We will now consider the distances and angles of some lines beyond the central horizontally lying rectangle. This is, for the most part, the secondary or backsight geometry related to the top end of the trapezoid or individual lines that track off the central rectangle.

1. The distance is 583.333333-feet and the angle is 226.8-degrees return.

This position at the top left corner of the trapezoid appears, positively, to be defined by distance and angle codes from the western surveying cairn of the rectangle. The distance, to within about 18-inches of the corner position, is 583.33333-feet or 100 Roman Paces.

The angle back to the cairn is 226.8-degrees and this value is highly important to navigation or lunar cycle calculations within the lunisolar Sabbatical calendar, as well as the duration of the lunar nutation cycle (6804-days).

2. The distance is 283.5-feet and the angle is 168.75-degrees return.

The Khafre Pyramid has a perimeter value of 2835-feet. By comparison, one ounce in the imperial British system (437.5 grains) = 28.35 grams in the metric system. This lends credence to the idea that the ancient French guilds hijacked the "Metrification" (Metrickery) incentive and fashioned it, as closely as their surviving knowledge would allow, to the ancient Roman standards. Consider the following:

Both Delambre and Méchain* (the so-called "fathers of the metre") were professional and much respected scientists, living during the French Revolution, in Catholic France, where ancient guild networks abounded. The incentive to create the metre originated with the Catholic Church and it seems apparent that its main purpose was to nullify the use of ancient "Pagan" measurement standards and, thereby, snuff out Pagan sciences that were encoded by specific numbers. As far as Delambre and Méchain were concerned, it was more common than not for individuals of their rank in society to rub shoulders with (or be affiliated with) the secret societies and Masonic orders that had opposed the church's insidious eradication ambitions for many centuries. These ancient guilds had a longstanding tradition of preserving geometries and measurements from pre-Christian times and secretly encoding those principles into the great cathedrals or public buildings of Europe. Even new cities of the time, like Washington D.C., were being laid out in accordance with preserved, age-old, Masonic geometric principles, gratis of the Masonic-guild affiliated, founding fathers of the United States.

The litre is the cubic capacity of 10cm X 10cm X 10cm and this weight of water represents 1 kilogram. It just so happens, quite by chance, that one ounce in the Imperial British system (437.5 grains) = 28.35 grams in the metric system. This also equates to 28350 milligrams. The selfsame value, rendered as 2835 feet, was the intended perimeter value for a full circuit around Khafre Pyramid's base (15/16ths of the base perimeter of the Great Pyramid). It appears obvious that the gram is related to the 437.5 grains of the British ounce of 10 Egyptian Deben. This grain count had a further affiliation to the system instituted by Charlemagne. King John and Edward III, who reigned virtually contemporaneously, introduced systems that accommodated the 437.5-grain ounce admirably. King John's Pile was intended to convey 432 ounces (4320 Egyptian Deben) or 27 latter English pounds of 7000 grains. There were 4375000 inches in 1-degree of equatorial arc, under the Roman navigational system, which viewed the equatorial circumference of the Earth as 25000 Greek miles or 131250000 British feet or 135000000 Roman feet of 11.666666-inches each.

The sum of 28.35 metric grams is simply the Roman Trade Standard Uncia adopted by Edward III in 1340 A. D…based upon a late surviving "Silver Standard" Mina of 7000 grains. It seems a little uncanny and a bit too convenient that 1 ounce = 28.35 grams...a significant, old world lunar number.

* It seems quite apparent that Delambre and Méchain were heavily influenced by the guilds and that the outcome leading to the metre's chosen length was dictated by others. What the guilds intended, it would seem, was 3.28125-feet or 39.375-inches for the metre. This would have been in compliance with their now scant and somewhat incomplete knowledge of what formerly constituted the Roman foot. The guilds appear to have assumed that the 11.664-inch foot was the basis of the Roman standard, when, in fact, the Romans only used that value in volume measures or lunar cycle calculations. The foot they used in calculating the equatorial circumference of the Earth or in overland marching was 11.6666666-inches in length (11 & 2/3rds). Their equatorial circumference value was based upon 75-Roman miles per degree of arc. Their mile was 5000 Roman feet and, using the 11.666666-inch navigational foot, this equated to 25000 Greek miles @ 5250-feet each or 131250000 British feet (135000000 Roman feet) for a circumnavigation of the globe. Inasmuch as the creators of the metre were quartering the globe (pole to equator), they seemingly wanted to divide the Roman figure (equatorial circumference) by 4. That means: 131250000 British feet ÷ 4 = 32812500 feet. But the metre was supposed to be one ten millionth of this quarter segmentation or 3.28125 feet. Instead, the guild authorities, if they were orchestrating the outcome, appear to have used the 11.664-inch Roman foot and calculated the circumference as 131220000 British feet ÷ 4 = 32805000... divided by ten million = 3.2805 feet. We know that the metre calculated by Delambre and Méchain fell short by something in the vicinity of .2 of a milimetre. This discrepancy was adjusted out later and the metre has gone through several subsequent minor increases since 1799 to now be 3.2808398-feet (with the tiny shortfall added). The original metre looks to have been modeled on the ancient Roman equatorial circumference of the Earth, with only minor drift off the original value....probably based upon flawed assumptions as to what constituted the original Roman overland foot.

