23046.6829824 this divided by 24883.2 = 0.9261945 This 0.9261945 ÷ 0.1925 = 4.8114 that divided by 5.0688 = 0.94921875 which is a reversed FP {Pythagorean Limma 256:243} given that 243 ÷ 256 = 0.94921875

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The GP {Great Pyramid} base side length: 756

At start, we observe: {A} "Subsequently: Comma x FP x FP = 1.125, obviously: 9 ÷ 8"  likewise we observe:  "Hence the Comma divided by the perfect fifth {3:2} of 1.5 = 0.675762176513671875"

Please note the GP base side length of 756 within the {A}: 0.675762176513671875 albeit "rearranged" as it were, moreover the FP {256:243} component 243 being the square root of 59049  Hence 756 ÷ 0.675762176513671875 = 1118.7367779301

The 1118.7367779301 multiplied by the 59049 obtains exactly 66060288, this, for example, being the Plato -Timaeus “Whole” 46656 x 1415.901234567 which is the GP base side length of 756 divided by exactly 0.533935546875 This 0.533935546875 x FP = 0.5625 which is 1 ÷ 1.777, one ninth of 16 However the 1.777 is the square root of: 3.160493827 which is the Rhind Papyrus "Pi" {256:81} in addition to the FP {256:243} is one third of the "Rhind"

The Schooldays Pi {22:7} of 3.142857 The "Rhind" {256:81} of 3.160493827 The Eye of Horus fraction {63:64} reversed as 64:63 = 1.015873……the "Eye" likewise being: 576:567 in that case: 10 divided by 567 = 0.0176366843033… that added to the Schooldays Pi of 3.142857 = 3.160493827…which is the "Rhind"

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Or the GP base side length of 756 ÷ 567 = 1.333 that multiplied by 7.5 = 10  Otherwise reversing as: 567 ÷ 576 = 0.984375 that multiplied by 256 = 252 that divided by 243 = 1.037037 that divided by the reversed Eye of Horus {64:63} of 1.015873 = 1.0208333 Subsequently 3.142857 minus 1.0208333 = 2.1220238095 that added to 1.0384700176366… = 3.160493827…which is the "Rhind"

Subsequently 1.0384700176366… x 273030912 = 283534416 that divided by the Comma component: 524288 obtains exactly 540.798980712890625 that minus the lead number 540 = 0.798980712890625 that multiplied by the FP {256:243} obtains 0.8417245370370, this plus exactly 0.1953125 will regain the above 1.037037 and this 0.1953125 x 256 = 50

The 273030912 divided by the "Rhind" of 3.160493827…= 86388687 that divided by tother Comma component, namely: 531441 = 162.555 that plus exactly 612.75 = 775.30555, furthermore the 612.75 multiplied by Gem: Tree of Life: 1625 = 995718.75 that divided by the 0.1953125 = 5098080 This 5098080 divided by Greek mile of 5068.8 = 1005.7765151 that is the 995718.75 divided by exactly 990 Or the 273030912 divided by the 5098080 then multiplied by 464.623376 = 24883.2, the NC Earth mean circumference, the employed 464.623376 multiplied by the modern-day furlong of 660 x 7 obtains exactly 2146560

Or the 1.0384700176366… x 243 = 252.3482142857 that minus 3.142857 = 249.2053571428 one seventh of 1744.4375 that multiplied by 256 = 446576 that divided by Gem: Eagle, Pneuma {Breath} namely 576 = 775.30555 as we observe above Furthermore 775.30555 is exactly 436.109375 x 1.777, which is the square root of 3.160493827…the "Rhind"

Likewise as we observe prior: "The 1118.7367779301 multiplied by the 59049 obtains exactly 66060288…"

Then again we perceive the Roman furlong of 608.256 “rearranged” within the 66060288 Accordingly 66060288 ÷ 608.256 = 108606.0606, which is the Egyptian foot of 1.14545 x 94814.814814 that multiplied by an FP {256:243} component, namely: 243 = 23040000 pertaining to the Maya, Sumerians etc

