The codification of number is, up to the present time, an unsolved ambiguity. It is feasible the erudite Ancients formulated number via such a manner that it would appear untold years later; furthermore, inquisitive researchers would attempt to disentangle its inscrutability. Did the enigmatic Plato {and those of similar ilk} possess suspicion as to the codification, thereby concealing various numerical signposts within their works, veiled, lest the apprehensive hierarchy learn of their attempts to inform unapprised humanity via coded works? Plato et al optimistic that future humanity would probe the vagueness of their works. An answer resides within the Great Pyramid, wherein we will discover: the Eye of Horus fraction {63:64}, the Rhind Papyrus fraction {256:81}, the Comma of Pythagoras {531,441:524,288} the Pythagorean Limma {256:243} in the company of actual Phi as well as the √2, and more besides. I aim to demonstrate that the Great Pyramid measurements connect with all other measurements, the reader will come to a decision with reference to the authenticity of this premise
Likewise, there being no manipulation necessary, since the numbers will speak for themselves, as it were. the Pythagorean Limma {256:243} often denoted as FP {Fraction of Plato} since it is mentioned via Plato within Timaeus as the fraction “left over” after the forming of the “World-Soul” that I denote as PWS {Plato’s World Series} the fraction being: 256 ÷ 243, the Rhind is three times the Limma since the Limma 243 is 3 x 81 and the 81 is within the Rhind Papyrus fraction {256:81}
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The Great Pyramid
The following may be one approach to, if not deciphers, then possibly aid the conundrum, regarding number codification. The Great Pyramid of Giza denoted as GP. Gematria values denoted as: Gem. I consider the intended measurements, modern-day Feet, and Inches, of the GP to be as follows, furthermore for no reason do I change direction regarding these “numbers” to assist a desired result, and they remain constant. Half of the GP base-side length of 756 Feet is 378 Feet , the opening two words of the Hebrew Torah “Bereshit bara” translate {approximately} to “In the beginning, “god” created” this being the Gematria Value 1116 perchance some require this “number” to be validated for its employment Accordingly 1116 x 2 = 2,232 that added to the GP base perimeter of 3024 Feet obtains the Maya 5,256 that multiplied by 260 = 1,366,560 the Maya “Super Number” likewise 1116 will obtain much more that simply a Maya association such as 1116 x 1116 = 1,245,456 that minus 123,456 = 1,122,000 that multiplied by 0.027 = 30,294 which is 30,240 plus 54 a much-employed ancient number. Henceforth the Ancient Gematria Values denoted as Gem:
The GP Edge length is the √516,168 = 718.44832799582…Feet .the 516,168 is the GP base area of 571,536 Square Feet {756 x 756} divided by 4 = 142,884 this is 378 x 378 {378 x 2 = 756} and so on
The GP Decimal Edge Angle obtained via dividing the GP height of 480 Feet by the 718.44832799582…thereby obtaining: 0.6681065029951…with this on a calculator click the Inv. button after that press the Sine button to obtain 41.92109147699…this being the Angle of the GP Edge length
The GP Apothem is √373284 = 610.96972101733…Feet the 373,284 is the 516,168 minus the prior 142,884 The GP height of 480 Feet divided by the GP Apothem of 610.96972101733…Feet obtains 0.7856363146781…whilst this is upon a calculator; click the Inv. button then the Sine button to obtain. 51.779567945149954….which is the GP Decimal Slant Angle.
Otherwise in reverse, whilst the 51.779567945149954……is indicated click the Tan button to obtain 1.269841… this is the GP Tan {480 ÷ 378} The 51.779567945149954…multiplied by √2 then multiplied by the Eye of Horus fraction {64:63} of 1.015873… next divided by 23.6789789 …= 3.1415926535…this is Pi correct to 10 decimal places
The GP Decimal Edge Angle is 41.9210914769945…afterward Phi multiplied by the 23.6789789… x 2.864555… ÷ 41.9210914769945…= 2.61803398…this is Phi x Phi correct to 8 decimal places, the 2.864555…x 9 = 25.781 the 23.6789789…x 65,934 = 1,561,249.8 this is the 25.781 x 23,131.1570020955 x 2.61803398874989…an improved Phi x Phi correct to 14 decimal places, in addition the 65,934 is 12.4875 Miles of 5280 Feet
This 12.4875 x 480 = 5,994 this is the GP height of 5760 Inches plus 234 this multiplied by 8,000 = 1,872,000 which is a component of the Maya Earth Formula: 1,872,000 ÷ 5,130 = 364.9122807017…that multiplied by the Maya Long Count 1,360,800 then by the 399 days for Jupiter obtains exactly 198,132,480,000 which is the Platonic Precession Cycle 25,920 x 7,644,000 that divided by the Seconds in 24 hours 86,400 = 88.47222…and this multiplied by 360 = 31,850 this being Gem: Founder of the City 1225 x 26 Gem: YHWH, likewise the number 26, or 13, play a major part in the Maya Calendar
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Soon to be seen being: 4.14644179350061703…denoted as W {10.08 ÷ 2.431} There will be numerous occasions whereby the end digit of the produced number will end with the number 5
The Greek Foot of 1.0022727…is W x 0.24171875
The Roman Remen of 1.202727… is W x 0.2900625
The Greek Cubit of 1.50340909…is W x 0.362578125
The Roman Cubit of 1.4432727…is W x 0.348075
The Greek Digit of 0.06264204545…is W x 0.015107421875
Likewise, later the following will be seen
The time interval between one opposition and the next is just about 780 days for Mars, 399 days for Jupiter, and 378 days for Saturn
The 399 days for Jupiter being W x 96.22708333…that divided by 2.4187577128753…then multiplied by 7 = 278.48576140873…this is the Eye of Horus fraction {64:63} of 1.015873…multiplied by exactly 274.13442138671875 The 1.015873…x 1.25 = 1.269841…the GP Tan {480:378} The 2.4187577128753…x 2.4187577128753…x 379.91320714285…= 918.918, the 379.91320714285…is exactly 221.6160375 Royal Egyptian Cubits of:1.714285… The 274.13442138671875 being the 221.6160375 x 1.2369791666…that multiplied by 15.36 = 19 the Metonic Cycle, the 13th PWS {Plato’s World-Soul} member is 1536
The W component: 2.431 x 378 = 918.918 the 2.431 x 189 = 459.459, and so on
W is the Royal Egyptian Cubit of:1.714285… x 2.4187577128…that is the 399 days for Jupiter divided by 96.22708333…which we observed prior within {6}
W is the Egyptian Cubit of:1.71818… x 844,800 that minus the GP base area of 571,536 Square Feet obtains 273,264 and this 101,376 plus 101,376 plus 62,208 plus 8,304 which is the GP 3024 plus 5280 the Mile, the 844,800 being 40,000 Persian Cubits of 21.12
There remain more options, nonetheless we best move progress, prior to, although the 62,208 is a Musical Scales number, it is also 60,000 Shorter value Greek Feet of 1.0368 likewise the 36th and final PWS member is 10368, more on this within this website essay: “Plato’s World-Soul” that, obviously I denote as PWS. The 1.0368 x 2 = 2.0736 a “Cubit” attributed to Sir Isaac Newton Then again via mixing the GP Apothem together with the GP Quoin {Corner} “numbers” we find that via temporarily disregarding the “labels” that we attach to them, such as Length, Angle and so on as well as merely employing the “numbers” the following statistics arise.