The point is that metric weights comply to old world standards of thousands of years ago and that the metre itself is only .0049224 of 1-inch (about 1/210th of an inch & virtually impossible to visually detect) off a common length standard shared by the ancient cousin European nations.

The angle in this instance (168.75-degrees) is also a lunar code. A mathematical progression based upon this value goes: 168.75, 337.5, 506.25, 675, 843.75, 1012.5, 1181.25 (note: the sum of 118.125-days equals 4 lunar months), 1350, 1518.75, .....3543.75 (note the lunar year is 354.375-days) etc.

3. The distance is 356.4 and the angle is 87.5-degrees.

A close scrutiny of the marked line indicates that it terminates short of the position where one would expect the corner, or intersection point, for line 4 to connect to line 3.

The 356.4 code is a much used one in navigation and features prominently at Nazca. Half of 356.4-feet is 178.2-feet, which is the width of the "Y Holes" Circle at Stonehenge. The value 356.4 is part of the "11" family of numbers and 35640-feet would be 6.75-miles of 5280-feet each or 5.4 chains of 66-feet each or 540 Links of 7.92-inches each, etc. A circuit based upon 3564 calibrations would have worked well for calculating degree angles in the 11 family of numbers. The sum of 3564 calibrations would be 360 X 9.9.

The 87.5-degree value codes a number much used in Sabbatical Calendar determinations. Under the very harmonious agrarian count system there were 13-months in a year and 28-days in every month (364-days). This system was allowed to run uninterrupted for 7-years and thereby accrued 8.75-days of error by the end of the Sabbatical Year (7th year). The error was corrected by holding a 9-day festival. The Hebrews, by comparison, observed a "Double-Sabbath" once a year at Pentecost, which meant adding one day per year (total 365). This Hebrew system meant that there was only 1.75-days of calendar error at the end of the Sabbatical Year and a much shorter festival. The Druids seemed to like the longer festival period (drank more mead, chased more women around the venerable Oak and had a more developed and meaningful hangover when the new calendar count began).

4. The distance is 270-feet and the angle is 175-degrees return.

The distance code of 270 feet sets up a very important navigational mathematical progression and 270-degrees (due west) would be 3/4ths of a 360-degree circle.

The angle of 175-degrees contains a much used value of antiquity, which worked admirably as a ratio to convert "7th" divisions within a 360-degree circle ito whole numbers. Therefore: 360 ÷ 7 = 51.42857143-degrees (51 & 3/7ths) X 1.75 = 90. This means that 7th divisions of a circle could be read on a 630 division by a simple ratio increase. (360 X 1.75 = 630)...note: the Greek stadia measurement was 630-feet. The ancient mathematicians needed these simple ratios to move fluidly between number families and calculation methodologies. A mathematical progression based upon 175 is of great importance to reading the equatorial circumference of the Earth according to Greek increments. The progression goes 175, 350 (the Swedish Mil was 35000-feet), 525 (the Greek "short stadia" was 525-feet), 700, 875, 1050 (the Hebrew Reed was 10.5-feet), 1225, 1400, 1575, ....6300 (the Greek long stadia was 630 feet), etc.

5. The distance is 480-feet and the angle back to the cairn is 141.75-degrees.

The distance aspect is based upon a line extending from the eastern cairn to the position where the line defining the side of the trapezoid appears to terminate near the corner. It appears strongly that a distance of 480-feet was encoded for tutorials to students. The Great Pyramid never had a capstone, but the position in the air, where all lines angling diagonally up from the four faces would intersect, would be very near to 480-feet in the air (a few inches over). A mathematical progression based upon 48 is very important to ancient navigation and 480-feet would be 1/11th of a mile of 5280-feet. Alternatively, in the 12 X 12 X 12 X 12 X1.2 = 24883.2 formula for the equatorial size of the Earth, it would be 51.84 X 480 = 24883.2. The true angle of each face of the Great Pyramid was 51.84-degrees, therefore, the degree angle X the symbolic (capstone included geometry) height of the Great Pyramid gave the reading (in miles) of the equatorial circumference.