Similarly the GP height: 480 x 480 = 230400, on the other hand, the GP volume of 91445760 divided by the 108606.0606 = 841.995 exactly, which is the Roman furlong of: 608.256 x 1.38427734375 which is the GP base side length: 756 ÷ 546.1333 which is the FP {256:243} component: 256 x 2.1333 one third of 6.4, otherwise the Comma component: 524288 is 960 x 546.1333 Therefore the 2.1333 obtains: square yards in one acre: 4840, square feet in one acre: 43560, then again the seconds in 24 hours: 86400 divided by 2.1333 = 40500 which is the Platonic Precession cycle: 25920 x 1.5625 that multiplied by 0.64 = 1 {one} Then again, we perceive a rearranged Sea mile of 6080 within the 66060288

Consequently 66060288 ÷ 6080 = 10865.1789473…which divided by the 546.1333 = 19.894736842105263157 Please make a note of 684 and 105263 within the 19.894736842105263157 in view of the fact that the 684 x 8.888 = 6080, the Sea mile, the 8.888 x 9 = 80 the 105263 resembles the Greek cubit of 1.52064 Consequently 19.894736842105263157 x 1.52064 x 1881 = 56905.39008 exactly, this is the Greek mile of 5068.8 multiplied by exactly 11.2266. The GP base side length of 756 divided by the 11.2266 then multiplied by the 1881 = 126666.666 which is exactly 14250 x 8.888

In that case the GP base side length of: 756 ÷ 19.894736842105263157 = 38, the Grand Gallery floor line length of 1881 ÷ 38 = 49.5, which is Gem: Weapons of god: 665 ÷ 13.4343 which is 3.2323 {6080 ÷ 1881} multiplied by exactly 4.15625

Subsequently Gem: Mary 192 ÷ 4.15625 x 1881 x 7 = 608256, obviously the Roman furlong of 608.256 increased Hence 1881 x 19.894736842105263157 = 37422, which is 756 x 49.5 The Comma component: 524288 divided by the Roman cubit of 1.4598144 = 359147.025813692480359147 that divided by the Eye of Horus fraction of 1.015873 = 353535.3535 that multiplied by 0.198 = 70000 Otherwise 524288 divided by the Greek mile of 5068.8 = 103.4343 that multiplied by 3.7125 = 384, the 1st PWS member, the 3.7125 multiplied by the FP {256:243} afterwards by 1350 obtains 5280 the mile


A few more examples then we move progress, in view of the fact that whilst one unit of measure is "found" so will numerous be "found" Such as: 524288 divided by 86400 = 6.06814814 that divided by the Arabian Hashimi foot of 1.064448 then multiplied by 18.144 will regain the above 103.4343 the 18.144 is 7 x 2.592

The 6.06814814 is the FP {256:243} multiplied by 5.76, then: 524288 x 0.891 = 467140.608 that is exactly 96 x 4866.048, the Roman mile, otherwise 467140.608 divided by the Greek furlong of 633.6 = 737.28 which is 5.76 x 128  Then again the 524288 divided by the Roman mile of 4838.4 = 108.359788 this added to 392.7765752 = 501.13636, the Greek Stade {500ft} 

The 392.7765752 x 12474 = 4899495 which for example, divided by Gem: Simon Peter: 1925 obtains 2545.1922077 that divided by the 108.3597883 = 23.4883460582386363 that multiplied by the yards in one mile: 1760 will obtain exactly 41339.4890625 To be brief, this 41339.4890625 is the 392.7765752 multiplied by exactly 105.249375 that is the 12474 divided by 118.518518 which is the musical scale, Pythagorean Minor Third {32:27} of 1.185185 increased one-hundredfold

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PWS total

Adding each and every one of PWS members {36 in total} from 384 up to and including 10368 obtains exactly 125606, the “Whole” that Plato intimates, nevertheless on no account mentions within Timaeus I fathomed as: 46656, formed via the Greek Lambda {letter L} furthermore the cubic inches in one cubic yard, being 46656 Otherwise the seconds in 24 hours: 86400 ÷ 46656 = 1.851851 that multiplied by exactly 13996.8 = 25920, the Platonic Precession, the employed 13996.8 x 34222.222 = 479001600 {=12!}