{A} The GP Apothem length of 610.969721017334…added to the GP Decimal Edge Angle of: 41.9210914769945…= 652.890812494…and this multiplied by Pi then by the Maya Temple steps 364 = 746,606.580766…which is 2,044.1414…x 365.2421381…a tolerable Earth Solar Year that multiplied by 360,000 Degrees then divided by the Mile of 5280 Feet obtains an Earth Equatorial Circumference of 24,902.8730551…Miles. The Maya Earth Year being: 1,872,000 ÷ 5,130 = 364.9122807017…{More on the Maya Temple steps 364 presently}
Exactly 22,253,769,520 divided by the Maya Calendar number 26 divided by Pi divided by the 2,044.1414…divided by the Maya Earth Year of 364.9122807017…= 365.242198909…another tolerable Earth Solar Year that, as per norm, multiplied by 360,000 Degrees then divided by the Mile of 5280 Feet obtains an Earth Equatorial Circumference of 24,902.8771983…Miles,
Whereas the Earth Year and Circumference I calculated via employing Pi with the British Admiralty Nautical Mile of 6080 Feet along with a few Maya Calendar numbers being 365.242198918…and 24,902.877199005….hence slight differences. However, the Maya Year of 364.9122807017…multiplied by the Pi Year 365.242198918…then by the Maya 5256 obtains exactly 2,200,770,000 which, for example, is exactly 361,968.75 x 6080 Feet
{B} the GP Edge length of 718.44832799582…Feet added to the GP Decimal Slant Angle of. 51.779567945149954…then multiplied by Pi x 10 = 24,197.4229947…that plus 704 = 24,901.4229947809…Miles, a tolerable Earth Equatorial Circumference whereas the Maya Earth Year {1,872,000 ÷ 5,130} component 5,130 x 3 x Phi obtains 24,901.5430868608…yet again, slight differences. The 704 being 100 x 7.04 Feet, the Stonehenge Lintel Pillars centre to centre distance
We are also able to obtain decent approximations of the GP measurements such as:
{C} Pi plus the 51.77956794514995…then minus the 41.921091476994…= 13.000069121745222657754552932153…this multiplied by 432 = 5,616.02986059…that plus 144 = 5,760.0298605…that multiplied by 1.575 = 9,072.0470304…which is 3 x 3,024.015676…which is 4 x 756.003919…that divided by the 1.575 = 480.002488…all being tolerable as the GP measurements: 5760, 9072, 3024, 756 and 480
The time interval between one opposition and the next is just about 780 days for Mars, 399 days for Jupiter, and 378 days for Saturn
{D} Pi divided twice by Phi then multiplied by the 13.000069121745222657754552932153… x 369.23444…= 5,759.999709… that multiplied by 1.575 = 9,071.999543…which is 3 x 3,023.99984…which is 4 x 755.9999619…that divided by the 1.575 = 479.999975…once more all being tolerable as the GP measurements: 5760, 9072, 3024, 756 and 480. Equally the 5,616.02986059…divided by 4.14644179350061703…= 1,354.421487212…one-seventh of 9,480.95041048…that is the 13.000069121745222657754552932153…x 729.3 and this is 300 x 2.431 that multiplied by the W: 4.14644179350061703… = 10.08 the Greek Foot, the 10.08 will obtain: 2016, 3024, 4032, 5040, 9072, 12,096, 1512, 24,192, 252, 362,880, 4838.4, 72,576, 96,768, 108,864, and much more, all Units of Measure albeit several are increased
The 4.14644179350061703… denoted as W, will be observed almost immediately as a product of dividing the GP Angles likewise this seemingly unremarkable number is virtually a ratio of every Ancient and Modern-Day Units of Measure The 369.23444…multiplied by the 399 days for Jupiter then by 360 Degrees obtains exactly 53,036,835.6 which is exactly 8,723.16375 x 6080 the British Admiralty Nautical Mile. One method being the Greek Foot of 10.08 ÷ 2.431 = 4.1464417935006170300287947346771…
Then again via reversing: 2.431 ÷ 10.08 ÷ 0.24117063492…a cyclic 063492 within, and 0.24117063492…multiplied by the GP height of 480 Feet obtains 115.761904… this is thehind Papyrus fraction {256:81} of 3.160493827…x 36.62779017857142…that multiplied by 1,792 = 65,637 which is 2.431 x 27,000
Likewise, 115.761904…is the Eye of Horus fraction {64:63} of 1.015873…multiplied by exactly 113.953125 and 1.015873…x 1.25 = 1.269841…the GP Tan. Also, the 115.761904…x 81 = 9,376.714285…this multiplied by 2.890606…x 7 = 189,730.71 which is 2.431 x 78,046.363636363636363636363636363…this I leave as is, for exploration Otherwise, the Earth Polar Radius of 20,854,491.428571…Feet divided by the 9,376.714285…then multiplied by the 2.431 obtains exactly 5,406.72 which is 536.380952…Greek Feet of 10.08 and the 536.380952…x 1,134 = 608,256 that is 1,000 Roman Furlongs of 608.256
Equally the 115.761904…x 63 = 7,293 that multiplied twice by Pi then divided by the 2.890606…= 24,901.0150079…Miles a tolerable Earth Equatorial Circumference that multiplied by the Mile of 5280 Feet then divided by 360,000 Degrees obtains an Earth Year of 365.2148867…Whereas the Maya Earth Year {1,872,000 ÷ 5,130} component 5,130 x 3 x Phi = 24,901.54308686… Miles that multiplied by the Mile of 5280 Feet then divided by 360,000 Degrees obtains an Earth Year of 365.22263194…hence slight differences.
Exactly 2,200,770,000 divided by the Maya Earth Year {1,872,000 ÷ 5,130} of 364.9122807017…then by the Maya Calendar number 5256 = 1,147.442208904…this is Pi x 365.24219891874….that multiplied by the 360,000 Degrees then divided by the Mile of 5280 Feet obtains an Earth Circumference of 24,902.877199005…Miles
The 1,147.442208904…x 5256 = 6,030,956.25 that is Pi x 1,919,712.9975169…while we reduce this considerably to read as 1.9197129975169…after that Pi divided by 1.9197129975169…= 1.63649079714…that multiplied by 15,164.635701527…= 24,816.7867675… a tolerable Earth Polar Circumference since it is 2 x Pi x 3,949.714285…Miles one-seventh of 27,648
The 2,200,770,000, as an example, is exactly 361,968.75 x 6080 Feet the British Admiralty Nautical Mile and the 361,968.75 is the 15,164.635701527…x 23.8692677571…that multiplied by 240 = 5,728.62426172…which added to 31.3853419954…= 5,760.009603…tolerable as the GP height of 5760 Inches likewise 5,760.009603…is 1.904761…x 3,024.005041…tolerable as 3024 Feet the GP base perimeter The 31.3853419954…being Pi x Pi x 3.18 a reduced Gem: Helios, 318 likewise within Genesis Abraham defeating his mortal enemies with the aid of exactly 318 trusted Manservants. The 1.904761…x 1.6592592…= 3.160493827…the Rhind Papyrus fraction,
Due to the cyclic 592 within this 1.6592592…in that case 1.6592592…multiplied by the Platonic Precession Cycle of 25,920 obtains exactly 43,008 which is the prior Greek Foot of 10.08 x 4,266.666…which, to be brief is one-third of 12,800 therefore 4,266.666…will obtain: 38,400, 51,200, 64,000, 76,800, 102,400, 11,520, 153,600, 192,000, 204,800, 230,400, 307,200, 345,600, 409,600, 460,800, 576,000, 614,400, 691,200,704,000, and much more such as 4,266.666…x 1.85765625 x Pi = 24,900.2633723…a tolerable Earth Equatorial Circumference in Miles, the 1.85765625 x 327.68 = 608.7168 that plus 0.4608 = 608.256 the Roman Furlong the 26th PWS member being 4608 the 327.68 being a reduce 32768 Musical Scales number
Otherwise, the 1.904761…x 81 = 154.285714…that multiplied by 25.6 regains the Earth Polar Radius of 3,949.714285…Then again, the 154.285714…x 7 = 1080 the Lunar, Yin-Yang number, in that case the Stonehenge Sarsen Circle Outer Diameter of 104.2724571428…Feet x 1.4796401515…= 154.285714…
The prior indicated Earth Polar factor 27,648 is the Stonehenge 104.2724571428…x 265.1515…which is 179.2 x 1.4796401515…the 179.2 x 16.875 = 3024 Feet the GP base perimeter and the 16.875 x 341.333…= 5760 the GP height, hence the 341.333…x 81 = 27,648 The 1.4796401515…multiplied by the 399 days for Jupiter obtains 590.3764204545…which is 1.00218219521604…x 589.0909…the Common Egyptian Stade {600 ft.} The 1.00218219521604…x 82,944 = 83,125 the 82,944 being a Musical Scales number and more besides, the 83,125 is Gematria Value : Founder of the City 1225 x 67.857142…this multiplied by the 56 Aubrey Holes obtains exactly 3,800
This 3,800 is the Metonic Cycle 19 x 200 otherwise 3,800 is the 399 days for Jupiter multiplied by 9.523809…which divided by the Rhind Papyrus fraction {256:81} of 3.160493827…= 3.01339285714…one-seventh of exactly 21.09375 that multiplied by 51.2 = 1080 the Lunar, Yin-Yang number The 4th PWS member is 512, hence the 9.523809…x 5.67 = 54 the much-employed ancient number, the GP height of 5760 Inches is 10 x 576 Gem Eagle, Pneuma {Breath} otherwise reduced to 5.76 then divided by the 5.67 = 1.015873…the Eye of Horus fraction {64:63} that multiplied by 1.25 = 1.269841…the GP Tan {480:378}
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Ancient Gematria Values denoted as Gem:
