Numbers and Geometry in the Bible
If we do a search of the King James Version of the Bible (KJV), we find that the word 'triangle' is not in there. A search for the world circle shows it to be in the KJV once, in Isaiah 40 which reads:
"Hath it not been told to you from the beginning, have ye not understood from the foundations of the earth, It is he that sitteth upon the circle of the earth, that stretcheth out the heavens as a curtain and spreadeth them out as a tent to dwell in." [What is being described is a nomadic camp site with a tent surrounded by a court with a curtain around it for privacy.]
Please take a look at the description of the New Jerusalem in Revelation Chapter 21.
 And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal.
The numbers that stand out are 3,4,12 and 144 (12x12). The geometric figures described are a square and a cube. Pearls are mentioned that are round, are numbered as 12, and are named as the tribes and apostles.
Now see page 43 of John Michell's City of Revelation, where he walks us through the design of the image of that saying, "Following the pattern of the New Jerusalem, a circle is inscribed within a square. Within the circle is placed a hexagon". That just goes to show what people can see in the book. He recommends that a series of circles is being described, rather than a cube and square? He uses double hexagons to achieve twelve points on a circle, instead of dealing with the square. Note how he bunches the circles.
The book is describing a square that is 12x12, but Michell converts to a circle divided 12 times. Also instead of using the 12x12 measurements, Michell is one of those who converts cubits to feet in order to analyze the figure he generates. In other words, he is neither using the figures in the book, nor the numbers that are given there. I challenge his interpretation of this. Below we see where Michael Schneider follows Michell's lead, calling this image the New Jerusalem. Notice that he un-bunches the circles on the outside.
If you look closely you can see that Schneider has reduced the size of Michell's circles. In the image below there are 12 circles with four gasps one half of a circle wide. He has divided the circle into fourteen parts, yet he calls the image the geometry of the twelve-part celestial canon? What he is trying to do is to include the number seven symbolism that is also in the Book of Revelation. He turns 3,4 and 12 into 7 and 14.
The magic squares are grids where each row, column and diagonal adds to the same number. The number of cells in the grid is the square of a number. Three squared is nine. We put each of the first nine numbers in cells in a grid. To figure the numeric constant we divide the total of the numbers by the number. The first nine numbers add to 45; dividing that by three we get 15. We recognize 3, 9, 15 and 45 as a number set from this square.
The planets (and sun and moon) are assigned numbers and positions on the Tree of Life according to the order of descent of the soul that is given in ancient legends. The Greeks taught that the soul resides among the stars (is a star) and that it comes to earth and returns by way of seven planetary spheres, Saturn, Jupiter, Mars, the sun, Venus Mercury and the moon. If you include the earth at the bottom and stars at the top you have 9 spheres. Adding the Throne of God gives you a 10 based system where the throne is One and the earth is 10.
Remember the Copernicus' model of the universe was just Ptolemy's model (above) with the earth in the sun's place. Then you get the correct order of Sat, Jup, Mars, the earth, Ven, Merc; but the earth can't be depicted as the 'goal' that way. That way, the sun is the goal like in Viking mythology. This system was designed with the sun at the center.
The Latin word for tent is tabernaculum, tabernacle. Here we see talk of the foundations of the earth, see the heavens described as a curtain, and a tent as a place for the Lord to dwell in. A tent also made of the heavens. If you are a Bible student, this should remind you of the tabernacle of the congregation that was built to house the Ark of the Covenant. It is clear to everyone that the ark, the tabernacle, and the court represent a model of the cosmos. The same model used by churches, cathedrals and Masonic lodge floors.
The ark is rectangular pointing east and west inside the tabernacle, a rectangle pointing the same way, inside the court, a rectangle pointing the same way. The outer curtain is the celestial sphere, the stars. The twelve loaves of bread in two rows of 6 are the zodiac signs (six north of the equator and six south of it), while the seven candles are the planetary spheres. The Glory of the Lord came into the house by way of the gate to the east and filled the house and the earth shined with his glory.