The 34222.222 multiplied by the FP {256:243} component: 243 = 8316000, which for example, is Gem {Gematria} Founder of the City: 1225 x 6788.571428, which is the Schooldays Pi {22 ÷ 7} of 3.142857 x 2160  Then again, the Plato Atlantis area, minus the central shrine of 4561920000 square units being 13996.8 x 325925.925925 that multiplied by the first PWS member: 384 = 125155555.555, which is the 34222.222 x 3657.142857, which is one seventh of 25600, noticeably tother FP {256:243} component, albeit increased

Timaeus

Within Timaeus, via the creation of the “World-SoulPlato encourages the reader to perform all manner of mathematical gymnastics in the company of the “numbers” produced

Quote

“This entire compound he divided lengthways into two parts, which he joined to one another at the centre, like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point”

Unquote

Subsequently the PWS total: 125606 multiplied by the "Whole": 46656 = 5860273536 The Comma components: 531441 x 524288 = 278628139008, this being the 5860273536 x 47.545244653…The GP base perimeter of 3024 ÷ 47.545244653 = 63.60257523148148 this multiplied by the FP components: 256 x 243 = 3956589 exactly that multiplied by 1.06787109375 = 4225127.02294921875, which divided by the PWS total: 125606 = 33.637939453125

As we observe prior the 1.06787109375 is the FP multiplied by the Comma In that case, merely as an example, the 33.637939453125 x 3145728 = 105815808, this "number" 105815808, resembles the Eye of Horus cyclic: 64 ÷ 63 = 1.015873  Accordingly 105815808 divided by 1.015873 obtains exactly 104162436, this being the GP base area {756 x 756} of 571536 x 182.25 which is one fourth of 729, which is the square root of the Comma component: 531441 The employed 3145728 being, merely as an example, the above 9709.037037 x 324

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GP Apothem

The GP Apothem being the square root of 373284 = 610.96972101… this multiplied by the GP base side length of 756 x Pi = 1451079.99825808 Re the prior "The Comma components: 531441 x 524288 = 278628139008" we will reduce this to read as: 27.8628139008

Then 1451079.99825808 ÷ 27.8628139008 ÷ 2.0915032679738562 = 24900.48659971, a tolerable Earth Equatorial circumference {miles} The Rhind Papyrus fraction {256:81} divided by the 2.0915032679738562 = 1.511 which is, for example, the Alexander Thom Megalithic Yard of 2.72 ÷ 1.8

GP: Tan

Via a GP base side length of 756 and a “finished” height of 480, the GP Tan will be: 480 ÷ 378 = 1.269841 The 1.269841 being 1.580246913 ÷ 1.2444, which is one ninth of 11.2, which is the GP base side length of 756 ÷ 67.5 {12 x 5.625}

On the other hand: 1.269841 ÷ 1.580246913 = 0.803571428 one seventh of 5.625 that multiplied by the FP {256:243} component: 256 = 1440 As illustrated prior, the British Admiralty mile being 6080, that I dub a Sea mile and the magnificent Grand Gallery floor line length being 1881 {modern-day inches}

Subsequently 6080 ÷ 1881 = 3.2323, this being 1.49393 x 2.16362407031 in that case Gem {Gematria} Weapons of god: 665 ÷ 2.16362407031 = 307.3546875 exactly, which is Gem: Mary: 192 multiplied by exactly 1.6008056640625 The Comma {531441:524288} component, namely: 524288 x 1.6008056640625 = 839283.2 which is the seconds in 24 hours: 86400 x 9.713925925

The GP height of 480 multiplied by 9.713925925 afterward by 1.0285714 obtains exactly 4795.904 {1.0285714 x 7 = 7.2} the options really are numerous, for example this 4795.904 ÷ 1.49393 = 3210.24 exactly, which is the GP base perimeter of 3024 x 1.06158730 This resembles the cyclic within the reversed Eye of Horus fraction {64:63} of 1.015873 Hence 1.06158730 ÷ 1.015873 = 1.045, which is the Sea mile of 6080 ÷ 5818.1818 one eleventh of 64000, therefore ample scope Equally the GP Tan: 1.269841 is 1.25 x 1.015873 the reversed Eye of Horus