The return degree angle from this position to the cairn was 141.75, which is a very important lunar code. A progression based upon this value goes: 141.75, 283.5 (note: the Khafre Pyramid was 2835-feet in perimeter value), 425.25, 567 (note: there are 12 periods of 567-days in the 6804-day lunar nutation cycle), 708.75 (note: the side length of the Khafre Pyramid was 708.75-feet per side... or in days = 2 lunar years), 850.5, 992.25, 1134 (note: 1/800th of the side length of the Great Pyramid was 11.34-inches ... the station stones rectangle at Stonehenge is 113.4-feet wide), ....1701 (note: 1/4th of the 6804-day lunar cycle was 1701-days...2268 (note: 3-sides of the Great Pyramid equated to 2268-feet), etc.

As has been stated, in our modern age we have the luxury of copious supplies of perishable paper to produce books or electronic gadgetry for storing information. The ancient "Masters of the Craft" enjoyed no such luxury and had to encode their sciences by distances and angles from a hubstone to an outer-marker or by coded geometric designs, etc. There is no mystery in finding the "same old, same old" Egyptian numbers encoded into the Nazca desert geometry. The "same-old, same-old" numbers are encoded into sites in New Zealand at the very ends of the Earth, where besieged and displaced ancient people of the Americas fled for safety, sanctuary and a new start.

6. The distance is 180-feet and the angle back to the corner position is 178.2-degrees.

The value of 180 was highly important to many functions, including the fact that 180-degrees is due south. The value 178.2 is a navigational value used in "11" family progressions and "Y Holes" Circle at Stonehenge is 178.2-feet in diameter.

7. The distance is 182.25-feet and the return angle is 176-degrees.

We are now working through a region which is slightly damaged, but the lines seem reasonably clear. A careful, on the ground assessment of some of these secondary lines might show that detritus obscures their end points and that they are marginally longer, meaning that they carry a different code than the one here identified. The most stable code-carrying element in this analysis is the degree angle, which cannot be affected to any great extent without throwing a superimposed line very visibly off the ground-marked line it's required to precisely overlay. Even if all lengths at Nazca were discounted, the degree angle information found there would be sufficient to prove that the many specific and repetitive values identified herein are present.

The distance @ 182.25 is a very important lunar code that also provides a relationship to the Roman (lunar and volume) foot of 11.664-inches. The 182.25-feet length would also equate to 187.5 Roman feet. A mathematical progression based upon this value goes: 182.25, 364.5 (this value is 1/7th of 2551.5-days or 7.2 lunar years), 546.75, 729 (The Bush Barrow Lozenge artefact of "Stonehenge" is 7.29-inches long or 1/8th of a Roman Pace), 911.25, 1093.5, 1275.75, 1458... 2551.5 ( In days this is 7.2-lunar years and the period counted within the Sabbatical Calendar alongside 7-solar years), etc.

The angle in this instance, 176-degrees, also provides a dynamic navigational code associated with the "11" family of numbers and the mile of 5280-feet. The sum of 1760-yards would be 5280-feet and 176-feet would be 1/30th of a mile. The value 1760 ("11" family) was used in navigational tutorials alongside 1728 ("6" family). At an ancient temple site in New Zealand called the "Crosshouse", one set of wings measured 55-feet and the 90-degrees opposed set measured 56-feet. Using PI at the navigational value of 3.141818182 (314 & 2/11ths ÷ 100), which was the form of PI used when navigating by the "11" family of numbers, the 55-feet diameter was turned into a circle which brushed porches on two wings and created a circumference stretching 172.8-feet. The circle created was easily reducible into 360-degrees and contained the same navigational tutorial as Silbury Hill in Southern England. Using the 56-feet diameter of the two 90-degrees opposed wings X 22/7 (3.142857143) = 176, teaches an alternative navigational system that could convert distances in Roman feet or miles into an "11" family number on the circumference.

