**The Geometric Origins Of ****Our Contemporary World’s**

**MEASURES OF LAND**

**An Analysis of Lengths and Areas**

This next chapter should be of particular interest to both *surveyors* and *architects*. None of them have ever been taught the true roots of the measuring units handed down to them from the past, and with which they work every day. Neither they, nor the rest of humanity, have any idea that the *inch,* *foot*, *yard*, and *mile*; the *acre* and *township*; even the *grain* and both *ounces *and* pounds *(troy and Avoirdupois) all are inextricably connected not only *to one another*, but to *America**’s system of gold and silver coinage*. The clear mathematical evidence in support of the above allegations has been hidden from the public *for thousands of years*!

When Edmund Gunter introduced his newly invented land measuring *chain* at the beginning of the 1600’s, in all probability he was releasing some very old and secretive knowledge along with it. Whether or not Gunter himself actually knew what I am about to disclose to you, the first readers of this manuscript, no one can say with any certainty. Personally, I think he knew everything I am about to disclose. What I do *know*, *and can* *prove*, is that the system of land measures designed *by man, for man,* corresponds to *the eternal geometric principles governing surface area* to a better than **99.999%**. . . approach to perfection! To the best of my knowledge, these simple mathematical and special relationships (that I am revealing here and now) never have been taught in any “traditional” classroom, public or private.

**The Geometric Origins of the**

**Surveyor’s Chain, Acre, and Mile **

By the time *The United States Of America *was established back in the late 18^{th} century, the science of land surveying had already evolved to a relatively sophisticated and disciplined art-form capable of producing very accurate results for their times. Surveyors were even using their own unique measuring rule, called the “surveyor’s chain”, complete with its own unique set of measures. All of this *science* had been established centuries earlier in England, and was brought to America by the British colonials.

To get at the true roots of our land measurement system it is important to understand the chronology of key events leading up to the creation of “townships” in America. The first was the codification of the “mile” (equal to **5,280** feet) into British law in 1593 under the first Queen Elizabeth. The second event involved a man named Edmund Gunter. History records that in 1607 Gunter’s work resulted in Parliament standardizing the “*rod*” as a survey measure of **16.5** feet. A few years later (ca. 1620) he introduced a land survey devise that quickly became known as “Gunter’s *chain*”.

In Gunter’s vision of land measurement, the unit known to the general public as a mile of **5280** *feet* was instead equal to **80.0** *chains*. Since there was no metric system in general use at the time, the natural division of the mile was into *halves*, *quarters*, *eighths*, and so on. Gunter’s mile consisting of **80.0** chains can be seen to first divide into **8.0** parts; and then, each part divided into **10.0** chains.

Edmund Gunter was a mathematician and astronomer and was certainly aware of a growing science that the general public had no knowledge. Scientific technicians of his time were aware of the “base-ten” system, and it is obvious Gunter was no exception. When he *chose* to divide the mile into “tenths”, after its first division into **8** parts, Gunter had *purposefully* broken with what until then had been tradition. This division into ten *was out of context for that time in history. *Nonetheless, soon these *one-tenth parts of an eighth of a mile increment* became customary to land ownership units, just as the “foot” measure was to the mile.

The “chain” that Gunter designed as a physical measuring tool was literally in the form of a chain. But this chain is of a very unusual and unique design. It bears little resemblance to what was recognized then and now as a common chain of uniform links. Overtly, the chain is **66** feet long. It is comprised of **100** “links” with every **10.0** links marked by a brass ring. *Property lines and distances in general were recorded in numbers of “chains and links”*. It was a simple scale based on **1.00** (chain) and **100** (links).

Since the chain is **66** feet long and there are **100** links, each link is then .**66** of a foot, which is also **7.92** inches. Once again these are the *overt* measures. To Gunter, the chain’s creator, and to his *behind the scenes* unnamed colleagues and collaborators, the true occulted symbolic measures lay hidden beneath the surface. For the fundamental unit chosen to be *the designed micro-measure* (on a scale where the chain of **66** feet is the *macro-measure*) is .**99** inch! In this way, each link of **7.92** inches is really the sum of **8.0** units each .**99** inch long. This makes the chain a unit of measure totaling exactly **800** “survey”, or “chain” inches, that are .**99** the length of the *standard inch*.

I know this sounds crazy, but it even gets crazier. Let’s look at the “mile” measurement again. To Gunter, and for the rest of Europe it measured **80.0** chains. Again, it was divided “traditionally” into **8.0** parts, and then each part further divided into **10.0** (chains). But *only* Gunter and his *illuminous* colleagues knew that the true length of his chain was **800** units of .**99** inch. *Now for them*, the mile measured an even **64,000** (“survey-chain” or *illuminati*) inches. The rest of Europe had no idea (until today) that their mile, measuring 63,360 inches, had just been “covertly” altered; nor *why*?