The GP volume is 91,445,760 Cubic Feet the Square Root of 91,445,760 is 9,562.7276443491…that divided by the base perimeter of 3024 Feet obtains 3.16227766016… and this is the √2 x √5 Otherwise 3.16227766016…÷ √3 = 1.8257418583505…which is the √3.333… {one third of 10}. Therefore the 3.16227766016…÷ √2 plus 1 ÷ 2 = Phi
Likewise, 9562.7276443491…divided by the GP height of 5760 = 1.660195771588…which is the Square Root of exactly 2.75625 this multiplied by 3.333…= 9.1875 which multiplied by 32 = 294 Gem: Church, this 2.75625 also obtains Gem: 882, 1176, 1764, etc The NC {Numerical Canon} Earth mean circumference: 131,383,296, Feet, the Maya “Super Number”: 1,366,560 is 5256 x 26 and 26 x 3 = 78, Gem: YHWH is 26
A reduced Earth of 131.383296 plus 0.78 afterwards divided by 26 = 5.083203692307…though we observe a cyclic 692307 we find that: Phi x Pi = 5.08320369231…Consequently The 5.083203692307… is Phi x 3.14159265358…which is Pi correct to 11 decimal places Therefore 5.083203692307… is Pi x 1.61803398874…which is Phi correct to 11 decimal places
The awe-inspiring Grand Gallery literally “entombed” within the GP denoted as Gallery, as indicated prior FP denotes the musical scale: Pythagorean Limma, The GP “top platform” perimeter of 2288 Inches, obtains an area of: 47.666…6 x 47.666… = 2272.111… The GP base side length of 756 Feet minus 47.666…= 708.333… this multiplied by 1.728 = 1224: Gem: Divine Circle, likewise there are 1728 Cubic Inches in one Cubic Foot The GP base area is: 756 x 756 = 571,536 that divided by the 2272.111…= 251.54403638319…this multiplied by 1.452 = 365.24194082…a tolerable Earth Solar Year that multiplied by 360,000 Degrees then divided by the Mile of 5280 Feet obtains a tolerable Earth Equatorial circumference of 24902.8596019…Miles
The late, great, esteemed author: John Michell within his stimulating publication: “The Dimensions of Paradise” mentions the ancient numerical interconnections, as a Numerical Canon, that in deference to the gentleman, I will denote as: NC {More on the “GP top platform perimeter of 2288 Inches”, soon}
Numerous Maya temples consisted of 91 steps per side hence 91 x 4 = 364 that added to the top platform itself counting as 1 obviously obtains 365,this is Gem Abraxas, Mithras, both Solar “gods” the prior 1.452 is 0.364 x 3.989010…this, for example, divided by the GP Tan {480 ÷ 378} of 1.269841… = 3.1413461538…that multiplied by Gem: YHWH 26 = 81.675 this is 51.857142…x 1.575 the GP ratio {756:480} and the 51.857142…x 840 = 43,560 the Square Feet in one Acre, likewise 51.857142…is 30.25 Royal Egyptian Cubits of 1.714285…
Otherwise the Stonehenge Sarsen Circle Outer Diameter of 104.2724571428…Feet is 51.857142…x 2.01076363…which is 1.170285714…Egyptian Cubits of 1.71818…accordingly this 1.170285714…x 3,375 = 3,949.714285…Miles, the Earth Polar Radius and this 1.170285714…, for example, is 0.673400…Long Geographical Royal Cubits of 1.7378742857…and this cyclic 673400 containing: 0.673400…x 399 x 1,881 = 505,400 which is the British Admiralty Nautical Mile of 6080 Feet multiplied by exactly 83.125 that multiplied by 256 = 21,280 which is the Maya temple steps: 364 x 58.461538…that multiplied by the Maya “Super Number” 1,366,560 = 79,891,200 which is the Maya Long Count of 1,360,800 x 58.708994…that is the 0.673400…x 87.18285714…
The interconnections continue since this 87.18285714…is 80.2662037037…x 1.0861714285…the Germanic/Assyrian Canonical Unit of Measure, and the 80.2662037037…x 20,736 = 1,664,400 a Musical Scales “number” A Cubit attributed to Sir Isaac Newton being 2.0736
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Ancient Gematria Values denoted as Gem:
A Cubit attributed to Sir Isaac Newton being 2.0736 and this 20,736 is twice 10,368, the 36th and final PWS {Plato’s World-Soul} member {more on this within this website} Likewise the 87.18285714…is 32.106481481…Astronomical Megalithic Yards of 2.715428571…This 32.106481481…x 20,736 = 665,760 which is 126.0909…Miles of 5280 Feet the 126.0909…x 33 = 4,161 that divided by the 399 days for Jupiter obtains 10.428571…This I leave as is since I am certain the reader is more than capable of calculating further furthermore there is much additional to calculate, since the distance from Stonehenge to Lundy Island Centre being 123.428571…Miles that multiplied by 32 obtains 3,949.714285…the Earth Polar Radius as indicated prior. And 10.428571…obtains the Maya 365, 584, 1460, 5256, 18,980, 1,366,560, likewise 10.428571…is 0.25 x 41.714285…the Maya STU the Maya 5256 is 10.428571…x 504 one-tenth of 5040 the “must-have” number to be employed within Magnesia, the idealistic City-State as envisioned by Plato, therefore there are more interconnections at hand
Since 504 obtains: 1008, 1512, 2016, 2520, 3024, 4032, 9072, 12,096, 12,600, 1,360,800, 1764, 24,192, 362,880 all, as prior being Units of Measure the 1,360,800, being the Maya Long Count. The number 504 likewise produces 479,001,600 {=12!}, 195,955,200,000,000, the Nineveh Constant, 20,901,888 Earth and dividing the following: 4,561,920,000, 93,312,000, 237,600, 131,383,296, 11,404,800, 35,831,808 and so on, will produce the numerical sequence of numbers: 124578 albeit rearranged, examples being: {A} 11,404,800 is 504 x 22,628.571428…{B} 4,561,920,000 is 504 x 9,051,428.571428…and so on. Equally due to these cyclic digits guarantees these division products will be ratios of even more Units of Measure since all are perfectly, flawlessly interconnected
The GP Tan {480:378} of 1.269841…is 1.25 x 1.015873… which is the Eye of Horus fraction {64:63} that multiplied by 3.111…= 3.160493827…the Rhind Papyrus fraction as indicated by the Egyptian Scribe Ahmes upon the Rhind Mathematical Papyrus Circa: 1650 B.C.E and the Rhind Papyrus fraction of 3.160493827…is three times 1.05349794238683…the Musical Scale Pythagorean Limma {256:243}. Multiplying the Ancient Comma of Pythagoras {531,441:524,288} of exactly 1.0136432647705078125 by the 1.05349794238683…obtains exactly 1.06787109375 otherwise 1.0136432647705078125 multiplied twice by the 1.05349794238683…obtains exactly, 1.125 which merely as an example is 9 ÷ 8 otherwise the GP 5760 ÷ 5,120 the 4th PWS member being 512, the 3.111…x 4.5 = 14 hence 3.111…will obtain 56, 91, 252, 294, 336, 343, 364, 378, 399, 5040, likewise 756, 3024, 294, 882, 1176, 10.08, 1.512, 1764, 2016,, 4032, 2304, 3456, 4608, 5760, 6912, 8064, 9216, 10,368, 13,824, 1728, 86,400, 20,736, 24,192, 27,648, and much, much more
The prior indicated Stonehenge to Lundy Island Centre 123.428571….is one-seventh of 864 hence it will obtain numerous Units of Measure. Likewise, the Maya “Super Number” 1,366,560 minus the Maya Long Count of 1,360,800 = 5,760 the GP height in Inches Therefore, whilst it may, at first glance, appear that I have multiplied Feet by, for example, a Musical Scale, there is nothing amiss in this action since all are totally, flawlessly interconnected within as I dub it the “Numerical Alphabet” as I have attempted hopefully with some success to show, now it is time to move progress else the end will never be As indicated prior, the time interval between one opposition and the next is just about 780 days for Mars, 399 days for Jupiter, and 378 days for Saturn
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Triangle
Seeing as the GP “face on” is a triangle and there being 180 Degrees in a triangle, we deduct the GP Slant Angle of. 51.77956794514995499… from 180 Degrees, twice to obtain 76.440864109700090016…. the Tan of this being 4.14644179350061703002 … denoted as W that as a guide is the Greek Foot of 10.08 ÷ 2.431
Prior to commencing 46,656 is W: 4.14644179350061703002 …x 11,252.0571428…one-seventh of 78,764.4 many Units of Measure are obtainable via both 11,252.0571428…and 78,764.4. The 46,656 being the Cubic Inches in one Cubic Yard, likewise the “Whole” discussed by Plato however never revealed, within Timaeus from which portions were extracted to fashion the “World-Soul” that I dub PWS {Plato’s World-Soul} my list contains 36 numbers nigh-on the equivalent to that of the late, great John Michell, nonetheless there being a slight difference in the 36 numbers as explained within this website essay “Plato’s World-Soul” The Platonic expert A. E. Taylor created a marginally different list, John Michell, the esteemed author of the thought provoking: “The Dimensions of Paradise” attributes 35 terms with an aggregate of 108551; Proclus produced 34 terms with an aggregate of 105947. Utilizing my list, a numerical pattern is created 11223344555666777888888899999999999, that assured me I was on the right track, as you might say.