After the ancient Viracocha people of Peru were besieged by the Olmecs-Incas, many escaped in their ships into the Pacific Ocean. A group of them found their way to Easter Island, where they carved and erected the huge European-looking, long-faced statues with the red-head topknots. A much larger migration traversed the entire Pacific to New Zealand, taking many of their distinctly South American food plants with them, along with their cultural symbolism and mathematical codes. Their sciences were immediately encoded into the New Zealand landscape or into the many meeting houses, domestic structures, "kupu" (quippu string knot calculators) or artefacts that they later built or fabricated. Unfortunately for these very ancient "kiri-puwhero" (reddish ... light complexioned skin) and "uru-kehu" (reddish ... golden-tinged hair) people, they were much later overwhelmed by the newly-arrived Polynesian-Melanesian cannibals. If one understands the geometry of the Crosshouse of Miringa Te Kakara in New Zealand (shown above) one can easily decipher the calculation matrix etched into the ground in the hill country near Nazca, Peru. A very similar matrix is found to be purpose designed into the terrain at Rennes Le Chateau in Southern France. In the above picture, one cross-measure extended for 55-feet (blue circle)and the 90-degrees opposed cross-measure extended for 56-feet (red circle). Each cross-measure acted as a standard tutorial for two, slightly different navigational systems, taught from Egypt to Southern England (Silbury Hill) to Teohuanacan (Mexico) to Nazca, Peru to New Zealand, etc., etc.

8. The distance is 181.44-feet and the angle is 176-degrees.

The distance code is navigational and the tutorial taught in this line could be applied to Earth equatorial circumference readings using the Greek mile @ 5250-feet or the British mile @ 5280-feet. Under the literal ("6&7") system found on the Great Pyramid the equatorial circumference was 24883.2 Greek miles or 130636800 British feet. The sum of 18144 feet would, therefore, represent 1/7200th of the equatorial circumference. If the Great Pyramid was elongated 3-inches, then the "11" family of numbers could be used for an Earth equatorial circumference of 24,750-miles or 130680000-feet and 1/7200th of this value would be 18150-feet. Obviously, the distance coding built into this position at Nazca could be interpreted either way, to teach each geodetic system.

The angle is again 176-degrees. A second tutorial was possible here also by reading the angle 180-degrees opposed and adding a small margin to the angle of .4 of a degree (356.4-degrees). On such a small length it was within the realms of possibility to do this and, thereby, introduce yet another navigational tutorial.

9. The distance is 414.72-feet and the angle is 158.4-degrees return to the eastern cairn.

This purple coloured line is shown as one example of a series of close proximity codes (line of markers), which sit outside the confines of the marked geometry. Subtle differences in the distances and angles to component parts of the lineup added to the available tutorials.

The distance of 414.72-feet contains a navigational code and a mathematical progression based upon this value goes: 414.72, 829.44, 1244.16 (note: half the equatorial circumference of the Earth was 12441.6-miles), ... 2073.6 (note: one of the largest Egyptian Royal Cubits was 1.728-feet or 20.736-inches, ... 2488.32 (note: the equatorial circumference was read as 12 X 12 X 12 X 12 X 1.2-miles or 24883.2), etc.

The angle is 158.4-degrees return and a mathematical progression based upon this value goes: 158.4, 316.8, 475.2, 633.6, 792, 950.4... 1900.8, ... 2376, ...2851.2, etc. This particular mathematical progression was very important to a range of "wet & dry" volume standards of ancient European civilisations. Some examples are shown below.


1 Homer….28512 cubic inches equals
10 Ephah….2851.20 cubic inches., or
30 Seah…..950.40 cubic inches, or
180 Cab….158.4 cubic inches, or
720 Log….39.6 cubic inches.


1 Amphora…..1584 cubic inches, equals
2 Urna……….792 cubic inches, or
8 Congius……198 cubic inches, or
48 Sextarius…33 cubic inches.


1 Amphora…….1900.8 cubic inches equals:
3 Modius………633.6 cubic inches, or
32 Choenix…….59.4 cubic inches, or
48 Sextarius……39.6 cubic inches, or
96 Hemina……...19.8 cubic inches.

These volume standards contain navigational codes. An example of how they work in with the equatorial size of the Earth would be to choose, say, the Roman Amphora volume of 1900.8-cubic inches and see how it relates as a number in various geodetic computations. Therefore:

10. The distance is 144-feet and the angle is 180-degrees.

A mathematical progression based upon 144 is one of the most fundamental, central and dynamic of antiquity and goes: 144 (a little known British measurement was the Geomancer's mile of 14400-feet), 288 (the width of the Aubrey Circle at Stonehenge was 288-feet and the Egyptian Pyramid acre was 28800 square feet), 432 (the length of the Great Pyramid was 432 Hebrew or Celtic Cubits of 21-inches each), 576 (the diagonal length up the faces of the Great Pyramid to the flat floor altar was coded to be 576-feet), 720 (twice 360), 864 (the sun is 864000-miles in diameter), 1008 (1-second of arc under the Great Pyramid's literal standard was 100.8-feet, which is also the internal diameter in one cross measure of the Sarsen Circle at Stonehenge), 1152 (the outer length average of each lintel stone at Stonehenge was 11.52-feet), 1296 (half the duration of the Precession of the Equinoxes is 12960-years), 1440, 1584 (The Alexandrian Amphora volume was 1584 cubic inches), 1728 (the circumference of Silbury Hill, based upon a diameter of 550-feet, was coded to be 1728-feet and the sum of 1 cubic foot = 1728 cubic inches), etc.