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GP measurements

I firmly believe we were initially “intended” to perceive a GP base side length of 756 with a “finished” height of 480, given that all ancient and modern-day units of measure, whether they be units of time, distance, volume, area, otherwise whatever will be discovered via employing 756 in the company of 480, mainly in view of the fact that they are divisible by 3 then again 756 = 360 + 360 + 36 in addition to 480 = 360 + 120

Subsequently via further probing additional, enhanced, numbers of import would emerge, likewise as I oft times state, cyclic numbers are vitally important hints, furthermore deserve far more credit and exploration than at present, moreover bear in mind, whilst a number, or cyclic pattern looks familiar, then it is, since it is “there” for a reason For example, the NC {Numerical Canon} Earth mean circumference being: 131383296 modern-day feet, and Gem {Gematria}: YHWH being 26  Then 26 x 3 = 78, this pertains to the Maya calendars, for example the Maya super number: 1366560 ÷ 78 = 17520, which is the Maya Tzolkins: 5256 x 3.333 one third of 10, accordingly the number 26 will obtain numerous, for example: Gem: Tree of Life: 1625 being 26 x 62.5

The NC Earth  circumference of 131383296 {feet} divided by the 62.5 = 2102132.736, which is exactly 3456 x 608.256, the Roman furlong, equally the GP base perimeter of 3024 x 43446.857142 = 131383296  The employed 43446.857142 x 0.014 = 608.256

Accordingly add a reduced 78 of exactly 0.78 to a reduced Earth of:  131.383296 to obtain 132.163296 which is Gem: YHWH: 26 x 5.083203692307 whereas authentic Pi multiplied by authentic Phi obtains 5.08320369231… Accordingly it follows that with regard to my “near-miss” 5.083203692307

5.083203692307 is Pi x 1.61803398874… hence Phi correct to 11 decimal places

5.083203692307 is Phi x 3.141592653585…hence Pi to correct 11 decimal places

In addition 5.083203692307 multiplied by Gem: Tree of Life: 1625 obtains exactly 8260.206 I calculated the GP “top platform” perimeter as 2288 {modern-day inches} in addition to YHWH: 26 x 88 = 2288, and Gem: Lord Jesus Christ: 3168 divided by the 2288 then multiplied by 26 = 36 As a result the 8260.206 is 2288 x 3.610229895104

In that case 3.610229895104 multiplied by exactly 1.408 = 5.083203692307

The properties of 1.408 being numerous, for example 1.408 x 93312000 = 131383296, the NC Earth mean circumference {feet} The NC distance re Earth to Sun being: 93312000 which is a cubit attributed to Sir Isaac Newton: namely: 2.0736 x 45000000

However within the "false" Phi x Pi, the cyclic 692307 hints at the 2.0736, therefore 5.083203692307 ÷ 2.0736 = 2.451390669515 this divided by the above 3.610229895104 = 0.679012345 that multiplied by 7776 = 5280, the mile, the 7776 being the Platonic Precession: 25920 x 0.3, in addition the 32nd PWS member is 7776, the 19th member being 2592 Otherwise the seconds in 24 hours: 86400 being 7776 x 11.111 which is one ninth of 100, or else the 3.610229895104 ÷ 2.451390669515 will obtain 1.47272 that multiplied by the 1.408 = 2.0736. Then again the very last PWS member: 10368 x 2 = 20736

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Roman units

Equally the cyclic 692307 hints at the longer value Roman foot of 0.9732096

Consequently 5.083203692307 being 0.9732096 x 5.2231335287975912 which, for example is the 2.451390669515 x 2.13068181 more than ample scope, since it is 6000 divided by 2816 which is the 1st PWS member: 384 x 7.333 one third of 22 Likewise the cyclic 895104 within the 3.610229895104 resembles the Roman cubit of 1.4598144, therefore 3.610229895104 ÷ 1.4598144 = 2.473074587 this being the above 2.13068181 x 1.1606963397

Subsequently re the employed Earth of 131.383296 + 0.78 = 132.163296 this is the 1.1606963397 multiplied by exactly 113.8655232, yet again more than ample scope.  For example: Gem: Simon Peter 1925 ÷ 113.8655232 x 312.31686363428571 = 5280 The 312.31686363428571 is the School-days Pi {22 ÷ 7} of 3.142857 multiplied by exactly 99.37354752, which is the longer value Greek foot of 1.01376 x 98.0247272 which is the above: 1.47272 multiplied by exactly 66.56 At this time we perceive the Roman furlong of 608.256 “hidden” within this 66.56