{1} The Egyptian cubit of 1.71818… is W x 0.414375 exactly that multiplied by the 378 then by the 9th PWS member 1024 obtains exactly 160,392.96 this divided by measurements such as 633.6, 608.256, 4838.4, 5068.8 and so on will produce more avenues to explore since in order the products are: 253.14545…then: 263.6931818…then 33.15 then 31.6431818…the cyclic digits within these, as I have mentioned prior, guarantee they are ratios of additional Units of Measure
Currently a different methodology that will produce additional Units of Measure
{2} The Egyptian foot of 1.14545… is W x 0.27625 exactly that multiplied by the Comma of Pythagoras {531,441:524,288} component: 524,288 = 144,834.56 which is the {1} Roman Furlong of 633.6 x 228.58989…that multiplied by 143.34841628…= 32,768 a Musical Scales number, the 143.34841628…multiplied by the {1} 263.6931818 …= 37,800
The 32,768 x 5,980,078,125 = 195,955,200,000,000, the Nineveh Constant and this 5,980,078,125 is Gem Founder of the City 1225 x 4,881,696.428571…that is exactly 1,235.9619140625 x 3,949.714285…Miles the Earth Polar Radius. The 1,235.9619140625 being the {2} commencing 0.27625 x 4,474.0702771…that multiplied by 7.32397972543209876…will regain the Musical Scales number 32,768 The 7.32397972543209876…is the Rhind Mathematical Papyrus fraction {256:81} of 3.160493827…x 2.31735296 which is 2.2858989…Longer value Greek Feet of 1.01376, we espy this 2.2858989…prior albeit as 228.58989…
Temporarily I will simply indicate the products, that all end with the number 5 after that all will be unveiled as we examine W: 4.14644179350061703002 …almost immediately
{3} The Greek foot of 1.0022727 …is W x 0.24171875 exactly
{4} The Roman Remen of 1.202727… is W x 0.2900625 exactly
Otherwise, the Greek Mile of 5068.8 is W x 1222.44571428… this being the Schooldays Pi of 3.142857… x 388.96 exactly Otherwise, the Egyptian Stade of 691.2 is W x 166.69714285…which is 3.142857… x 53.04 which is the {1} 0.414375 x 128. There being numerous options, therefore I best leave as is until later. Perhaps the reader may wish to investigate the interconnectivity further, however, soon there will be a, on the face of it, endless list of Ancient and Modern-day Units of Measure to observe
The GP Decimal Edge Angle is 41.92109147699452557… this converts to degrees, minutes, seconds, as: 41° 55′ 15.929 this converts to 364,409 feet and 364,409 x 360 ÷ 5280 = 24846.068181… this multiplied by the {3} Greek foot of 1.002727… will obtain 24902.5365185…Miles a tolerable Equatorial Circumference
The GP Decimal Slant Angle of 51.77956794514995499… converts to Degrees, Minutes, Seconds as: 51° 46′ 46.4446″ Whereas W. F. Petrie maintained : “Casing stones, in situ, N. Side, by theodolite 51°.46′.45″ ± 2’…
Hence, I consider my 51° 46′ 46.4446″, is acceptable equally it obtains an Earth Equatorial Circumference of 24901.3558716…Miles, once more a tolerable approximation Likewise, via entering the GP base side length of 756 into a calculator, afterwards click the Cos button to observe 0.80901699437…that multiplied by the GP Tan {480:378} of 1.269841… x 1.575 = Phi, the 1.575 x 480 = 756
The prior 4.14644179350061703002 … denoted as W {10.08 ÷ 2.431}
Ancient Gematria Values denoted as Gem:
The 1st calculation within the following list being W x 2.431 = 10.08, the Greek Foot, the 2nd calculation being W x 0.4134353741496…= 1.714285…a Royal Egyptian Cubit. As regards the {1}: 2.431 the {2}: 0.4134353741496…and the other multiplications of W it is feasible to employ multiples of the number 7 to obtain additional avenues to obtain more Units of Measure.46656
For example, the {1}: 2.431 x 7 = 17.017, the numbers from 1 to 17 add to 153 this being the number of “Fishes” landed upon the Sea of Galilee by Simon Peter Gem 1925, likewise Gem: Divine Circle is 1224 which is 8 x 153, hence Simon Peter 1925 gained 153 accordingly 1925 x 153 = 294,525 which is Gem: Founder of the City 1225 x 240.428571…that multiplied by 5.0909…= 1224
The 5.0909…being 4.444…Egyptian Feet of 1.14545….the 4.444…is 2.5 x 1.777…which is the Square Root of 3.160493827…the Rhind Papyrus fraction {256:81} more on this later The 240.428571…is exactly 140.25 Royal Egyptian Cubits of 1.714285…equally the Stonehenge Sarsen Circle Outer Diameter of 104.2724571428…Feet multiplied by 2.305772569444…will regain the 240.428571…which multiplied by 16.427807486…= 3,949.714285…Miles the Earth Polar Radius in addition this 16.427807486…multiplied by the {1}: 2.431 obtains exactly 39.936
The 2.305772569444…is the prior 4.444…multiplied by exactly 0.518798828125 which multiplied by 294.912 = 153 the 294.912 being the 39.936 x 7.384615…that multiplied by Gem YHWH 26 = 192 Gem Mary and the British Admiralty Nautical Mile {Mary, Mare Sea} of 6080 Feet is 192 x 31.666…obviously one-third of 95 which is 5 x 19 the Metonic Cycle, equally 19 x 320 = 6080 yet the 31.666…divided by W: 4.14644179350061703002 …= 7.6370701058…that divided by the {2}: 0.4134353741496…= 18.47222…which, I leave as is since I am convinced the reader is more than able to discover the numerous options,
As an example the 7.6370701058…multiplied by 48,384 obtains exactly 369,512 which is exactly 60.775 x 6080 Feet the Nautical Mile, the 48,384 being ten Roman Miles of 4838.4 the 6080 is the 18.47222…x 329.142857…one-seventh of 2304 the 16th PWS member, likewise the GP so-called “King’s Chamber” Wall height being 230.4 Inches or 19.2 Feet and Gem Mary is 192 hence the 329.142857…will obtain 4608, 6912, 9216, 11,520, 13,824, 18,432, 20,736, 27,648, 34,560, 4838.4, 5068.8, 57,600, 76,032, 82,944, 96,768, 10,1376 here I will break since whilst the Longer value Greek Foot of 1.01376 albeit increased to 101376 is obtainable, so are numerous additional Units of Measure as within these already indicated, some being PWS members, some are Units of Measure, Musical Scales numbers some are all combined and so on
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It is undoubtedly problematic to comprehend what exactly Gem {Gematria Values} have in common with the information I am demonstrating, however they were awarded during a period of mayhem which required the utmost clandestineness else life would most undeniably be put in peril. Hence the requirement to formulate a cryptic system which no more than the initiate would be capable of understanding, moreover to “read” the veiled message. However. these numbers have traversed time and transformed into Modern-day Units of Measure, Such as Simon Peter 1925 x 2.7428571 …= 5280 Feet the Mile and the 2.7428571…x 70 = 192 Gem Mary, likewise Gem Lord Jesus Christ 3168 is 0.6 x 5280 equally the 2.7428571…x 390.46875 = 1,071 which is 7 x 153 and the 390.46875 is Gem Founder of the City 1225 x 0.31875 that multiplied by 3840 = 1,224 Gem: Divine Circle, the 3840 is 20 x 192. One particular: “Divine Circle” being the Platonic Precession 25,920 which is 0.3 x 86,400 the seconds in 24 hours another: “Divine Circle” the 1st PWS {Plato’s World-Soul} member is 384 obviously twice 192, there being an essay regarding Plato’s World-Soul within this website
Accordingly, 25,920 is the 1224 multiplied by 21.17647058823529411764…that multiplied by 55.533…= 1176 Gem Only/begotten son the 55.5333…x 5.29411764705…= 294 Gem Church and the 5.29411764705…x 166.6 = 882 Gem City of god the 166.6 x 10.5882352941…= 1764 the Plato number of fusion which for example the lunar, Yin-Yang number 1080 plus 684 that multiplied by 8.888…= 6080 Feet the “Sea” Mile the 8.888…x 9 = 80, The 10.5882352941…x 2 = 21.17647058823529411764…We espy 1764, 882, 294 and 1176 within the 21.17647058823529411764…Then Pi minus 0.1176 x 1,000 = 3.023992653…one-thousandth of 3,023.992653…tolerable as the GP base perimeter of 3024 Feet
Obviously to discover W is straightforward however to save the reader searching as well as calculating it is: 4.1464417935006170300287947346768…which I have previously and will continue to abridge to read as 4.14644179350061703…One inkling of interconnections being Pi x 2.431 ÷ 10.08 x 4,000 = 3,030.639579…that minus 6.65 = 3,023.98957…tolerable as 3024 Feet the GP base perimeter. The 6.65 being a reduced Gem 665 Weapons of god, likewise the British Admiralty Nautical Mile of 6080 Feet is 665 x 9.142857…one-seventh of 64 hence 9.142857…will obtain: 192, 384, 512, 576, 7.04, 768, 1024, 1152, 1536, 1728, 2048, 21.12, 2304, 2368, 3072, 3456, 4032, 4096, 4608, 5184, 6080, 6144, 633.6, 6912 and so on, the majority being PWS members otherwise Units of Measure several being both. Gem Mary is 192, the GP so-called “King’s Chamber” Wall height being 19.2 Feet or 230.4 Inches ,
Likewise, Gem Jesus Christ is 2368 which is the 64 x 37 that multiplied by 18 = 666, no affront intended to those of a religious predisposition, however the numbers are what they are. The cyclic 142857…within the 9.142857….guarantees it is a ratio of more Units of Measure as I trust will be evidenced as we progress, equally Gem: Only/begotten Son 1176 reduced to 0.1176 obtains: Pi minus 0.1176 x 1000 = 3,023.99265…a slight difference from the prior 3,023.98957…
The first section allows the reader to notice the multiple avenues to follow, the numerous interconnections between all the Units of Measure. Prior to commencing it must be stated that it is unattainable to specify all the numerical interconnections in one fell swoop, as it were, hence the “numbers” I indicate are, by no stretch of the imagination, the sole “numbers” obtainable, likewise as I assume is obvious, I dub all as “numbers” since, at the end of the day this is all they truly are: “numbers” Equally of interest being the numerous occasions when a number will end with the number 5 given that when a number ends with a 5 {or zero} it is divisible by 5. For example, a “Pi” of exactly 3.141592653589795 is 5 x 0.628318530717959, it makes no distinction what the mathematical properties of this 0.628318530717959 are since we are able to obtain a “Pi” of 3.141592653589795 via employing it.