Now, when Gunter *overtly* divided his chain of **100** links into increments of **10.0** links (marked by brass rings) he was also concealing its more important *covert* division into **8.0** parts. For to the *illuminated ones*, just as each **7.92** inch link *became* **8.0** units .**99** inch long, *the chain itself* naturally divides into **8.0** units, making each of the eight segments **8.25** *feet*; or, **99** *inches* in length! So from this vantage point, the chain is sub-divided into eight **99** inch units, with each one containing one-hundred .**99** inch units.

It doesn’t stop here. No, as we continue, it just gets more and more unbelievable. *But it will also all start making sense*. For example, a length of **5280** feet becomes **640** units, each exactly **99**” long. This means that a “square-mile” (which is one “township” *section*) measures **640** of these **99 **inch “units” per side. Moreover, **640** *squares* measuring **99**” per side, laid out in a single line edge-to-edge across the earth’s surface, not only equals *one mile* in *length*, but also covers an *area* __exactly__ equal to **1.0** *acre*. Since there is **640** acres in **1.0** square mile you can repeat this process **640** times perfectly covering every square inch contained within that square mile.

Let’s take a closer look at this very unique **99 ***inch* square. First, sub-divide it in the same manner that a standard “township section”, one square mile, is typically sub-divided. This is into “quarter-sections”. The **99** inch edge-measure, sub-divided, creates four “quarter-sections” with **49.5 **inch long edges. But to Gunter and his collaborators, and to the contemporary *custodial illuminati* in charge today, the occulted expression of this “quarter-section” square’s edge-measure is twice **24.75** *inches*; and/or equally **4.125** *feet*. Readers of the previous chapters will recognize these *quantities* as ( powers of) respectively the pure gold content (in *grains*) in the $**10** “*eagle*”, and the gross weight of America’s foundational monetary unit, the $**1.0 ***silver *coin**.**

Forget it! It’s NOT a coincidence! It gets better. Remember, America’s *coinage* system, and its system of *land* division, were enacted into law at about the same time in our history; generally, the early 1790’s. So, when the occulting veil is pulled still further back, and we see deeper into the mathematical and geometric composition of this **99** inch *square* we also find that each quarter-section contains an *area* of either:

**66** times **37.125** square inches

or

**99** times **24.75** square inches

Again, both quantities are (powers of) the foundational monetary measures of weight *right out of the 1792 Coinage Act*, where it specified *there be precisely* **371.25** *grains* of pure silver in the dollar coin; and, **247.5** *grains* of pure gold in the ten dollar “eagle”. And those behind the scenes, who made “damn certain” that *these* were the measures America use for her new monetary system, also were fully aware that the two coins they had designed contained *exactly* **99** *troy* ounces of pure silver in every two times **64** silver dollar coins; and, that there is **66** *troy* ounces of pure gold in every two times **64** gold *eagles*. Of course, we just saw the **99**, **66**, and **64**, to be the occulted foundational quantities of Gunter’s system of land division.

Look at these monetary measures of weight, and the inter-play between them, when instead of *weight* these “magical quantities” are units of *length* or *area*:

**41.25** square *feet* = **371.25 **square *inches* times 16

**41.25** square *feet* = **247.5** square *inches* times 24

Now watch how these quantities *as area* morph into actual physical replicas of the monetary *weight* measures:

**66 **sq.’ / 16 = **4.125 **sq.’ = **594 **sq.”

**594** sq.” = **24.75 **sq.” (X) 24; or, **37.125 **sq.” (X) 16

and

**594** (**27**milli** gram** “cubets”) =

**247.5**041632…

*grains* Once again we look to the “cuboids” in the previous photograph that model the weights of the pure silver (**371.25** grains) and pure gold (**247.5** grains) that was specified for each coin in America’s 1792 Coinage Act. The $**10** gold Eagle is the cuboid behind the larger cuboid in front. Its **594** cubets, comprising its allocation of pure gold, is the aggregation of the white **27**mg cubets. The remaining **54** red cubets is the amount of *alloy* in this coin’s **27**0 grain gross weight. Note that:

**594** white cubets + **54** red cubets = **648** cubets;

**648** X **.027 **gram = 17.496 grams;

17.496 grams = **270**.0045417… grains

( i.e., the gross weight of the $10 gold *eagle*)

There are **891** white **27**mg cubets comprising the cuboid in the foreground of the above photo. This is the **371.25** grains of pure silver contained in every $**1.0** coin. The remaining **99** red cubets is the amount of copper alloy specified for this coin. This cuboids’ **990** “cubets” in all, add up to this coin’s gross *weight* of **412.5** grains. Now, morphing back into measures of *area*, we see that:

(**99 **sq.’ /16) = (**24.75**sq.’ /4) = **891**sq.” = (**4.125**sq.” (X) 216) = (**37.125** sq.” (X) 24)

and

**(110**sq.’ / 16) = (**41.25**sq.’ / 6) = **990**sq.” = (**24.75**sq.” (X) 40) = (**41.25**sq.” (X) 24)

and

**990** (**27** milli** gram** “cubets”) =

**412.5**069387…

**grains**

** ** Clearly, the coinage *weight* measures, specified in America’s 1792 Coinage Act, are quantities arising from the same occulted math and geometry as that which created Europe’s *much earlier* terrestrial measures of *length* and *area*. We can see this in the number of increments of **41.25** *lineal *feet in *one mile*: two times **64**. Half this length is **20.625** *lineal* feet. If this length is used as one edge of a rectangular tile and **20** *lineal* feet the other, then the area of this tile is **412.5** *square* *feet*. Using [(2)^{10 }X **66**] tiles of this size an entire *square mile*, **1.0** township *section*, can be perfectly covered. Tiles **20.625** *inches* by **20** *inches* measure **412.5** *square inches* in area; and precisely [3(2)^{15} X **99**] of these will likewise perfectly cover **1.0** *square mile*.