The angle of 180-degrees to 360-degrees codes the line from due South to due North.

11. The distance is 189-feet and the angle is 177.1875-degrees (177 &3/16ths).

The Great Pyramid is 189-feet X 4 = 756-feet in length.

The duration of a lunar year is 354.375-days or 177.1875-days X 2.

12. The distance is 201.6-feet and the angle is 354.375-degrees.

The 201.6-feet distance is a navigational code, based upon the Great Pyramid's literal method for reading the equatorial circumference. A mathematical progression goes: 201.6, 403.2, 604.8 (note: two circuits of the Great Pyramid is 6048-feet for 1-minute of equatorial arc), 806.4, 1008 (note: 1-second of equatorial arc is 100.8-feet, 1209.6, ... 1814.4, etc.

The angle of 354.375-degrees is self explanatory as coding the value of the lunar year in days.

13. The distance is 186.624-feet and the angle is 175-degrees.

The distance code is based upon a mathematical progression much used in antiquity, which was incorporated into volume measures of the earliest European cousin nations and related to navigation. The progression can start at: 31.104, 62.208, 93.312, 124.416, 155.52, 186.624, ... 248.832 (the Earth was coded to be 24883.2-miles in circumference), ... 777.6, 933.12, ... 1306.368 (the equatorial circumference by the Great Pyramid's system was 1306.36800-feet), etc.


1 Amphora…1492.992 cubic inches equals:
2 Urna………746.496 cubic inches, or
8 Congius……186.624 cubic inches, or
48 Sextarius…31.104 cubic inches.


1 Metretes…….3732.48 cubic inches equals:
2 Maris………..1866.24 cubic inches, or
12 Choes………311.04 cubic inches, or
48 Chronicles….77.76 cubic inches.


1 Talent………933120 grains, equals:
60 Mina…….. @ 15552 grains, or:
3600 Shekel… @ 259.2 grains.

The Babylonian-Sumerian Royal Double Standard referred to in the third column is based, in part, on the grain weight of a grey basalt duck weight (British Museum exhibit 104,724) inscribed, "Two talents, correct weight". Comparative analysis undertaken by Donald L. Lenzen over ten years, who compared all the known ancient weights of the Mediterranean region, establishes the validity of the standards seen above. Amongst the Babylonians the slightly heavier standard was for payments to the royal treasury and some weights of this type bear the inscription, "of the King".

The value of 3110.4-miles would be 1/8th of a 24883.2-mile equatorial circumference under the 12 X 12 X 12 X 12 X 1.2 reading.

The angle of 175-degrees contains a much used value of antiquity, which worked admirably as a ratio to convert "7th" divisions within a 360-degree circle ito whole numbers. Therefore: 360 ÷ 7 = 51.42857143-degrees (51 & 3/7ths) X 1.75 = 90. This means that 7th divisions of a circle could be read on a 630 division by a simple ratio increase. (360 X 1.75 = 630)...note: the Greek stadia measurement was 630-feet. The ancient mathematicians needed these simple ratios to move fluidly between number families and calculation methodologies. A mathematical progression based upon 175 is of great importance to reading the equatorial circumference of the Earth according to Greek increments. The progression goes 175, 350 (the Swedish Mil was 35000-feet), 525 (the Greek "short stadia" was 525-feet), 700, 875, 1050 (the Hebrew Reed was 10.5-feet), 1225, 1400, 1575, ....6300 (the Greek long stadia was 630 feet), etc.

14. The distance is 172.8-feet and the angle is 170.1-degrees.

The distance codes a very important navigational principle: 55 X 3.141818182 = 172.8.

The angle code is lunar and 1701-days would be 1/4th of the lunar cycle of 6804-days.

15. The distance is 201.6-feet and the angle is 150-degrees. The return angle is 330-degrees.

A progression based upon this length value goes: 201.6, 403.2, 604.8, 806.4, 1008, 1209.6, ...3024, ...3628.8, etc. The value of 201.6-feet is merely 2 X 100.8, which is 1-second of equatorial arc under the Great Pyramid's literal assignment. This distance at Nazca would, therefore, be 1/648000th of the equatorial circumference and it's more than likely that many a student was required to do the calculation and report the correct answer to the tutor.

Both the angle of 150-degrees and its return angle of 330-degrees set up useful mathematical progressions, the latter of which had application to the British mile of 5280-feet.