Equally Gem Founder of the City 1225 {end digit:5} divided by the 0.628318530717959 will obtain 1,949.6480528757… which is exactly 6,125 divided by 3.141592653589795 Likewise, whilst we observe a Unit of Measure {number} with the numerical sequence: 124578 in any order within it is guaranteed to obtain additional Units of Measure with the numerical sequence: 124578 in any order. For example, the Schooldays Pi {22:7} of 3.142857…contains the 124578 albeit as a cyclic 142857 therefore the Royal Egyptian Cubit of 1.714285…contains a cyclic 714285 within therefore 1.714285…multiplied by 1.8333…= 3.142857…and the 1.8333…which contains a cyclic number 3 multiplied by 2,880 = 5280 Feet the Mile and so on
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As indicated: 4.14644179350061703… denoted as W {10.08 ÷ 2.431}
Regarding the magnificent Grand Gallery literally entombed within the GP W. F. Petrie wrote: “From this the length of the roof of the gallery is 1688.9 – 40.45 = 1648.4 horizontal, or 1838.6 sloping”…and: “By plumb-line measure at the S. end, the roof on the E side is inside the floor edge (or overhangs) 20.50, and on the W. side 20.40”…And “S. wall, in same line: 1883.6” {Referring to “distance on the slope”}
Although I have never set foot within the GP let alone measure the dimensions of the Grand Gallery, I believe the “intended” measurements to be 1836 and 1881 both differ 2.6 Inches from those of Petrie, which I deducted from the Petrie, “1838.6 sloping” along with in the “same line: 1883.6” The number 26 being Gem: YHWH likewise 26 features strongly within the Maya Calendar. The 1836 is 918.918 x 1.998001...that multiplied by 4.931723671875 = 9.85359375 Feet that I calculated to be the base-side length of the GP “missing” Pyramidion with a height of 6.25625 Feet, hence the Pyramidion being a miniature GP since the GP base-side length of 756 Feet is 1.575 x 480 Feet the GP height. Consequently, I considered my thinking was on the right track, as it were. Since the 9.85359375 Feet is 1.575 x 6.25625
The 4.931723671875 x 10.01 x 1881 x 1.0534979423868…= 97,826.2260308666…that is 9,732,096 x 0.01005191749…that multiplied by the Timaeus Whole 46,656 = 468.982262576953125 which is the 4.931723671875 x 95.095 obviously 10.01 x 9.5 that multiplied by 42 = 399 days for Jupiter. The 9,732,096 being an increased Longer value Roman Foot of 0.9732096 likewise, the Stonehenge Sarsen Circle Inner Diameter being 97.32096 Feet
The 1.0534979423868…is the Musical Scale Pythagorean Limma {256;243} which is one-third of 3.160493827… this is the fraction {256:81} as written by the Egyptian scribe Ahmes upon the Rhind Papyrus Mathematical Papyrus Circa 1650 C.B.E. that, obviously I term the Rhind Papyrus fraction, the 2.4888…x 1,215 = 3024 Feet the GP base perimeter. Multiplying the Comma of Pythagoras {531,441:524,288} of exactly 1.0136432647705078125 twice by the Pythagorean Limma obtains exactly 1.125 which, for example is one-eighth of 9
I calculated the 9.85359375 Feet by dividing exactly 10.01 by the Eye of Horus fraction {64:63} of 1.015873 …that multiplied by 1.25 = 1.269841…the GP Tan {480:378} likewise the “Eye” on the reverse of the American Dollar Bill, separating a Pyramid into two sections is, to my rational, for a purpose. Likewise, the GP Tan of 1.269841…x 2.4888…= 3.160493827…
The 1.998001…multiplied by 1881 x 399 x 26 = 38,988,000 which is the GP base perimeter of 3024 Feet multiplied by 12,892.857142…which is 7,520.8333…Royal Egyptian Cubits of 1.714285…the 7,520.8333…x 3 = 22,562.5 which is the 1881 x 11.99494…which is the 1.998001…x 6.00347222…that multiplied by the 1836 = 11,022.375 this is Gem Founder of the City 1225 x 8.997857142…which multiplied by Gem Divine Circle 1224 = 11,013.377142857…that divided by the 12,892.857142…then multiplied by the Metonic Cycle 19 = 16.23024 this being the 918.918 divided by 56.61764705…Then Gem: Only/Begotten Son: 1176 divided by this 56.61764705…obtains 20.770909…this being 18.1333…Egyptian Feet of 1.14545…the 18.1333…x 0.15 = 2.72 the Alexander Thom Megalithic Yard
As indicated prior, Pi minus a reduced 0.1176 then multiplied by 1,000 = 3,023.99265…more than tolerable as the GP base perimeter of 3024 Feet, likewise the 1836 is 1.5 x 1224 and the 1881 is 99 x 19 the Metonic Cycle otherwise 1881 is the 399 days for Jupiter multiplied by 4.714285…that multiplied by the GP 3024 Feet obtains exactly 14,256 which is 2.7 Miles of 5280 Feet, due to the cyclic 714285…within the 4.714285…this indicates it will obtain many Units of Measure
Hence at the end of the day I settled for the Grand Gallery measurements being 1836 and 1881, for those who adhere to, swear by the statistics of W. F. Petrie I can but answer: each to their own, however an examination of his adding up is worth a little peek, similarly the actual measurement differences between Petrie and J. H. Cole are worthy of note. In any case I will employ 1881 in conjunction with 1836
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As indicated: 4.14644179350061703…denoted as W {10.08 ÷ 2.431}
Gem: Church is 294, Gem: Founder of the City is 1225
The GP Tan {480:378} of 1.269841…is W x 0.30624842529…that multiplied by 918.918 = 281.417190476…this is the Rhind Mathematical Papyrus fraction {256:81} of 3.160493827…x 89.042157924107…and this multiplied by the 1225 x 65,536 = 7,148,446,905.6 that is 2.431 x 2,940,537,600 which is exactly 556,920 Miles of 5280 Feet. This 556,920 is the GP base perimeter of 3024 Feet multiplied by 184.1666…which is exactly 103.59375 x 1.777…the Square Root of the Rhind Papyrus fraction of 3.160493827…and the 103.59375 multiplied by W = 429.5454…that is 375 Egyptian Feet of 1.14545…otherwise 250 Egyptian Cubits of 1.71818…likewise 429.5454…x 1.76 = 756 Feet the GP base-side length. The Square Root of the prior employed 65,536 is 256
The commencing 0.30624842529…x 3.3171534348004…=1.015873…this is the Eye of Horus fraction {64:63} which multiplied by 1.25 will regain the GP Tan of 1.269841…this 3.3171534348004…multiplied by the 918.918 will obtain exactly 3,048.192 which is a reduced Gem: 1225 of 0.1225 x 24,883.2 Miles, which is the NC {Numerical Canon} mean Earth Circumference And yet the 3,048.192 is 3048 together with 192 Gem Mary that multiplied by 31.666…= 6080 Feet, the British Admiralty Nautical Mile , the 31.666…is 1.666…x 19 the Metonic Cycle and 19 x 320 = 6080.
The 3048 being an increased 0.3048 the Feet to Metres conversion factor, hence one Metre being 1 = 3.280839895013…that multiplied by the 3,048.192 = 10,000.6299212…this is the Mile of 5280 Feet multiplied by 1.894058697…that multiplied by 199.571428…= 378 which is one-half of the GP base-side length of 756 Feet Equally 3048 divided by 25,920 then multiplied by 3.024 = 3.141592592…although containing a cyclic 592 this is Pi correct to 6 decimal places that multiplied by W = 13.0264308240778829…which multiplied by 67.708492979…= 882 Gem: City of god accordingly this 67.708492979…x 3.141592592…= 212.7125 that is Gem: 1225 x 0.1736428571…one-seventh of exactly 1.2155 which is 2.431 x 0.5
The 199.571428…x 7 = 1,397 which is 2.431 x 138.59126984…x W which is indicated as 4.14644179350061703… {I will cease highlighting this} The 138.59126984…is the GP Tan of 1.269841…x 109.140625 that multiplied by 11.22405153901…= 918.918 this 11.22405153901… x 81.87043660714285…= 918.918
Hence the 1225 x 109.140625 = 133,697.265625 which divided by W = 32,243.8544379…this multiplied by 38.69528649…= 1,247,685.185185…and the 38.69528649…x 81.87043660714285…= 3168 Gem: Lord Jesus Christ otherwise 0.6 Miles of 5280 Feet The 1,247,685.185185…is the Musical Scale Pythagorean Minor Third {32:27} of 1.185185…x 1,052,734.375 that otherwise, the ancient much employed number: 54 x 1,247,685.185185…= 67,375,000 which is 5280 x 12250 x 1.041666…which is the conversion factor Greek to Roman Units of Measure: 25:24 that obtains the 1.041666…
The 81.87043660714285…is 47.7577546875 Royal Egyptian Cubits of 1.714285…and the 47.7577546875 x 2,799.4880936057…= 133,697.265625 the 2,799.4880936057…x 2.431 = 6,805.555…that multiplied by 9,900 obtains the 67,375,000 which divided by the Square Yards in one Acre 4840 = 13,920.4545…that divided by the Egyptian Foot of 1.14545…= 12,152.777…that divided by the Square Root of the Rhind Papyrus fraction: 1.777…= 6,835.9375
This 6,835.9375 is the 1225 x 5.5803571428…that multiplied by 1.792 = 10, the 1.792 x 1,687.5 = 3024 Feet the GP base perimeter and the 1,687.5 x 3.41333…= 5760 the GP height in Inches, this 3.41333…x 1.5 = 5.12 the 4th PWS member is 512 accordingly 3.41333…will obtain: 192, 384, 768, 1024, 1536, 2048, 2304, 27,648, 32,768, 3072, 4096, 4608, 6144, 8192, 9216, 13,824,16,384, 1792, 18432, and so on, all PWS members otherwise Musical Scales numbers, likewise several Units of Measure are within albeit increased
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As indicated: 4.14644179350061703…denoted as W {10.08 ÷ 2.431}