Ten silver dollars contain **3712.5** grains of pure silver. And, **3712.5 **square feet equals **412.5** *square yards*. Tiles of this size won’t perfectly cover a township “section”, but precisely [(2)^{12} X **66**] of them fit perfectly on *one entire township* of **36** square miles (quite fitting for a yard equaling **36** inches). The edges of this tile, like the other tiles mirroring the silver dollars gross weight of **412.5** grains, are in a **20.625** by **20** proportion. This can be converted to a simple **66/64**, or a **33/32** ratio between the two edges. This shape is very close to being a perfect square. And if we scale this form down to “the fundamental micro-unit of land measures”, the *square inch*, so that the shorter edge equals one inch (**1.0**”), then the other edge is exactly **1.03125**”, which is 1/**32**^{nd} of an inch longer. One side is **32** thirty-seconds of an inch, and the other **33**. This “difference” is key to understanding the reason “land” and “monetary” measures share powers of the same quantitative units.

Also at this point, it may be important that we take note of the following excerpts from “The Great Pyramid of Giza” by Eckhart R. Schmit regarding our ancestral “Royal Cubit”:

The units of measure used in the construction of the Great Pyramid are the Royal Cubit and the Pyramid Inch. There is some evidence that the measurement unit known as the Royal Cubit was already in use as much as one hundred years prior to the building of the Great Pyramid, and perhaps even somewhat earlier. It was employed as a unit of measure for the construction of buildings, for the measure of land, grain quantities etc. The Royal Cubit was of central importance as a standardized unit of measure at the time of unification of upper and lower Egypt^{(2)}. One can infer that the dimension of this unit of measure could be geodetic in nature, that is to say, having some specific relationship with the physical attributes of the Earth’s shape. Generally the Royal cubit is understood to have been 524 millimeters +/- 2mm (**20.63** inches) in length. Professor Flinders Petrie, who is regarded as the founder of Egyptology, and had studied the Temples and Buildings of Ancient Egypt with utmost exactitude in the 1880’s assigned a value for the Royal Cubit of **20.632** +/- .004 Imperial British Inches based for the most part on the dimensions found within the King’s Chamber in the Great Pyramid^{(3)}. (and) In review of the dimensions of the King’s Chamber, Sir Isaac Newton ascribed a value of **20.63** Imperial British Inches for the Royal Cubit^{(4)}.

If the “Royal Cubit” is in fact “524 millimeters +/− 2mm”, then the **20.625** inch measurement also being 523.875mm, certainly must now be a strong candidate for assumption to that *Royal* honor.

** ****Measures of Land and Coinage Measures**

**Are Powers of the Same Units**

Generally, “land measures” are units of *length* and *area*, whereas “coinage measures” describe *weight* and *volume*. But in the light of occulted geometry, we find both *land* and *coinage* measures derive from *the same geometric properties of form*.

Euclid showed us that the fundamental units of both *length* and *area* are inherent to a simple “square”. An area of **1.0**^{2} (one *square* unit) in the form of a square has an edgelength equal to **1.0**^{1} (one *line*al unit). All of “geometry” ultimately is scaled to this basic form, and from it, so too do our measures of *land* and *money*.

Geometry shows us that there is a *maximum amount of volume* that **1.0** unit of *surface* is capable of completely enclosing *within the confines of its surface*. This amount is 0.**0940**31597… of **1.0** *volume* unit; and this volume will be in the form of a perfect sphere (these quantities are depicted in the image at the beginning of this chapter). The mathematical relationship between one square unit of *surface* and this ideal *volume* quantity is expressed by this ratio: **1.0** ∕ 0.**0940**31… i.e., **1.0** surface “unit” to 0.**0940**31… “unit” of volume. But there is another *equal* mathematical description of this *same* relationship since:

**1.0 ****∕ 0.094031… = 10.63472310… ****∕ 1.0**

These *portions*, these *quantities* are etched into the foundational bedrock of geometry, and as we will see, lead directly to the measures of land and coinage.

In its pure form, geometry refers only to *the unit*, not to “The Unit”. For to do so, requires assigning a “name” to that original *square* “unit” of *surface* area. It could be (**1.0**^{2}) square *inch*, *foot*, *yard*, *meter*, *acre*, *hectare*, . . . or any other *named* unit, and an entirely *unique* geometry would unfold from each one. Some time in the past, *someone* made that *name* choice, *at least for measures **here on earth*. You be the judge after reading the following.