The courtyard is the element of earth, the altar is fire, the laver of brass with water is between the altar and the tabernacle. The incense altar inside the Tabernacle is the element of air. Now think about a Catholic Mass. You look across the altar from the nave into the holiest area that used to be separated by a screen in some churches. In a Cathedral, this is where the cathedra, the Bishop's chair goes. In a Masonic Lodge, the Worshipful Master occupies this position in the ceremony.
The curtain around the court of the tabernacle was 50x100 cubits, 5 cubits high. Doubling these numbers we get 200x100x10, two 100x100 squares 10 tall. This is a depiction of two hemispheres of the globe. The altar in front of the tabenacle was a 5x5 square 3 cubits tall. the Ark of the Covenant was 2.5x1.5x1.5. The tabernacle was 10 cubits wide. The brazen sea in front of the Temple was 10 cubits across and 5 tall. The Temple was 20 cubits wide. The altar there was 20x20 by 10 cubits tall.
The Oblation in Ezekiel is 25,000 x 25,000 reeds. The suburbs of the city are 5,000 x 5,000 reeds. The sanctuary is 500 x 500 reeds. The sum of the numbers from 1 to 10 is 55. The round Templar Church in London has a 55 foot diameter. St. Paul's Church is 555 feet long with the steps. The base of the Washington Monument is 55.5 feet and it is 555.5 feet tall. Egyptian obelisks were built to this 10:1 ratio, and when Jacob sets up his pillar stone he says, of all that you give me, I will give the tenth to thee.
We are reminded of the ten spheres on the Tree of Life where the earth occupies shpere 10. Sphere 5 is related by virtue of the number. Mars is at sphere five; he was a fertility and war god. Mars was an earthy type, not a heavenly type, or sky god. We see that the number five is associated with the concept of the microcosm, while the number six is associated with the macrocosm, the earth and sky in this case. The sun is at sphere six.
Now consider the Rebis, where we focus on the numbers 3 and 4. Think about what Dan Brown says in The Lost Symbol about the Bible containing the secrets of the Mysteries, and about the circumpunct (point in a circle) being the symbol of the Mysteries. You can see his circumpunct above. Other than that, the only thing from the rebis that he has mentioned is the seven planetary spheres. He recommends that a table was 7x7 because there were seven planets, and that the room was 12x12 because there were 12 zodiac signs.
This reminds us of the numbers in the book of Revelation, but there are no tables/altars there. We find an altar in Ezekiel 43 that is 12x12. In Exodus 27 the altar of fire is 5x5 cubits. the number seven is not associated with altars in the Bible, it is associated with the days of the weeks, stars, churches and candles.
In the rebis we see the numbers 1, 3 and 4 associated with a circle, a triangle and a square. We know that a mason's square is half a square. Above we see that a woman holds that. The female half of things is associated with 4, a square and a cube, all symbols of materiality. The male half holds the compasses which are used to drawn circles, and which look like a triangle. The circle, triangle and the number 3 are associated with the heavens and are considered masculine.
[Note that this is not so in all systems and that Osiris mother was a sky goddess and his father an earth god. It doesn't take much to get from earth god to fertility to Mars. If the leader god is moved to the sky, the earth god suffers. Think of the stories of Saturn overturning Uranus, and Jupiter overturning saturn. Saturn was associated with the harvest and symbolized by a scythe for cutting wheat. The message is that meanings change depending on who is in charge at the time.]
Looking in the circle, you will note that the bottom half of the square makes the Masonic square, while the top half of the triangle is the compasses. The compass and square are the triangle and square, and are the male and female symbols in this system. That is also the sign of the Mysteries. (Note the G formed in the center.)
While the words triangle and circle are not used, rectangles and squares are emphasized, and circles are hinted at. See Psalm 118:10 where we read that they compassed him about. That is repeated four times. In 15 and 16 he says 'right hand' three times in a row. See the compasses in the right hand. Psalm 118 also mentions the head stone of the corner. I am reminded of the vesica.