Accordingly 608.256 ÷ 66.56 = 9.1384615 that multiplied by YHWH: 26 = 237.6, the NC distance re Earth to Moon being: 237600 {miles} and the NC Earth to Sun distance: 93312000 ÷ 237600 =  392.7272 The modern day mile of 5280 ÷ 200 = 26.4 that multiplied by the 392.7272 = 10368 the final PWS member,

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NC Earth mean circumference

The NC Earth mean circumference of 24883.2 {miles} being the prior 392.7272 x 63.36, the Greek furlong is: 63.36 The Egyptian cubit of 1.71818 x 228.571428 = 392.7272 that multiplied by 1.1 = 432, the employed 228.571428 x 7 = 1600 On the other hand the Greek foot {441:440} of 1.0022727 x 391.83673469 = 392.7272

The employed 391.83673469 multiplied by exactly 12.348 = 4838.4, which is the Roman mile, the employed 12.348 x 49.25947521 = 608.256 this we identify as the Roman furlong The 49.25947521 multiplied by Gem: Founder of the City: 1225 = 60342.857142 which is the modern-day mile of 5280 x 11.428571, which is one seventh of 80 The Royal Egyptian cubit {12 ÷ 7} of 1.714285 multiplied by the Greek foot {441:440} of 1.0022727 = 1.71818 which, as illustrated, is the Egyptian cubit Conversely the 1.714285 divided by exactly 1.6875 = 1.015873, which is the reversed Eye of Horus fraction {64:63}

The employed 1.6875 multiplied by the FP {256:243} component: 256 = 432 Otherwise in view of the fact that the Comma component: 524288 is 256 x 2048, which is the 16th PWS member {Plato World Series} In that case 1.6875 x 2048 = 3456 the PWS 22nd member, therefore Gem: Mary 192 ÷ 3456 x 12.348 = 0.686 which is 343 ÷ 500, besides 343 is: 7 x 7 x 7 Therefore  mix up each and every one of the foregoing numbers, via whichever method is so desired, additional interconnections will forever emerge, in view of the fact that all are totally interconnected, however it is oft times necessary to close the eyes to appellations such as, feet, inches, seconds etc, afterward simply employ the “numbers”

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The Comma of Pythagoras {531441:524288}

The 25th Phi sequence number: 75025 increased to 7502500 minus exactly 2056916 = 5445584 that minus an increased Comma component of 5242880 = 202704 which divided by the GP base perimeter of 3024 x 67.031746 {Please see 2056916 below}

The Gem: Church is 294 and 294 x 3 = 882: Gem: City of god and 294 x 4 = 1176 Gem: Only-begotten son The 1176 plus 570 = 1746 which is 666 plus 1080, the lunar, Yin-Yang number The 570 is 30 x 19 Gem: Eve likewise 19 pertains to the Metonic cycle The 570 x 10.666 = 6080, the British Admiralty as I dub it Sea mile Gem: Mary: 192 ÷ 10.666 = 18

Subsequently 1746 divided by the 67.031746 afterwards multiplied by 1.2427302769252232142857 = 32.369842529296875, this multiplied by 65536 {256 x 256} = 2121390 Otherwise the 67.031746 divided twice by the Rhind Papyrus “Pi” {256:81} of 3.160493827 then divided by the Schooldays Pi of 3.142857 then divided by the Egyptian cubit of 1.71818 = 1.2427302769252232142857 as we observe prior This 1.2427302769252232142857 multiplied by 2293760 = 2850525 the employed 2293760 is the modern-day mile of 5280 x 434.4242

The GP base perimeter of 3024 ÷ 434.4242 = 6.9609375 exactly, that multiplied by 42.235690 = 294 this as we see prior is Gem: Church The 2293760 divided by this 42.235690 = 54308.571428 one seventh of exactly 380160 this divided by the Sea mile of 6080 then multiplied by the Greek cubit of 1.52064 x 1881 {Gem: Eve: 19 x 99} will obtain exactly 178845.51168, which to be brief, divided by the 2293760 = 0.0779704553571428 that multiplied by 7 = 0.5457931875 exactly