** ****1.0**^{2}** “FOOT”**

** The Fundamental Unit**

**Of Terrestrial Measurement**

** ** By assigning the name “*one foot*” to geometry’s originating square of one surface unit, a *scale* was imparted to these forms. But why *choose* one “foot”? Well, remember the ancient maxim “Man is the Measure of All Things”? Maybe there really is something to it?

Now, **1.0** ∕ 0.**0940**31597…means **1.0** “*square* foot”, and a 0.**0940**31597… portion of **1.0** “*cubic* foot”. This means that **10.63472310**… ∕ **1.0**, __its equivalent mathematical description__, is also scaled in “feet”. And it is here, at

*this*strange quantity of area, where we have finally arrived. We are now in possession of

*the mathematical key*to a doorway, which when opened,

*will reveal some of the world’s best kept secrets*. Let’s start by looking at the following equation:

**10.63472310… sq. ft. = 1531.40**01**… sq. in.**

** **and then this equation:

**41.25 in. X 37.125 in. = 1531.40**62**… sq. in. **

The results of these equations are *identical* to a **99.999**6001…% approach to *perfection*. And in them, we can clearly see the quantities **41.25 **and** 37.125** “inches” to be the essential (sub-unit) building blocks, *at what is literally the very birth of geometry itself*. And remember, all of this was gleaned from the geometric properties of a simple square equal to *one square unit.* It’s also worth noting here that these *lengths* are in a **9/10** ratio, just like the pure silver alloy in their counterpart *coinage weight* measure. Geometry is telling us that this *square* area, equal to **10.63472310**… square feet, is something *unique*, something *very* *special*. And indeed it is! For it is quite literally ** the seed of the acre**; and from it are derived

*all*of the other standard

*measures of land*we (in America and much of the world) have come to know today. Here is how it works.

Traditionally, from America’s birth in 1789 through today (2014), the “township” has been the “macro-unit” of land area sub-division. A “township” is simply a square area measuring **6** *miles* per edge and encompasses **36** square miles. Each square mile is called a township “section” and is the first sub-division of the macro-unit.

This **1.0** square mile traditionally subdivides first into “¼ sections”, then “¼, ¼, sections”, and finally into “¼, ¼, ¼ sections” subdividing the edge of the square mile into **8** parts. Now, like the classic “checkerboard”, the area of the square mile has been subdivided into **64** sub-unit squares. The area of each one of these squares is **10** “*acres*”. No further subdividing of the mile’s edge is possible because the resulting smaller parcels won’t contain *whole* increment *acre* units.

So far it works like this. The “township” square sub-divides once into **36** sub-squares, each a square mile. The square “mile” first subdivides into **4**–**160** acre parcels. Next, by quartering each quarter, there then are **16**–**40** acre parcels. One more quartering brings us to **64**–**10** acre *square* parcels. That’s it for the *square* **mile**, leaving only *the 10 acre *parcels for further sub-division.

Here arises a geometric “problem” in that a square cannot be easily sub-divided into **10** acres. That is, unless you have the correct *measuring rod.* Gunter shows us the solution to this problem in the early 1600’s with his special “chain” measuring **4** “rods”. . . i.e., **66 ***feet*. Since a **10** acre square measures **66**0 feet per edge, or **10** chains, the **10** acre square naturally sub-divides into **100** square chains. **1.0** acre then is simply **10** square chains. Each square chain is **66** feet per edge. And it is *this “square chain”*, **100** in all, that *constitutes the ***10*** acre square’s next sub-divisional unit*.

The most efficient geometrical arrangement of **10** square chains into **1.0** acre is a *rectangle* measuring **2** chains by **5** chains. Each **1.0** of the **10** square chains is 1/10^{th} acre.

Thus far, beginning with the “township” unit, down through the sub-divisioning all the way to the “square chain”, there really is no *mystery*. The “traditional information” just summarized in these last 5 paragraphs is all out in the open for anyone interested in the subject of *surveying*. But, what now follows here, *you will find nowhere else but here*.

If one sub-divides the “square chain” exactly in the manner as a square mile, i.e. into ¼ sections; ¼, ¼ sections; and ¼, ¼, ¼ sections, we’ll have divided *it* into **64** smaller squares. This means that the “chain” itself has just been *covertly* divided into **8** parts. I say “covertly” because, as was stated earlier in this chapter, Gunter’s “overt” divisioning of the chain is into **100** links marked off with brass rings every **10** links.

The division into **64** sub-unit squares makes each square’s edges measure **99**” X **99**” (twice **4.125**’) enclosing **9801** square inches. Now, sub-divide *this* square into **64** more sub-unit squares. The edge-length of each one of these squares is **12.375**” (which is **33/32** of a “*foot*”); and each encloses an area of **153.140625** square inches (which is **4.125” X 37.125”)** . . . or, **1.06347**6563… square feet. The following *simple arithmetic* shows just how deeply the three powers of *America*** ’s foundational coinage weight measures** combine

*together*to form this

*basic unit of length*for land measurements:

**(.2475) + (.37125) + (**.**4125) = 1.03125**

** ** If the measures highlighted in *red* in the above equation are portions of **1.0** “__foot__”, then their sum is **1.03125** “foot” (or **12.375** “inches”). And again:

**(24.75” / 2) = 12.375” = (37.125” / 3)**

** ** Ten of these **12.375**” squares arranged in one rectangle measuring **2** squares by **5** squares is itself a micro-model of the **10** combined to form one acre. This rectangle measures **10.6347**6563… square feet.