The court around the Tabernacle was 50x100; two 50x50 squares, which is the middle half of a 100x100 square. The diagonal of a 1x2 rectangle (blue above 50x100) forms a 26.5 degree angle. If we inscribe a circle in the 10x10 square, the lines of the blue rectangle cross at 30 degrees from the equator. The parallel lines of a hexagram are the same as the blue lines of the rectangle. The diagonals of the red rectangles form 30 degree angles. The 1:2 rectangle in a square indicates a hexagram in a circle. As the Temple was 60x20x30 a 1:2 rectangle is indicated there too (60:30). The Tabernacle was 30x10x15.
Note the equal armed cross that is formed at the center, like the Templar and Teutonic crosses. If the court was 50x100 (5x10), then our inner square is 5x5, the size of the altar in front of the tabernacle. The 10 cubit width of the Tabernacle was one tenth the side of the square. In a ten by ten square the cells are 2.5 wide, the width of the ark. If the outer square is 100x100, the red square is 25x25. If you imagine this to be twenty five 5x5 squares, the altar is the center square.
So we know that we have two methods of finding 30 degrees and of quartering the diameter of a circle and square. As it turns out, while the sun ranges to 23 degrees above and below the equator, the moon moves beyond 28 degrees, and Mercury ranges as far as 31 dgrees from the equator. This associates Mercury with the notion of limits and boundaries (surveying), and associates the star of David with the range of Mercury. The dimensions of the court defined the range of Mercury (within one degree). The 26.5 degree diagonal of the 1:2 rectangle was an average of the range of the sun and Mercury. 30 degrees north was the location of the Great Pyramid.
As you can see, the game is to name whole number ratios that produce diagonals that you want. If we replace the tens in the dimensions of Noah's Ark (300x50x30) with twelves, we get 360x60x36. The square of the sun consists of the first 36 numbers. 360x60 is a band 60 degrees wide around the globe that stretches from 30 north to 30 south latitude. (Here we see 1:6 instead of the 1:3 ratio of the Temple/Tabernacle.)
But the number we really want is thirty one degrees. If we double the dimensions of the Ark of the Covenant it is easier to see that it represents a square and a 3x5 rectangle. 3/5 is .6, and the tangent of thirty one degrees is .601. The dimensions of the altar in front of the Tabernacle are 5x5x3; the sides are 3x5 rectangles. The dimensions of Noah's Ark, 300x50x30, shows the 3x5 rectangle. NA is ten double AoC's, at 5x3x3 each. Noah's Ark is decsribed in Genesis Chapter 6 and Noah is 600 years old. The water prevails to 15 cubits for 150 days.
We note at this point that Mercury rules Virgo while the sun rules Leo. Outside the tabernacle we have the earth, fire and water and the utensils are made of brass. Inside the Tabernacle everthing is made of wood covered with gold and the incense altar stands for the element of air. It is 1x1x2 by the way, a double cube. That, the table for the bread and the candlestick form a trinity in the holy place.
In the Holy of Holies, the outside dimensions of the ark gives us Mercury's range, so we presume that the inside, lined in gold, is the sun's region between the tropics at 23.5 degrees. With the mercy seat (lid) and cherabim, the ark looked like an Egyptian coffin, complete with a goddess with spread wings on either end. Outside would be Isis and Nephthys (the moon and Venus) while inside the lid was Nuit as the sky (seen below); despite being a protector of the dead, she was a personification of the sky - a cosmic deity - no temples or specific cult centres are linked to her?
Looking closely at the image on the right you can see the two other goddesses on either side of her head. On the left you can see the zodiac signs from Leo to Capricorn. The boat containing the sun is beside her head here. Note the two rows of seven oblique squares. Below we see the goddesses with wings surrounding the djed pillar which symbolizes the spine. You can probably see this as the source of the cadeusus of Mercury who rules Virgo.