Prior to exploring W and its interconnectivity, initially we deducted the GP Slant Angle of. 51.77956794514995499… from 180 Degrees to obtain W, which, in full is: 4.1464417935006170300287947346771…yet via reversing the process we find that 2.431 ÷ 10.08 = 0.24117063492…now we have obtained a cyclic 063492 within and the 063492 not as a cyclic but as the “number” 63,492 is 30,240 plus 30,240 plus 3,012 that plus 12 = 3024 otherwise 63,492 is 57,600 plus 5,892 which is 5760 plus 132 one-fortieth of 5280 Feet the Mile, then again the 5,892 plus 1,440 = 7,332 which is 10 x 733.2 the Maya Pyramid of the Sun base-side length being 733.2 Feet, hence in my mind this is a decent outcome
Hence 0.24117063492…multiplied by the Egyptian Cubit of 1.71818…= 0.414375 whereas W x 0.414375 = 1.71818…hence either can be employed. Yet given that the Maya entered the arena, the 0.24117063492…multiplied by Gem: Founder of the City 1225 = 295.43402777…that divided by the Maya Temple steps 364 = 0.8116319444…that multiplied by 373,248 = 302,940 this is the GP base-side length of 3024 Feet increased to 302,400 added to 540 the Ancients employed the number 54 a great deal in addition 540 x 2 = 1080 the Lunar, Yin-Yang number. The GP Apothem length being √373,284 = 610.9697210173…Feet this 373,284 is the 373,248 plus 36. Yet it is best we employ the produced W: 4.1464417935006170300287947346771…although there are additional options, various avenues to delve into
{1} The Greek Foot of:10.08 is W x 2.431, half the GP base side length of 378 Feet multiplied by the 2.431 = 918.918 that multiplied by W = 3,810.24 which is 294 x 12.96 this multiplied by the {2} 0.4134353741…x 1225 = 6,563.7 this is the {4} 3,326.4 x 1.9732142857…that multiplied by the {5} 0.244489142857…x 1225 = 590.9761 which is 2.431 x 243.1 The 1.9732142857…x 1.232 = 2.431 and the 1.232 is 1.225 x 1.00571428…the Longer to Shorter Units of Measure conversion factor {176:175}, that multiplied by 3,927.2727…= 3,949.714285…Miles the Earth Polar Radius, the 3,927.2727…divided by the Greek Foot of 1.0022727…= 3,918.3673469…and this multiplied by the 1225 = 4,800,000
The 3,927.2727…x 11 = 43,200 hence 3,927.2727…will obtain: 86,400,12,960, 17,280, 21,600, 25,920, 30,240, 34,560, 29,160, 90,720, 103,680, 108,000, 1,166,400, 120,960, 138,240, 151,200, 207,360, 237,600, 241,920, 276,480, and much more all Units of Measure mixed with PWS members {mostly increased} and the odd Musical Scales number here and there. Equally the 1.00571428…will obtain 7.04, 1.056, 1760, 21.12, 237,600, 3168, 5280, 5068.8, 633.6, 76,032, 7920, 101.376, 11,404,800, 152,064, and much more, again all Units of Measure albeit several being increased
Likewise the 918.918 is 1.00571428…x 913.696875 that is 2.431 x 375.8522727…which is the commencing 3,927.2727…divided by 10.44897959183… that multiplied by the {1} 10.08 = 105.32571428…which is exactly 61.44 Royal Egyptian Cubits of 1.714285…the 29th PWS member is 61.44 that obtains: 122,880, 184,32, 24,576, 3072, 1536, 4608, 768, 9216, 13,824, 2304, 27,648, 3840 and so on, all Musical Scales numbers otherwise PWS members some being both. Equally 10.44897959183…x 1225 = 12,800 or 10.44897959183…x 378 = 3,949.714285…Miles the Earth Polar Radius one-seventh of 27,648
{2} The Royal Egyptian Cubit of:1.714285…is W x 0.4134353741…that multiplied by 2,222.64 = 918.918, the 2,222.64 is the GP base-side length of 756 Feet x 2.94
{3} The Egyptian Cubit of:1.71818…is W x 0.414375 x 2,217.6 = 918.918 the 2,217.6 is Gem Only/begotten Son 1176 x 1.8857142…that multiplied by 2,800 = 5280 Feet the Mile the 1176 is the 294 x 4. The 1.8857142…x 55.296 = 104.2724571428…Feet the Stonehenge Sarsen Circle Outer Diameter and the 55.296 multiplied by 9.49609375 will obtain the {6} 525.096 the 9.49609375 x 0.256 = 2.431
{4} The Egyptian Foot of:1.14545…is W x 0.27625 x 3,326.4 = 918.918, the 3,326.4 is Gem City of god 882 x 3.7714285…that the 882 is 294 x 3 the 3.7714285…x 1,400 = 5280 Feet, the Mile
{5} The Longer Greek Foot of:1.01376 is W x 0.244489142857…x 3,758.522727…= 918.918 the 3,758.522727…is 6.5625 x 572.7272…The Egyptian Stade {500ft.} otherwise, 3,758.522727…is 5.46875 x 687.2727…the Egyptian Stade {600 ft.} and much more. The 0.244489142857…x 12.8547922665…= 3.142857…the Schooldays Pi {22:7} the 12.85479226655…x 918.918 = 11,812.5 that is the 1225 x 9.6428571…and this multiplied by 0.9333…= 9 the 0.9333…x 10.8 = 10.08 the 10.8 being the Lunar, Yin-Yang number 1080 reduced hence the 9.6428571…multiplied by the 56 Aubrey Holes obtains 540 obviously 1080 divided by two
{6} The Shorter Greek Foot of:1.0368 is W x 0.25004571428…x 3,675 = 918.918 the 3,675 is 3 x 1225 otherwise 3,675 is Gem Tree of Life 1625 x 2.2615384…that multiplied by 130 = 294 The 0.25004571428…multiplied by the Royal Egyptian Cubit of 1.714285…x 1225 = 525.096 that is 918.918 x 0.571428…one-seventh of 4
As is obvious we could continue obtaining the 918.918 however I will indicate additional options, although prior to: 918,918,918 minus 314,159,265 minus 302,400,000 = 302,359,653 this added to exactly 40,347 = 302,400,000. This 40,347 plus 2,700 = 43,047 that added to 513 = 43,560 the Square Feet in one Acre Otherwise, the 40,347 plus 513 plus 5760 plus 36 = 46, 656 the Cubic Inches in one Cubic Yard
The 513 being a reduced Maya Earth Year component 5,130 as within {1,872,000 ÷ 5,130} that obtains 364.9122807017…the 5130 x 3 x Phi = 24,901.5430868…Miles a tolerable Earth Equatorial Circumference The Maya Earth Year of 364.9122807017…multiplied by the 399 days for Jupiter then by 86.82142857…obtains exactly 12,641,200 which is W x 3,048,686.2301587…this divided by the Eye of Horus fraction {64:63} of 1.015873…will obtain exactly 3,001,050.5078125 And the 86.82142857…x 28 = 2431 obviously the {1} commencing 2.431 increased
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As indicated: 4.14644179350061703…denoted as W {10.08 ÷ 2.431}
{7} The Longer Roman Foot of:0.9732096 is W x 0.2347095771428…x 3,915.127840909…= 918.918 the 3,915.127840909…is 2,604.1666…Greek Cubits of 1.50340909…The 2,604.1666…x 0.384 = 1,000, the 1st PWS member is 384 The 0.23470957714285…multiplied by 1.775568181…obtains the {18} 0.4167428571…and the 1.775568181…x 563.2 = 1,000. The 563.2 is the commencing Longer Roman Foot of:0.9732096 x 578.703703…that multiplied by 2.1168 = 1225 the 2.1168 x 1,428.571428…= 3024 Feet the GP base perimeter and the 1,428.571428…, for example, is 833.333…Royal Egyptian Cubits of 1.714285…the 833.333…x 1.2 = 1,000
Now we introduce 46,656 the Cubic Inches in one Cubic Yard, likewise the “Whole” discussed by Plato however never revealed, within Timaeus from which portions were extracted to fashion the “World-Soul” Upon completion there being a residual in the ratio 256:243 which is the Musial Scale: Pythagorean Limma of 1.053497942386831…which is one-third of 3.160493827…the Rhind Papyrus fraction as indicated via the Egyptian scribe Ahmes upon the Rhind Mathematical Papyrus Circa 1650 B.C.E The “Rhind” of 3.160493827…is the Eye of Horus fraction {64:63} of 1.015873…x 3.111…the “Eye” of 1.015873…x 1.25 = 1.269841…the GP Tan {480:378} that multiplied by the 3.111…x 46,656 = 184,320 a Musical Scales number and much more
The 3.111…x 18 = 56 Aubrey Holes, the 3.111…is also 1.75 x 1.777…the Square Root of the Rhind Papyrus fraction of 3.160493827…The GP Tan {480:378} of 1.269841…is W: 4.14644179350061703…x 3.265322912381…that multiplied by the prior produced 918.918 = 3,000.564 this divided by the GP base perimeter of 3024 Feet obtains exactly 0.99225 that multiplied by Gem Founder of the City 1225 = 1,215.50625 that multiplied by 256 = 311,169.6 this is the Platonic Precession : 25,920 x 12.005 this multiplied by the GP height of 480 Feet obtains exactly 5,762.4 that minus the GP height in Inches: 5760 = 2.4
The GP Tan {480:378}: 1.269841…x W: 4.14644179350061703… x 232.654296875 = 1225 The 232.654296875 x 46,656 = 10,854,718.875 this is the 3,000.564 x 3,617.55952380…which is 1,144.6184430803571428 …x 3.160493827…the Rhind Papyrus fraction
The 1,144.6184430803571428…x 7,168 = 8,204,625 this being the 918.918 x 8,928.571428…that multiplied by 112 = 1,000,000. The 112 x 27 = 3024 and the 7,168 is 3024 x 2.370370…that multiplied by 81 = 192 Gem Mary, therefore 2.370370…will obtain 288, 384, 480, 5760, 768, 864, 1056, 1152, 1536, 1728, 2016, 2112, 2304, 2592, 3072, 3168, 3456, 4608, 5184, 5280, 6144, 6336, 6912, 7776, 9216,10,368, 10,560, and much more, all PWS members or Units of Measure some being both also 2.370370…x 4.2525 = 10.08 the Greek Foot which opens additional doors, the 4.2525 x 256 = 1,088.64 further doors to open, I best come to an end here else the end will never be I mentioned prior regarding numbers ending with a number 5 this applies here
{8} The Shorter Roman Foot of 0.96768 is W x 0.233376 that multiplied by 3,937.5 = 918.918 the 3,937.5 being 1225 x 3.2142857… one-seventh of 22.5
……………………….