Therefore, it must be concluded that this **10.6347**6563… square foot rectangle is to the *acre* as the **1.06347**6563… foot square is to the *square chain*. And, it is this **1.06347**6563… *foot* square that is, in practice, *The Fundamental Unit* at the very basis of *all* land measures predicated on the *mile, yard, foot, and inch*.

Readers don’t need to be “rocket scientists” to conclude for themselves that all of the quantities above already had been exposed a few pages back, having been distilled directly from the properties of geometry’s “*Fundamental Unit of Surface Area*” . . . a simple square with its edge **1.0** unit in length. From this square area, by following a path well marked by simple geometry, we were led to conclude that a surface area equal to **10.6347**2310… square “units” is an equivalent mathematical expression describing geometry’s *Fundamental Unit of Surface Area*.

Now remember, the **10.6347**6563… foot *rectangle* that we just discovered three paragraphs back began with an investigation of the *largest* square “unit” called a “township” comprised of **36** square miles. Its sub-unit, the “square mile”, was then sub-divided into **64** smaller squares of **10** acres each. Each of these **10** acre parcels are further sub-divided into **100** “square chains”. The “square chain” divides into **64** squares **99**” per edge, which are in turn *finally* divided into the **64** squares. As stated just above, these last **64** *Fundamental Units* of land measurement “square chains” each contain **1.06347**6563… square feet and measure **12.375** inches per edge.

Now, let’s see how *they* compare; “they” being “*man’s* measures”, compared to “*geometry’s* measures”, *which existed before time itself*.

When geometry’s *special* area of **10.6347**2310… square feet is sub-divided into **10** squares and arranged like the **10** “square chains” comprising an acre, the *exact *edgelength of each one of these *geometric *squares is **12.37497526**…inches. This compares to the **12.375** inch square arrived at working back from the “township” as:

**12.37497526**… ∕ **12.375 = 0.999998001…**

These two measures are literally **99.9998**% *identical*! But how can this be? Surely “they” should have taught this to all of us in school; why isn’t this in our history or science textbooks?

Even *today’s* surveys don’t approach this degree of accuracy. For example, the *statute* mile of **528**0 feet contains **512**0 units, each **12.375** inches in length. This is a total of **63,360** inches. And **12.37497526**… inches **512**0 times equal **63,359.87333**… inches (which I propose be called “**The Geometric Mile**”). The difference between these two measures is a mere 0.**12667**0000… *inch*, *exact*! It is .00**167**” over 1/8^{th} inch.

It should be noted here that one can lay out a perfect rectangular *acre* using U.S. *silver* *dollar* *coins*. One side of this *acre* will measure **528**0 dollar coins and the other **528** (Note: the coin’s diameter is 1.5”; **528** X 1.5” = 792” or **66**’, or **1.0*** chain*.). It is also important to note here, that by using the *long* *edge* of the old United States issued “large” paper “bills”, printed from 1862 through 1928, precisely **512**00 of these laid out (small) edge to edge will perfectly delineate the six mile edgelength of a “township” (see chapter titled “The Geometry of Paper Money”). And in keeping with the land measures schematics thus far exposed above, these quantities **528 **and **512 **are related as

**1.03125 **/ **1.0**; which we also know to be **33/32**.

**A Tale Of Two Squares**

** **** **Lets return to the early 1600’s and revisit Gunter’s chain and the “mile” measure that was already well established and written into English law. Since the mile is equal to **80** chains, a “square mile” contains **64**00 *square* chains. An since the chain of **66** feet is *actually* **8.0** units each measuring **99**”, then a single *square* *chain* contains **64** of these **99**”squares; again, just like the classic chessboard. Using these measures, a square mile becomes an assemblage of **99**” squares; **409,600** of them in all; **64**0 per edge.

Now, remember earlier in this chapter it was demonstrated that the relationship between **1.0** unit of *surface* and the maximum amount of *volume* it is capable of containing is expressed by the ratio **1.0** / .**0940**3…. and equally expressed by its reciprocal **10.6347**… / **1.0**. These are two *different* mathematical expressions meaning exactly the *same* thing. They are *equal* (=) to one another.

Apply this same logic to the *edge*–*length *of the square mile with its **64**0 measures of **99**”. This is to say, *look at the same mile measure as consisting of ***99*** units, each ***640***” in length*. In this way, the *square mile* is subdivided into a grid **99** units by **99** units mirroring its interior sub-division into **99**” by **99**” squares. The *white squares* in the following grid number **99** per edge. Each of these squares measure **640**” by **640**”. And the sum of their individual areas equals the **640** *acres* comprising **1.0** square mile.

