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Cube ot the Cube

CUBE OF THE CUBE

MEASUREMENT COLUMNS (2 & 3)
Part One

FOREWORD

These connected chapters will start a series of explanations in accord with the rules of ancient geometry from which it is possible to conclude how ancient geometry solves many “impossibilities” and unknowns, and which were befittingly used in various ways. However the most perceptible were the wondrous ancient structures that amaze us to this very day and make us wonder about their underlying intent and purpose, how and why they were built in precisely that way. But it could be, when looked at from the aspect of their concordance with nature, that the cause is the presence of some geometrical figures of some other dimension unknown to us, which we can for the time being only surmise on basis of various myths, legends, fables or we don’t know how to “read” the versatile artifacts since they have with the passage of time developed into ornaments. Therefore we find their explicitness unacceptable and their originality unrecognizable and we simply refuse to accept them.

As for measurements, they are mentioned most distinctly in the Five Books of Moses and the prophetic books of ancient prophets. There are references to human and angelical measurements. We never ask who these “angels” were, but human measurements do engross our interest. One of these measures is the cubit, or the measure of six cubits, or the measuring rod (6 x 6 = 36 palms). On the other hand, the angelical measurement says that 1 angelical cubit = 6 palms + 1 palm = 7 palms, and the rod is 6 x 7 palms = 42 palms. Hence the angelical measuring rod is 1/7 larger than the human rod. Therefore, we are speaking of series of digits 2, 3, 7 – of sixths, sevenths, in other words, of parts of a whole. We do not ask what for and why, but consider it necessary to show the series and compare them, and only then to see what they bring – in their ancient way, only with a compass and unmarked straightedge.

CUBE OF THE CUBE

Incisively in the example of partitioning the cube 9 x 9 x 9 = 9^3 we have the presence of the digit 3 column of measurement (and we have previously with regard to angle trisecting mentioned the compatibility of digits 6 and 4, and 3 and 2 respectively. In other words, the proximity of halves and fourths are always present, “invisible”, in the background, and this partitioning of the cube among other things “indicates” that it is possible to solve every enigma that the old mathematicians left us with (in the encyclopedias) and to gain new knowledge that was withheld from us if we use the series of digit two (2) column of measurement that has come down to us from ancient Greece. The other series (3, 5, 7) are “impossible” due to the incorrect comprehension of the decimal as an infinite number, rather than as parts or fractions. Parts of a whole. And parts can be depicted like in ancient times, only with a compass and an unmarked straightedge.

Therefore, in order to solve yet another enigma (doubling the cube), we will proceed step-by-step by becoming familiar with the columns of measurement, their relationships, their parts, quadratic, cubic… And all this begins with the code template – the circle (full angle) – the hexagon. From a computational aspect, it seems that we are technologically “ready” to systematize all the data, and then it can “impart” knowledge to us about the micro and macro cosmos, elements, and so on. Perhaps even about the “invisible”, since everything in nature is based on equilibrium. Therefore, it is good to acquire the language of geometry in order to learn more about nature and in the process avoid the esoteric and stylization.

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- With radius circumscribe a circle and divide it with the radius – the hexagon with its sides and diameters (from pole to distended pole) – the cube

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- inscribe star-shaped polygon of hexagon (pole – every other one)

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Correctness (sequential order) is important.
– intersections of star-shaped polygon in a vertical direction on the vertical diameter

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Left intersection (parallel with left diameter)
(left and right is unimportant)

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In line with right diameter

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Drawing in this way opens new intersections on the sides of the hexagon and we connect them (first of all vertically)

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Right (in line with sides of the hexagon)

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Left. And we have now divided the cube into 3 x 3 x 3 = 3^3 or 27 cubic parts

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Now we divide (each) central section of the star-shaped polygon i.e. its cubic part respectively

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We also divide the vertical part as the layout (scheme) in line with the vertical diameter – vertically

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… and everything on the left (using the intersections of all the star-shaped hexagon perpendiculars (diameters) …

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… and then on the right – (we acquire intersections on the sides of the cube)

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We simply connect those intersections on the (perpendicular) sides. Therefore, we have terminated cycle 3 (9 x 9 x 9), and at the same time partitioned the diameter into 10 parts, and we can also divide eighteen in half, and thus acquire 36 parts. In other words, we have acquired a column of measurement and the cube of the cube.

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COLUMNS OF MEASUREMENTS (part 1)

THIRDS AND HALVES AND THEIR SERIES

There is no doubt that anyone who has studied the world of ancient cultures admired their ornamentations, preciseness, appearance, harmony , symmetry – the artifacts of ornamental characteristics – the „calendars“ that the ancient generations that made them were not able to read because script was still unknown; the written letter or number was still nonexistent; only the “ornament”, of which many were contrived artifacts stylized to such an extent that their primordial nature became unrecognizable, and in addition to this they (logically) metamorphosed into the esoteric. Confined only to an “enlightened” inner circle, they also failed the test of materialism and “survival” of every man for himself. In the end this brought about a general oblivion, as happens to a person who goes through a shock, experiencing something that he does not want to remember – rather than confronting himself with the help of a mirror that would acquaint him to himself and prompt him to correct his mistakes. Perhaps this will become somewhat clearer after we go through all 4 columns of measurements and their series – hence the series of digit 2, digit 3, digit 5 and series of digit seven, and after we mutually compare them in pairs, threes, and all at once. Maybe much more will be readily apparent (or won’t), but nevertheless it will in someone inspire that ancient spiritual energy gene and move it again in its assignment to act in the creating of natural science.

All this is coming about and happening in the manner of ancient geometry – only with a compass and unmarked straightedge (since measurements and other accessories are not needed).

Therefore, two series of parts of a whole (no example) until we arrange the series. Otherwise, just one small example: 2/3 of a dimater divides the circle into 54 parts or angle of 6,666…° Therefore, the columns of series of parts were the protractors of the ancients.

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We therefore use – the circle – the hexagon (cube) and its star-shaped polygon and the circumscribed square of the circle as an assistance in drawing because we are drawing – straight line drawing – abridged column d = 4/4 = column of digit two (halves, quarters)

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We divide each part with diagonals – eighths
(8 parts d) = column of digit 2

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Applying the intersections of the hexagon star-shaped polygon we have acquired three hexagonal parts on the diameter – three parts d = thirds d – column digit 3

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On each of the three parts we inscribe their star-shaped polygon, divide it and we get 6 parts of a diameter – sixths – column of digit 3

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By utilizing the sixths we can split them in half and get twelfths of a diameter. It shows the compatibility of 2 and 3 – column of digits 2 and 3

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In the case of sixteenths we utilize two star-shaped polygon halves (halves are two hexagonal diameters). Therefore, divide the diameter of each (radius of the circle) into four and thereafter eight into halves – 16 parts of a diameter – sixteenths of a diameter

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On partitioning the diameter into 24 parts, we split the twelfths in half – series of digits 2 and 3

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eighteenths and thirtysixths

We have seen this system on occasion of division of the cube into 9 x 9 x 9. Here we will stop with columns of digits 2 and 3. In part two of columns we will show columns for digits 5 and 7 and their series.

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