At around 18 and 19 degrees, both the tangent and the sine equal .333. That is the one short side is one third the length of one of the other sides. We see this in the Temple where it is 20 wide and 60 long. If you use the hypotenuse, the sine of 19.47 is .333. We find Pennsylvania Avenue between the WH and CB at 19.5 degrees. The statue of Freedom on top of the CB is 19.5 feet tall. The statue of Jefferson in the monument is 19 feet tall. The interior dimensions of the coffer generate 19 degree diagonals. When the moon runs high in its orbit it moves to 28+ degrees, but when it runs low, it only moves to 18+ degrees.
Comparing the Ark of the Covenant to the altar at 5x5 and the Tabernacle that was 10 cubits wide, we find that 5/1.5 is 3.3333, and 10/1.5 is 6.666. Below we see a 50x50 square, the same red square seen above. Vertical lines divide the square into five strips ten wide each. Horizontal lines complete the 10x10 square on the center. Inside that we see a 5x5 square centered. The ark was half that long. The ark was 2.5 long. The altar was 5x5. The Tabernacle was 10x30; three 10x10 squares. The Temple was 20x60, and the altar there was 20x20x10.
The sine function relates the y dimension (vertical) to the radius of a circle. Our radius here is 25 cubits. Here we are dividing half the circle into five bands five cubits wide. Lines from the center (radii) are directed to .2,.4,.6,.8 and 1.0. In the 10x10 central square you see depicted the relative dimensions of the altar and the ark. With the ark centered in one square, the side of the third square matches the big square.
What this shows is that a band 10 wide on a 50x50 square generates 11.5 degree angles, but that a 20 cubit band generates 23.5 degree angles, like the tropics. Rememeber that the holiest place in the Tabernacle was 10x10, but that the dimensions of the Temple were double that. The floor area is 4 times as great, and the volume 1s 8 times as great in the Temple. The size of the altar was increased from 5x5 to 20x20, the same size as the Holy of Holies.
That is, if we place the Temple on the court of the Tabernacle, the 20 cubit width defines parallel lines at 23.5 degrees from the equator. Above we place the 20x60 Temple on the court of the Tabernacle. It is centered as is the 20x20 altar. As you can see the 60 cubit long rectangle laps the 50x50 square 5 cubits on each side. If we make the Tabernacle square 10x10 (rather than 50x50), the Temple dimensions prove to be one third of a square that surronds that which is 12x12; the size of the altar that we see in Ezekiel and the dimensions of the New Jerusalem in Revelation 21.
You will recall that five represents the microcosm (the little world) and that six represents the macrocosm (the big world). The Tabernacle is the micro to the macro of the Temple. In the Tabernacle five and ten dominate, in the Temple six and twelve are used. [The Temple was 60x20 cubits.]
Above St. Paul's by Wren, below a Masonic Lodge floor.
The three degrees of 'blue' Masonry represent three stations of the sun, the June Solstice, the December Solstice, and the Equinoxes in March and September. In the Masonic Lodge on conceptually faces east. The first degree is associated with the June Solstice, when the sun rises to the north (left) of due east. The second degree is associateed with the December Solstice when the sun rises to the south (right) of due east. At the two Equinoxes it rises due east, on the center line.
If we stand west of the altar looking east across the Tabernacle, the candelsticks are on the right (to the south), and represent the December Solstice when we see the Festival of Lights. Saturn is the last sphere before reaching the stars and it rules Capricorn, so Capricorn has been called the Gate of Death. It represents the death of the sun god. The moon is the last sphere before reaching the earth and rules Cancer, which is called the Gate of Birth. Capricorn is an earth sign, and Cancer a water sign.
Mars is a fire sign, and Venus is an air sign. Those two rule Aries and Libra where the equinoxes occur. The sign for Libra is a pair of scale indicating the equinox and the sign for Aries is a ram. Note that the fire altar is outside the Tabernacle and available to the people; inside the Tabernacle was not. Outside we see the elements of earth, fire and water, while inside we see the element of air in the incense altar. The spring ceremony celbrated the element of fire and the fall ceremony celebrated the element of air, inside the Holy of Holies.