With the addition of the indicated *red squares* to the grid, we have a slightly larger square; it now has an *even* **100** squares per edge, rather than **99**. It also measures an *even* **64,000** inches compared to the mile’s **63,360** inches.

If each of the **100** links in Günter’s chain was **8.0** inches rather than its overt measure of **7.92** inches, then the mile *would* measure **64,0**00 inches . . . but it doesn’t. It’s obvious that one line of (**640**”) squares was removed from each of two adjacent edges to create the remaining *perfect* **640** acre square area. So how many *acres* were *subtracted* from the larger square to create the smaller? Or equally, how many *acres* were *added* to the smaller square to achieve the larger?

Since there are **100** red squares on one edge, and **99** left on the other, there is a difference altogether amounting to **199** squares with edges measuring **640**”. Each of these individual square’s areas measures **409,600** *square inches* (and is itself a reflection of the greater *square mile unit* and its division into **409,600** squares with **99**” edges). Next, we multiply this area by **199** units and arrive at a total of 81,510,400 square inches. If we divide this by 144 we have the number of square feet: 566,044.444…; and if we divide this by 43,560 (the number of sq. ft. in **1.0** acre) we will have found the number of acres: **12.99**459239…

So by subtracting **12.99**459239… “acres” from the large square we arrive at a little smaller square containing __precisely__ **640** acres; **1.0** square mile. To be consistent with all that has been revealed thus far, one would *expect* this **12.99**459239… quantity to be a *very* special unit. Let’s see how this quantity relates to *measures of area* with respect to *The Geometry of Form*. This investigation will bring us full circle, back to the “beginning”, and the **1.0** Surface Unit in the form of a sphere’s *surface*. . . and from there, *the geometric origin* of the “t**own**ship”.

Once again, look at the image on the first page of this chapter. The spherical *volume* rests on top of its *surface area*, which is laid out flat in the form of a square. This construct is *quanta-sized* by the sphere’s surface area being equal to **1.0** areal or *square* unit. In the previously uncharted *dynamic transformational geometric system*, that I have been independently exploring now for nearly forty years, and which I have long referred to as *The Geometry of Form*, __changes in surface and volume are strictly accountable__. The following example is typical of this accounting principle, and at the same time will show the significance of this

**12.99**459239… quantity with respect to measures of

*surface area*.

What happens when *geometry* divides the *volume* of this sphere into two new spheres? Remember, its volume is .**0940**3159… so the volume of each new sphere (made from the original’s volume) is .**0470**15799… In this sphere’s *transformation by division*, one-half of the original sphere’s surface area (**0.5**000…) is likewise imparted to each new sphere. But that’s not enough. A sphere with a .**0470**15799… volume has a .**629960**526…surface area. Thus each of the two new spheres is *missing* a .**1299**60526 portion of **1.0** unit of *surface*.

This specific quantity of missing *surface* *area* is a *geometric constant*. We know this because regardless of *whatever shape or form* that the **1.0** surface unit assumes, if it divides its *volume* into two new forms *identical* to the original form each will be in need of an additional .**1299**60526… surface unit.

Look at the data thus far. We have two components of surface area: one has been distilled from *terrestrial land measures*, and the other from a *spherical* *geometric transformation*. Though differing by a magnitude of 100, the *essence* or *root unit* of these two quantities is **99.99**% the same:

**12.99**459239… / .**1299**60526… = .00**99988**76…

At the heart of this quantity’s *essence *is a prime numeric expression: **1299. **This is a *magnitude*, used in conjunction with various *powers*, to form *proportions* defining geometric objects and their *surface*, *volume*, and *lineal* transformations through *distortion*, *division*, and *fusion*.

Here are some examples of how *The Geometry of Form* uses *this* very special **1299** quantity. In order for the *sphere* with a *surface* *area* equal to **1.0 ^{2}** unit to be able to “distort” into a

*cube*(with a surface area equal to

**1.0**unit) it must first

^{2}*eject*a quantity of what is now

*excess volume*amounting to two times .0

**1299**5108…

**volume**unit. Another example is if two times .

**1299**5108…

*surface*unit is added to an

*octahedron*with a

**1.0**unit

^{2}*surface area*, its

*volume*can then “distort” into a

*tetrahedron*al form. And another simple (2-dimensional) example begins with a

*circle*with a

**1.0**

*lineal*unit radius and an inscribed equilateral triangle;

**1.299**0381… units is the amount of

*surface*area enclosed by the triangle. Or if instead, the

**1.0**

*lineal*unit is the edge of a tetrahedron and one imagines it as sitting flat on a table top, then one of the tetrahedron’s four sides is this pyramid’s

*base*and is unexposed; the amount of remaining exposed

*surface area*is

**1.299**0381… units.

The correspondence between what I’ve termed *the Illuminati’s system of weight measures based on the 27 milligram cube* and their

*system of land measures*was exposed earlier is this chapter and previous chapters. In the same way that the two cuboids constructed from these

**27**mg cubets (depicted in the earlier photo) replicated the weights and

*exact*alloy proportioning for America’s flagship gold and silver coins, so too is the much older