As indicated: 4.14644179350061703…denoted as W {10.08 ÷ 2.431}
There will be many occasions whereby the end digit of the produced number will end with a 5
{9} The Greek Foot of: 1.0022727…is W x 0.24171875
{10} The Roman Remen of:1.202727… is W x 0.2900625
{11} The Greek Cubit of: 1.50340909…is W x 0.362578125
{12} The Roman Cubit of:1.4432727…is W x 0.348075
{13} The Greek Digit of:0.06264204545…is W x 0.015107421875
Therefore, why does this number 5 emerge almost a constant, initially we must examine this occurrence beginning with the {9} product 0.24171875 The Gem: Founder of the City 1225 x 0.24171875 = 296.10546875 yet another end digit of 5 therefore Gem: Divine Circle 1224 x 296.10546875 = 362,433.09375 which divided by the GP base perimeter of 3024 Feet obtains 119.852213541666…which is 1.777…x 67.4168701171875 The 1.777…being the Square Root of: 3.160493827…the Rhind Papyrus fraction {256:81} consequently we understand we can maintain the end digit number 5 although which method do we employ do we establish a number that return us to the {9} Greek Foot of: 1.0022727…
The 67.4168701171875 multiplied by the Eye of Horus fraction {64:63} of 1.015873… x 5760 = 394,485 which is the Greek Foot of: 1.0022727…x 393,590.47619…that multiplied by 567 = 223,165,800 which is 3,966.666…x 56,260.285714…one-seventh of 393,822 which is W: 4.14644179350061703… x 94,978.3017857142…one-seventh of 664,848.1125 we have returned to the end digit being 5
Therefore the {9} 0.24171875 x 2,750,502.857142…= 664,848.1125 accordingly this 2,750,502.857142…multiplied by the Greek Foot of: 1.0022727…obtains exactly 2,756,754 Hence the calculation will now be {9} The Greek Foot of: 1.0022727…is W x 0.24171875 x 11,404,800 = 2,756,754 Accordingly, the NC {Numerical Canon} mean Moon Diameter of 11,404,800 Feet enters the area since:
{9} 11,404,800 multiplied by 0.24171875 = 2,756,754 = 3024 x 911.625
{10} 11,404,800 multiplied by 0.2900625 = 3,308,104.8 = 3024 x 1,093.95
{11} 11,404,800 multiplied by 0.362578125 = 4,135,131 = 3024 x 1,367.4375
{12} 11,404,800 multiplied by 0.348075 = 3,969,725.76 = 3024 x 1,312.74 {No number 5}
{13} 11,404,800 multiplied by 0.015107421875 = 172,297.125 = 3024 x 56.9765625
Therefore, with an end digit 5 we realize we can employ 11,404,800 likewise divide the product by the GP base perimeter of 3024 Feet, equally the GP base area of : 756 Feet x 756 Feet obtains 571,536 Square Feet, the GP Tan {480:378} of 1.269841…the GP 142884 and more
{14} The Common Egyptian Cubit of:0.98181…is W x 0.2367857142… one-seventh of 1.6575 that multiplied by 11,404,800 = 18,903,456 which is 571,536 x 33.074829931…that multiplied by W: 4.14644179350061703…= 137.142857…that multiplied by exactly 2.909375 obtains the 399 days for Jupiter
The 2.909375 multiplied by the 22nd PWS member 3456 = 10,054.8 which is the Persian Cubit of 21.12 x 476.0795454…that is the Egyptian Foot of 1.14545…x 415.625 which multiplied by 77,238.857142…= 32,102,400 this is the “Land” Mile of 5280 Feet multiplied by 6080 Feet the “Sea” Mile
The 77,238.857142…divided by the Earth Polar Radius of 3,949.714285…Miles obtains 19.555…which multiplied by 90 = 1760 the Yards in one Mile
The 77,238.857142…is also the Stonehenge Sarsen Circle Outer Diameter of 104.2724571428…Feet multiplied by 740.74074…that multiplied by 729 = 540,000 the 729 being the Square Root of 531,441 a Comma Of Pythagoras component {531,441:524,288}
The 77,238.857142…is 72.0896 x 1,071.428571…the Ring of Brogar base perimeter The 72.0896 is the GP Tan {480:378} of 1.269841…x 56.77056 that divided by the Longer value Greek Foot of 1.01376 = 56 Aubrey Holes
The 77,238.857142…is 35,555.555…x 2.1723428571…the Geographic Megalithic Cubit. The 35,555.555…x 18 = 640,000
The 77,238.857142…is 44.444…x 1,737.87428571…Feet the Silbury Hill base perimeter The 44.444…x 129.6 = 5760
{15} The Common Egyptian Cubit of:1.47272…is W x 0.35517857142… one-seventh of 2.48625 that multiplied by 11,404,800 = 28,355,184 which is the GP 142,884 x 198.44897959183…that multiplied by W: 4.14644179350061703…= 822.857142…this being one-seventh of 5760 The 198.44897959183…x 1225 = 243,100
{16} The Sacred Foot of:1.374545…is W x 0.3315 that multiplied by 11,404,800 = 3,780,691.2 which the GP Tan {480:378} of 1.269841…x 2,977,294.32… that multiplied by W: 4.14644179350061703…= 12,345,177.6 which is 86,400 x 142.884
{17} The Sacred Cubit of: 2.061818…is W x 0.49725 that multiplied by 11,404,800 = 5,671,036.8 which is the GP 571,536 x 9.92244897959… that multiplied by W: 4.14644179350061703…= 41.142857…this is the Maya STU, that I calculated likewise 41.142857…x 3.45205479…= 144, the 3.45205479…multiplied by the Maya 18,980 = 65,520 which is the GP base perimeter of 3024 Feet multiplied by 21.666…that multiplied by 1.2 obtains the Maya Calendar much employed number: 26
Hence the Maya STU of: 41.142857…will obtain: 288, 432, 5760, 86,400, 1008, 1152, 12,960, 1728, 2016, 2160, 2304, 25,920, 3024, 3168, 3456, 4032, 4608, 5040, 6336, 6912, 7920, 8064, 10368, and much, much more since it also obtains the Maya Earth Year component: 1,872,000
Equally the 9.92244897959…multiplied by Gem Founder of the City 1225 = 12,155 which is Gem Tree of Life 1625 x 7.48 that is the 364 Maya Temple steps multiplied by 0.02054945…that multiplied by the Maya “Super Number” 1,366,560 = 28,082.0571428…which is the Maya STU of 41.714285…multiplied by 673.2 which is the 2.431 x 276.92307692…that multiplied by Gem YHWH 26 = 7,200
Equally this 28,082.0571428…divided by the prior continually employed 77,238.857142…obtains exactly 0.36357421875 that multiplied by 1.3676712328… will regain the very commencing 0.49725 This 1.3676712328…multiplied by the Maya 5256 = 7,188.48 which is the Maya Temple steps 364 x 19.74857142…that obtains: 6912, 13,824, 20,736, 27,648, 34,560, 48,384, 76,032, 82,944, 96,768, 10,368, 24883.2, 145,152, 152,064, 172,800, 241,920, 11,404,800, 2,0901,888, 35,831,808, and so on, all Units of Measure {some increased} Musical Scales numbers, PWS members and much more
Here, the Moon 11,404,800 maintains the interconnection
{18} The Egyptian Cubit of:1.728 is W x 0.4167428571…one-seventh of 2.9172 that multiplied by 11,404,800 = 33,270,082.56 that divided by the above 19.74857142…obtains exactly 1,684,683 which is the GP 142884 x 11.7905643738…that that multiplied by W: 4.14644179350061703…= 48.888…that multiplied by the Lunar, Yin=Yang number 1080 reduced to 108 = 5280 Feet the Mile
{19} The Greek Cubit of:1.52064 is W x 0.366733714285… one-seventh of 2.567136 that multiplied by 11,404,800 = 29,277,672.6528 that divided by the GP base area of 571,536 Square Feet obtains 51.22629659…which divided by the {18} 11.7905643738…= 4.3446857142…one-seventh of exactly 30.4128 hence as is the normal result, this 4.3446857142…will obtain 15.2064, 364,953.6, 486.6048, 4,561,920,000, 608.256, 729.9072, 76.032, 91.2384, 973.2096, 106.4448, 121.6512, and so on, all Units of Measure {some increased}
{20} The Shorter Greek Cubit of:1.512 is W x 0.36465 that multiplied by 11,404,800 = 4,158,760.32 that divided by the 4.3446857142…obtains exactly 957,206.25 which is 2,625,000 x 0.36465
And this 4.3446857142…x 0.35 = 1.52064 the Greek Cubit therefore this 4.3446857142…will obtain 608.256, 4,561,920,000, 7.6032, 9.12384, 10.64448, 12.16512, 364953.6, 4866.048, 729.9072, 97.32096, as prior, all Units of Measure albeit some increased, some decreased
……………………….