The 0.5457931875 divided by a reduced Greek mile {5068.8} of 0.50688 = 1.07677001953125 this multiplied by the Pythagorean Limma {256:243} obtains exactly 1.134375 that multiplied by 960 = 1089 which is one ninth of 9801 a reversed 1089 Then the increased Phi number 7502500 minus the 2850525 = 4651975 that divided by Gem: Simon Peter: 1925 divided by the Eye of Horus fraction {64:63} of 1.015873 divided by the Greek foot of 1.0022727 subsequently multiplied by Gem: Founder of the City 1225 will obtain exactly 2907484.375, this multiplied by a component of the Pythagorean Limma {256:243} and the Rhind Papyrus “Pi” {256:81} namely 256 obtains exactly 744316000 this divided by the aforementioned lunar number: 1080 = 689181.481481 that multiplied by Gem: Jesus Christ: 2368 then by Mr. Nasty: 666 x 3 will obtain exactly 3260699532800


This 3260699532800 divided by the Comma {531441:524288} component, namely 524288 obtains exactly 6219290.7958984375 that divided by the 2907484.375 will obtain exactly 2.1390625 that multiplied by the acres in one square mile: 640 = 1369 which is 37 x 37 The aforementioned exact 2056916 minus the Comma component: 531441 = 1525475 that divided by Gem: Simon Peter: 1925 = 792.4545 ample scope given that we observe a cyclic 45 {Please see 2056916 below, another time}

For example: 792.4545 x 10 x 3.142857 x 3.142857 x 1225 = 95887000 this is 5280 x 18160.41666 one third of exactly 54481.25 that multiplied by 28 will regain the 1525475 This 792.45454 x 10 x 3.142857 = 24905.714285 one seventh of exactly 174340 this multiplied by exactly 8.75 will regain the 1525475 However 24905.714285 minus the NC Earth circumference of 24883.2 = 22.5142857 one seventh of exactly 157.6 that multiplied by 40 = 6304 that minus 6080 = 224 that multiplied by 13.5 = 3024

Or 6304 minus 3024 = 3280 that minus 3024 = 256, or 6304 minus 5280 = 1024, or 6304 minus 2592 = 3712 that minus 2592 = 1120 that multiplied by 2.7 = 3024

The 3712 minus 1024 = 2688 multiplied by 1.125 = 3024

{A} the aforementioned exact 2056916 ÷ 3 = 685638.666

{B} Then 685638.666 ÷ 423748 = 1.6180339887… Phi correct to 10 decimal places

{D} 423748 ÷ 261890.666 = 1.6180339887… Phi correct to 10 decimal places

{E} the 261890.666 ÷ 161857.33333636 = 1.618033988749… Phi correct to 12 decimal places

{F} The 261890.666 x 3 = 785672 this divided by the {A} 2056916 = 0.38196601125179 Then exactly 0.6180339887 ÷ 0.38196601125179… = 1.618033988… Phi correct to 9 decimal places

{G} the {E} 161857.33333636 x 5280 = 854606720.016

The Comma component: 524288 minus the {B} and {D} 423748 = 100540, which divided by the musical, scale Pythagorean Minor Third: {32:27} of 1.185185 obtains exactly 84830.625 that multiplied by the Pythagorean Limma {256:243} obtains 89368.888

Sea mile: 6080 with Gem: Mary: 192

Seeing as the Sea mile of 6080 is exactly 684 x 8.888 in addition to: 684 is Gem Mary 192 x 3.5625 in that case, the 89368.888 x 8.888 = 794390.123456790 which is the prior 100540 x 7.901234567 that multiplied by 81 = 640

Phi

The 28th Phi sequence number 317811 ÷ 1881 x 6080 ÷ 634886.4646 = 1.6180339887…which is Phi correct to 10 decimal places

The Eye of Horus {64:63}

The employed 634886.4646 being the reversed Eye of Horus fraction {64:63} of 1.015873 x 624966.3636, which is the Egyptian cubit of 1.71818 x 363737.037037