*Avoirdupois ounce*of

**437.5**grains represented by

**1050**of these

**27**mg cubets. And we find that

**1050**

*surface*units, each measuring

**1.299**0381… units, equals the surface area of (what in

*The Geometry of Form*is called) the

*equilibrious*icosahedron, which is so scaled that its

*surface area*is equal to its

*volume*. Then again, we shouldn’t be surprised since

**1.299**0381… units is also:

**(27) ^{1/2 }**

**∕ 4**

** ** Now, I’ll remind the reader that the silver dollar coin’s gross weight of **412.5** grains, which is modeled as the larger cuboid in the foreground of the previous photograph, consists of **990** (**27**mg) cuboids. And we just saw how important the **640** inch measure is with respect to deriving the square mile from a **100** X **100** grid. So too may we derive the *mile measure* by performing any of the operations below:

**640**” ∕ [(**1.0** / .**990**) −**1.0**] = 1 mile

or

**640**” ∕ [(**1.0** − .**990**) ∕ .**990**] = 1 mile

or

**640 X 99” = **1 mile

or

**64.0**” X **990** = 1 mile

or

(two times) **64**’ X **41.25** = 1 mile

Earlier in this manuscript, it was shown how the medieval **42** *gallon* “tierce” later became the 20^{th} century’s adopted “petro-barrel”; and how *geometry* determined *why* the modern gallon is a measure of **231** cubic inches, and why there is **42** *gallons* in the petro-barrel. It was also shown how **42** *gallons* disassembles into its constituent **9,702** *cubic* *inch* sub-units, and how they can be neatly arrange 2-dimensionally into a near perfect square measuring **99** cubes by **98** . . . and how, in practice, additional capacity within the barrel *is required* for fluid expansion due to changes in temperature and pressure. The “completed” square, measuring **99** X **99** *cubic* inches, accomplishes that function. Also, it is recognized *as the same* **99** X **99 **inch square that was shown to be a fundamental sub-unit of the *acre*, with its sub-divisioning into quarter-sections measuring **4.125** feet per edge.

With this in mind, let’s now transfer some of the previous* quantitative units from geometry* into some of *humanity’s actual measures of volume and area*, and then see how they relate among one another.

For example, one *petro-barrel* of **42** *gallons* equals (**4.125/**3) *barrel dry*; **1.333** *barrel fluid*; and is **9702** *cubic inches*. But here is the *covert* “quanta-sization” of some of our common *units of volume* based on the *cubic inch*.

A .**37125 **portion of one *petro-barrel* equals:

2 X **.2475** barrel fluid; as well as

120 X **.129937**… gallons

or, a

**.4125** barrel oil = **1.333**… X **.129937**… gallons

or, a

**.4125** barrel fluid = **12.9937**… gallons

When we look at the quantities immediately above we see the familiar monetary weight measures (in red), which are also, as we have just seen in this chapter, measures of land (i.e., length and area). Obviously, they are *standards* in our *volume* accounting system as well. And here too, they appear working in conjunction with powers of the geometric constant governing *surface transitions*: **.129937**…

Now, let’s look at the *volume* of the originating **1.0 **unit *surface* *area* in the form of a sphere and some more of *man’s measures* deriving from it.

This spherical, geometrically special *volume* measure is **.094031597… **cubic “unit”. It was discovered by “naming” its surface area *one square* *foot*; and from it, we’ve been able to derive all of our measures of land (and the entire system of *dry measures* culminating in the *Winchester* *bushel*). Now we find that this *volume* measure, as a portion of *one cubic foot*, also has left its mark in some of our *other* measures of volume. For example, a volume of **.094031597… **cubic foot, which is also [**1.0 / (36***pi***) ^{1/2}**] cubic foot, is

*at the same time*

**1.570**8990… Scottish

*pints*, which quantity is simply (

*pi*

**/ 2**); again at the same time, this quantity is

**4.8359**497…

*pint dry*measures. In geometry, this quantity

**4.8359**758… is the

*surface area*of a sphere having a

**1.0**cubic unit

*volume*; and it is also related to the

*pi*portion:

**(36**

*pi*

**)**And this quantity

^{1/3}.**1.06347**572…, so special to measures of land,

*as volume*of a

*barrel dry*can be re-written (

**0.1**/

**.094031**295…) and is equal to

**33/32**

*barrel fluid*. It is also a (

**371.25**/

**480**) portion of one

*barrel oil*, which portion is at the same time describing

*the number of grains of pure silver*in the American dollar coin (as a portion of the

**480**

*grain*troy ounce). And

**480**

*chains*is the length of one

*township*. This fraction (

**371.25**/

**480**) equals .

**7734375**, and as a portion of one

*barrel oil*measures 259.86159…

*pints*. But 259.86159… is (2 X

**), once again a power of the (previously described)**

__129.93__07…*geometric constant governing surface transformations*of a

*volume*Unit.