Looking at the Rebis, we are reminded of the 3,4,5 triangle, where the 3 side is masculine and the four side is feminine and the 5 side is the child (the synthesis). The sides total to 12, and it has an area of six being half a 3x4 rectangle. In the Tarot, the numbers are reversed and the Emporer is four and the Empress is three. Looking at the cards you can see the ram's head on the Emporer's throne that indicates Aries. He is described as 'a solar figure Martian in character'. Mars rules Aries but the sun is exalted there.
Note that the Empress card bears the sign of Venus, that she has seven pearls around her neck and a crown of 12 stars on her head (each with six points denoting dominion over the macrocosm). "She is the inferior Garden of Eden, the Earthly Paradise. She is not Regina coeli (Queen of Heaven), but she is still refugium peccatorum, the fruitful mother of thousands." Like Mars, she is earthy not heavenly.
Egyyptian columns were six units tall with a one unit capital. The Egyptians defined their country as seven degrees tall (6+1), running from 24 degrees to 31 degrees; starting at the high point of the sun and running to the high point of Mercury. Behdet was located above 31 degrees north, as was Jerusalem. Recall that the dimensions of the Ark of the Covenant indicate 31 degrees.
Here we see the planetary spheres depicted as six around one, which reminds us of the stars in the Revelation. We also see 12 around one in the tribes around the Tabernacle. That is the months, while 24 around one is the hours of the day; twenty four stones around one stone in a 5x5 floor, twenty four elders around the throne.
Notice that the sun is at the center, the closest is at the bottom, and Saturn, the farthest, is at the top. The parallel lines indicate 30 degrees and Mercury's range. Below we see an astrology chart drawn by Johannes Kepler in the vedic style. Just as with the Hebrew Camp in the desert, we have the sanctuary and Tabernacle on the center, with three gates to the north, three to the east, three to the south and west. These are the zodiac signs.
On page 81 of City of Revelation, John Michell writes of the New Jerusalem as consisting of a square, a circle and a hexagon, and "the foundations are the 12 corners of a double hexagon inscribed in a circle, following the customary pattern of an astrological chart". As you can see the round chart is not customary everywhere at all times. As a matter of fact, the square chart (below) matches the camp and New Jerusalem better than a circle does.
You can see that the square in the center is bounded by 30 degrees, just as the hexagram shows; the range of Mercury, the most eccentric planets. That is, in this image, the planets fit in the inner square surrounded by the signs; three north, three east, south and west.
As 30 degrees of latitude cuts the radius in half, we know that the sides of the inner square are half those of the outer square, and that it has one quarter the area and one eighth the volume. We can repeat the halfening or doubling process ad infinitum. Beginning with 10x10 (100), we get 25, 6.25, 1.56 for areas, and sides that are 5, 2.5, 1.25. Doubling we get 2, 4, 8, 16.
Looking at the oblique (tilted) square, we note that it has half the area of the big square (50). You can prove this by conceptually folding the corners toward the center. The four (half square) corners fill the inner square. The square root of 50 is 7.07. The next inner oblique square has an area of 12.5 (50/4) the square of which is 3.538 (7.07/2). If we go the other direction, the next area would be 200 with a sq rt of 14.14 (the sq rt of 2 x 10).
Curiously, when we make the earth's orbit equal one, the distance to Venus from the sun is .7, the distance to Mercury is .39, and the distance to Mars is 1.5, and the distance to Saturn is 9.6. The dome of the capitol in DC measures 96 feet.
In the image above the right squares measure 10x10, 5x5, 2.5x2.5, 1.25x1.25, etc. The oblique squares meausre 7.071x7.071, 3.538, .76, etc. The grey square is 1/32nd the area of the large square. Pix32 =100.