The Rhind Papyrus {256:81}

The 363737.037037 x 243 = 88388100, this is the mile of 5280 x 16740.1704545 which is the Egyptian foot of 1.14545 x 14614.434523809 which is the Rhind Papyrus fraction {256:81} of 3.160493827 x 4624.09842354910714285 which is the Schooldays Pi {22:7} of 3.142857 x 1471.3040438565340909, this is exactly 3.5625 x 412.9976263456… which is equivalent as: the 4624.09842354910714285 ÷ 11.196428571 which is 3.142857 x 3.5625 

The Pythagorean minor third {32:27}

The prior: 363737.037037 divided by the 412.9976263456… subsequently multiplied by Gem: 3168 = 2790134.518518, this is the musical scale, the Pythagorean minor third {32:27} of 1.185185 x 2354176 which is the modern-day mile of 5280 x 445.8666 As indicated prior, the Sea mile of 6080 divided by Gem: Mary: 192 x 31.666, in that case the 445.8666 ÷ 31.666 = 14.08 exactly, that leads to myriad

Comma multiplied by the Limma

Via employing the FP {256:243} and Comma {531441:524288} numbers 256…243531441524288, we discover that The FP numbers: 2 x 5 x 6 x 2 x 4 x 3 = 1440 Furthermore the Comma x FP = 1.06787109375

Subsequently: omitting the zeros of:  1.06787109375 we find that:  1.x 6 x 7 x 8 x 7 x 1 x 9 x 3 x 7 x 5 = 2222640, which is, for example, the Platonic Precession cycle: 25920 x 85.75, this being one fourth of 343, which as illustrated prior, is: 7 x 7 x 7

Re the Comma we find that: 5 x 3 x 1 x 4 x 4 x 1 = 240

Re the Comma we find that: 5 x 2 x 4 x 2 x 8 x 8 = 5120

Then 240 x 5120 = 1228800 more than ample properties {please see below} we will perceive numerous avenues to explore with regard to the FP {Pythagorean Limma: 256:243} and the Comma {531441:524288} given that all number is totally, undeniably interconnected. Whether the numbers involved pertain to musical scales, units of distance, area, volume, time or whatever, it creates no difference, seeing as practically all numbers will connect to the number 3

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An Earth “year”

A tolerable “year” being: 1881 x 6080 x 30 ÷ 299008 ÷ Pi = 365.242198…that multiplied by 68.1818 {360000 ÷ 5280} obtains a tolerable Earth Equatorial circumference of 24902.8771990053… The 299008 being, for example, the Sothic Cycle: 1460 x 204.8 which divided by the FP {256:243} obtains 194.4 the 15th PWS member being 1944, this 194.4 is, the Platonic 25920 ÷ 133.333, which is one third of 400, the 204.8 obviously one tenth of 2048 the 16th PWS member

Otherwise the 4th PWS member: 512 multiplied by the Maya Synodic period of Venus: 584 = 299008 on the other hand, the Comma {531441:524288} multiplied by 204.8 x FP obtains exactly 218.7, the 17th PWS member being 2187

A few properties of the employed 299008 being

{1} 299008 is Abraxas, Mithras: 365 x 819.2, which is 4 x 204.8

{2} 299008 is Gem: Son of Man: 2190 x 136.5333 which is one sixth of 819.2

{3} 299008 is the Maya super number: 1366560 x 0.2188034

The 33rd PWS member being 8192

The Comma component: 531441 minus 299008 = 232433 then 232 + 433 = 665 Gem Weapons of god, furthermore 299008 ÷ 665 = 449.636090225 that multiplied by the 1881 = 845765.4857142 one seventh of 5920358.4 that divided by the Maya Synodic period of Venus: 584 = 10137.6, the longer value Greek foot is 1.01376

Or the Comma multiplied by the 845765.4857142 x 7 = 6001131.4171875 which multiplied by the FP {256:243} obtains exactly 6322179.6, which is the above 232433 x 27.2000086046301… tolerable as the Alexander Thom Megalithic Yard of 2.72  Or the 6322179.6 is 531441 x 11.8962962 that divided by the {3} 0.2188034 = 54.369791666 that multiplied by the 6th PWS member: 768 = 41756 which is the Maya Third Sun: 312 x 133.8333 that divided by the 54.369791666 = 2.461538, that multiplied by Gem: YHWH: 26 = 64  The 0.2188034 x 3744 = 819.2