There is something else of great importance that should be noted here. It will be picked up again, and expanded upon in a later chapter but should at least be mentioned now in the context of the last few paragraphs. Remember, “the Unit” acquires *a* *physically defined actuality* only after being *named*. If in this example we name the Unit “**1.0** *meter*” then **.094031…** describes a portion of *one cubic meter* and its *surface* area *as a sphere* is exactly *one square meter*.

Now, only when we go further and assign a *name* to the *material substance* comprising that sphere’s volume is it then possible to calculate a *weight*. If it is made of *pure gold*, then it ** must** weigh

**2.0**

*tons*;

**4000**

*pounds*: (gold weighs 19,300 kg/m

^{3}, and .094031… X 19,300 kg/m

^{3}= 1,814.8098… kg. Since there is 2.204624… pounds/kg we multiply that by 1,814.8098… kg which equals

**4000**.974… pounds). So are we to believe it is just coincidental that

**1.0**

*square meter*comprising the surface of a sphere made of pure gold

*just happens*to weigh

*precisely*

**2.0**tons? That is, at least as

*precise*as the “pure gold” in America’s coinage which is refined to a .

**999**purity:

**4000** / **4000**.974… = .**999**756…

When applied to *gold*, the above geometry uses *commensurate whole units* of *meters*, with *whole units of* *pounds* and *tons *in the *same* system. Modeling *weight* using the (*illuminati’s*) system of **27** *milligram* cubets shows the very same commensuration. We can easily see this by forming a cuboid out of **27** *milligram* cubets: make this cuboid’s base layer of cuboids a square measuring **480** cubets by **480** cubets. Stack them **437.5** layers high. Calculate its weight: **480** X **480** X **437.5** X .0**27** *gram* = 2,721,600 *grams*. Given 15.43235835… *grains*/*gram* equals 42,000,706.49…grains. Given 7000 grains/lb equals **6000**.100927… pounds…i.e., exactly **3.0** tons to a .**9999**83… degree of perfection! Again, this shows a natural affinity, a geometric commensuration uniting, in this example, both the *troy ounce* (**480** *grains*) and *avoirdupois ounce* (**437.5** *grains*) working in conjunction with the *gram based* **27** *milligram* cubets to create a greater unit obviously denominated in *whole unit* measures named “*ton*”.

If we continue to follow the geometry (embedded in the DNA, so to speak) of the **.094031**… volume unit, it will lead us straight to the source of the *township’s* unique configuration . . . and beyond. I promise the reader some very interesting geometry, and I am reasonably confident that, in all probability, it has *never* been seen in any public classroom or textbook.

In the beginning of this chapter, we saw how (**1.0** / .**0940**31…) described the relationship between geometry’s *fundamental unit of surface* and it’s maximum potential to contain *volume*. And, we saw how this ratio was perfectly equal to (**10.634**72310… / **1.0**).

Now we’re going to see another view of this very special volume unit:

**.094031597… / (1.0) ^{1/2} = (10.63472310…) / 36**

This equation reads: “the **.0940…** spherical *volume* unit is to the *square root* of its **1.0** unit *surface* *area* . . . as **10.6347…** *is the square root* of the surface area of its **36***pi *spherical volume”. Of course this is a *special* *case*, since the right hand side of the above equation is a description of geometry’s unique “*equilibrious sphere*” with its *surface area being equal to its volume*: __neither has precedence over the other__.

The left hand side of this equation is pictured in the photograph on the first page of this chapter. The graphic to the left illustrates these relations. On the right side of the sketch there is a **6** by **6** grid above the line. This represents the *surface area* of the sphere having a *volume* equal to **36**. This surface is also equal to **36***pi*, and is naturally subdivisible into **36** separate *areal* units.

In this sketch, the square above the sphere on the right side describes the same *quantitative *information as the sphere above the square on the left side.

What this is showing us is the primordial geometric relationships between *surface* and *volume*. Clearly, ** at the very inception of geometry’s organizational structuring** we discover a grid subdivided into

**36**sub-units, with each one’s

*area*equal to

*pi*. This leads directly to, and is inseparable from,

*the one surface unit in the form of a sphere*; and from there, as was previously demonstrated, humanity’s measures of

*length*and

*area*. The fact that geometry’s

*equilibrious sphere*has a diameter equal to

**6.0**units (6 X 1.0), and that its

*surface*naturally sub-divides into a

**6.0**unit grid, is strong evidence (in light of everything else thus far presented) that the

*macro land unit measure*named “township” derived directly from this specific geometric arrangement. In all probability, so to did the “foot’s” sub-division into 2 X 6 “inches”. And its radius of three units is also (

**27**)

^{1/3}and models as the edge of a cube which is

*identical*in structure to the

**27**

*milligram cubet*at the heart of the

*illuminati’s*systems of

*weight*measures.

Before moving on we should take note of another significant correlation between this quantity of 36*pi* and the *exact *(.12667″) *difference* between *the statute mile* and what I’ve previously referred to as *the geometric mile*:

**.12667 inch = (7 feet, 4 times, times 36***pi***) / 3(10 ^{5})**

and for future reference

**.12667 inch = ***pi***(1008.0 feet) / 3(10 ^{5})**

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