As indicated: 4.14644179350061703…denoted as W {10.08 ÷ 2.431}
As referred to prior the products can be divided by the GP measurements including the volume of 91,445,760 Cubic Feet, for example the {21} product: 22,180,055.04 is the 91,445,760 x 0.24254875283…that multiplied by 52,920 = 12,835.68 which is exactly 2.431 Miles of 5280 Feet, the 52,920, for example, being the Platonic 25,920 x 2.041666…that multiplied by 600 = 1225 Gem Founder of the City and so on. Therefore, the choices of numbers to employ are numerous and varied, far too numerous to specify right now.
{21} The Longer Egyptian Foot of:1.152 is W x 0.2778285714… one-seventh of 1.9448 that multiplied by 11,404,800 = 22,180,055.04
{22} The Roman Cubit of:1.4598144 is W x 0.35206436571428… one-seventh of 2.46445056 that multiplied by 11,404,800 = 28,106,565.746688
{23} The Shorter Roman Cubit of:1.45152 is W x 0.350064 that multiplied by 11,404,800 = 3,992,409.9072
{24} The Arabian Hashimi Foot of 1.064448 is W x 0.2567136 that multiplied by 11,404,800 = 2,927,767.26528
A slight change of tack
As indicated prior, the time interval between one opposition and the next is just about 780 days for Mars, 399 days for Jupiter, and 378 days for Saturn
{25} The Standard Geographical Megalithic Rod of: 6.95149714285…is W x 1.676496979591…that multiplied by 1225 = 2,053.7088
Resuming: the Megalithic Rod of: 6.95149714285…x 7 = 48.66048 that multiplied by 11,404,800 = 554,963,042.304 Therefore, the Moon 11,404,800 Feet, otherwise ratios of will suffice, likewise the 48.66048 x 100 = 4866.048 the Roman Mile. However, the question at this time being what are the mathematical properties of the numbers which we produced via employing the Moon 11,404,800 Feet. I will begin with: {9} 11,404,800 multiplied by 0.24171875 = 2,756,754
The 2,756,754 is the GP base perimeter of 3024 Feet multiplied by 911.625 that is the 0.24171875 x 3,771.428571…the numerical sequence: 124578 remains in place, yet as per norm, rearranged therefore all is running well. Since the 3,771.428571…x 1.4 = 5280 Feet the Mile . Therefore, we can obtain exactly 1,132,832,250 every time, which, for example, is the Maya Long Count of 1,360,800 x 832.4751984126…that multiplied by the 378 days for Saturn obtains exactly 314,675.625
This 314,675.625 is the GP height of 480 Feet multiplied by 655.57421875 which is Gem: Abraxas, Mithras: 365 x 1.79609375 that multiplied by the Maya Earth Year {1,872,000 ÷ 5,130} of 364.9122807017…= 655.41666…which is Gem: Tree of Life 1625 x 0.40333…that multiplied by 12,000 = 4,840 the Square Yards in one Acre, hence the 0.40333…x 2,700 = 1,089 one-ninth of 9,801 hence reversed.
The only four-digit numbers that are integral multiplies of their reversals {G. H. Hardy: Mathematician’s Apology} are 8712 and 9801, likewise the numbers 2178 and 1089 are the only two numbers smaller than 10,000 with multiples that are reversals of themselves {discounting the insignificant number 3443 x 1} There is much more to the 1,132,832,250 than I could demonstrate in one fell swoop as it were, for example it is exactly 186,321.09375 British Admiralty Nautical Miles of 6080 Feet and this 186,321.09375 divided by the prior 655.57421875 = 284.21052631578…that multiplied by the Greek Cubit of 1.52064 then by the Metonic Cycle 19 obtains exactly 8,211.456 which is exactly 8,100 Longer value Greek Feet of 1.01376. The again the 284.21052631578…multiplied by the 399 days for Jupiter obtains exactly 113,400 which is the Platonic 25,920 x 4.375 that multiplied by 691.2 = 3024 Feet the GP base perimeter, the 691.2 being an Egyptian Stade and the 31st PWS member is 6,912
……………………….
Resuming the: “Since the 3,771.428571…x 1.4 = 5280 Feet the Mile”
There being no dire need to employ the 3,771.428571…twice, it simple saves space and time, likewise, as per norm, there are various other options available
{A} 3,771.428571…is 4,166.666…Common Mycenaean Canonical Feet of 0.905142857…The 4,166.666…x 271,879.74 = 1,132,832,250 Otherwise, the 4,166.666…x 12 = 50,000,
The 271,879.74 is the “Sea” Mile of 6080 Feet multiplied by 44.7170625 that multiplied by the commencing 3,771.428571…= 168,647.20714285…one-seventh of 1,180,530.45 which is the GP base perimeter of 3024 Feet multiplied by the Royal Egyptian Cubit of 1.714285…x 227.72578125 that multiplied by 10,240 = 2,331,912 which is the Square Feet in one Acre 43,560 x 53.5333…that multiplied by 108 = 5,781.6 which is the GP height of 5760 Inches plus 21.6, the 9th PWS member is 1024, the 108 being a reduced Lunar, Yin-Yang number 1080
I will not maintain the rest for such an extended period since I am convinced the options available are recognizable, for example the {B} product 1,416,636.54 is the {A} 5,781.6 x 245.025 that multiplied by 40 will obtain the prior indicated 9,801
{B} 3,771.428571…is 3,472.222…Assyrian/Germanic 1.0861714285…{Likewise the Belgic Foot} The 3,472.222… x 326,255.688 = 1,132,832,250 Otherwise, the 3,472.222…x 144 = 500,000
The 326,255.688 is the “Sea” Mile of 6080 Feet multiplied by 53.660475 that multiplied by the commencing 3,771.428571…= 202,376.64857142…one-seventh of 1,416,636.54 that is the 1.0861714285…x 1,304,247.65625 The 1.0861714285…x 96 = 104.2724571428… Feet the Stonehenge Sarsen Circle Outer Diameter
{C} 3,771.428571…is 2,170.13888…Long Geographical Royal Cubits of 1.73787428571…The 2,170.13888… x 522,009.1008 = 1,132,832,250 Otherwise, the 2,170.13888…x 9,216 = 20,000,000 the 35th PWS member is 9216.
The 522,009.1008 is the “Sea” Mile of 6080 Feet multiplied by 85.85676 that multiplied by the commencing 3,771.428571…= 323,802.637714285…one-seventh of 2,266,618.464 that is the 1.73787428571…x 1,304,247.65625 The 1.73787428571…x 37.5 = 104.2724571428… Feet the Stonehenge Sarsen Circle Outer Diameter
{D} 3,771.428571…is 1,356.33680555…Megalithic Yards {S: Geographic} of 2.780598857142…The 1,356.33680555… x 835,214.56128 = 1,132,832,250 Otherwise, the 1,356.33680555…x 36,864 = 50,000,000
The 835,214.56128 is the “Sea” Mile of 6080 Feet multiplied by 137.370816 that multiplied by the commencing 3,771.428571…= 518,084.2203428571…one-seventh of 3,626,589.5424 that is the 2.780598857142…x 1,304,247.65625 The 2.780598857142…x 60 = 104.2724571428… Feet the Stonehenge Sarsen Circle Outer Diameter
{E} 3,771.428571…is 3,616.89814814…Royal Athenian Geographic of 1.042724571428…The 3,616.89814814… x 313,205.46048 = 1,132,832,250 Otherwise, the 3,616.89814814…x 829.44 = 3,000,000 The 313,205.46048 is the “Sea” Mile of 6080 Feet multiplied by 51.514056 that multiplied by the commencing 3,771.428571…= 194,281.5826285714…one-seventh of 1,359,971.0784 that is the 1.042724571428…x 1,304,247.65625 The 1.042724571428…x 100 = 104.2724571428… Feet the Stonehenge Sarsen Circle Outer Diameter
{F} 3,771.428571…is 723.37962962… Roman Pace of 5.21362285714…The 723.37962962…x 1,566,027.3024 = 1,132,832,250 Otherwise, the 723.37962962…x 248,832 = 180,000,000
The 1,566,027.3024 is the “Sea” Mile of 6080 Feet multiplied by 257.57028 that multiplied by the commencing 3,771.428571…= 971,407.913142857…one-seventh of 6,799,855.392 that is the 5.21362285714…x 1,304,247.65625
The 5.21362285714…x 20 = 104.2724571428…Feet the Stonehenge Sarsen Circle Outer Diameter The 5.21362285714…x 70,000 = 364953.6 Feet one Degree of Latitude, since 360 Degrees multiplied by 364953.6 Feet obtains 131,383,296 Feet the NC {Numerical Canon} Earth mean Circumference otherwise 24883.2 Miles. Equally the 364953.6 Feet is the Stonehenge Sarsen Circle Outer Diameter of 104.2724571428…Feet multiplied by 3,500
Until the next essay {Khufu Pyramid Two}
Copyright © 2006 Derek. A. Skhane All Rights Reserved
Gnosis Regained 