The 3744 being 12 x 312, which, as indicated, is the Maya Third Sun Otherwise 819.2 x 0.2188034 = 179.24376068 Then Gem: Tree of Life: 1625 x 179.24376068 = 291271.111 The Comma component: 524288 being 291271.111 x 1.8 otherwise: 12244400640 ÷ 291271.111 = 42037.8134765625 exactly, that multiplied by the FP {256:243} component: 256 = 10761680.25, this is the 1228800 multiplied by exactly 8.7578778076171875

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GP base area

The GP base area {756 x 756} of 571536 ÷ 8.7578778076171875 = 65259.64537926, which is the FP x 61945.679012345, which is the Rhind {256:81} of 3.160493827 x 19600, the above employed: 12244400640 divided by the Platonic Precession: 25920 then divided by the end PWS member: 10368 then multiplied by 120 x FP = 5760 this is the GP height {480 x 12} Likewise Gem: Eagle, Pneuma {Breath} being 576 otherwise the 34th PWS member: 8748 x 1399680 = 12244400640

The Plato “Whole” likewise the cubic inches in one cubic yard: 46656 multiplied by the above 19600 = 914457600, this is obviously 10 x 91445760, and furthermore the GP volume is: 756 x 756 x 480 ÷ 3 = 91445760. The 91445760 divided by the 1399680 = 65.333 that multiplied by the PWS member: 8748 = 571536, that, as indicated is the GP base area {756 x 756}

As we recognize, the square root of the Comma component: 531441 being 729 which multiplied by the FP {256:243} obtains exactly 768 the 6th PWS member moreover 768, is 819.2 multiplied by exactly 0.9375 which is 1 ÷ 1.0666 Nonetheless: 531441 x 524288 = 278628139008, this is the 1228800 x 226748.16 Whilst we divide this 226748.16 by the GP base perimeter of 3024 we obtain: 74.98285714, ample properties since: 479001600 {=12!} divided by 74.98285714 = 6388148.148148 which is exactly 6063750 x FP, in addition to the 6063750 divided by the modern-day mile of 5280 = 1148.4375 whilst we multiply this 1148.4375 by the FP {256:243} we obtain 1209.876543209

The above produced: 1228800 ÷ 1209.876543209 afterwards multiplied by Gem {Gematria} Founder of the City: 1225 obtains exactly 1244160, this being the NC {Numerical Canon} Earth mean circumference of: 24883.2 x 50, otherwise 1148.4375 multiplied by the above 1.0666 = 1225 Gem:  Founder of the City .It is literally impossible to illustrate the myriad interconnections in one fell swoop, as it were, since In addition to, as I illustrated prior, the “Whole” that Plato alludes to within Timaeus, I calculated to be 46656, not merely the cubic inches in one cubic yard, it is also formed via the Greek Lambda, in addition to the Comma component: 531441 ÷ 46656 = 11.390625 exactly which is the 1148.4375 ÷ 100.82304526…

Subsequently Gem: Founder of the City: 1225 ÷ 100.82304526 = 12.15, which is tother Comma component: 524288 ÷ 43151.2757201… that multiplied by the FP {256:243} component: 243 obtains exactly 10485760, plenty of options Since I calculated the GP “finished” height being 5760 {modern-day inches} the Gem {Gematria} Eagle, Pneuma {Breath} being 576, clearly observed within the 10485760 Accordingly 10485760 ÷ 5760 ÷ FP = 1728, the cubic inches in one cubic foot, furthermore obviously 1728 x 27 = 46656 and the 14th PWS member is 1728

Moreover please bear in mind that numbers are no more than “letters” of a numerical alphabet, for this reason as with the factual “letters” alphabet, the numerical alphabet be obliged to be interrelated to compose assorted “numbers” {words} whether the amalgamation of time, distance, area, volume, in the company of musical scales etc, be anathema to mathematicians, and purists, I know not. Perchance so, the cynic ought to, courteously, depart, else they be infuriated, to those whose minds are receptive, please read on {in part 2}

Until the next essay