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The Saviour's Smile in Eclogue 4

RISU in the Names of MARIA and IESUS I. Aspects of the Decimal System in the names of MARIA and IESUS

#### I. Aspects of the Decimal System in the names of MARIA and IESUS

1.      The numerical values (NV) of MARIA and IESUS are 40+70 = 110 = 2*55. The sum of the numbers 1-10 is 55. While the 10 numbers can be placed on the points of one tetraktys, the twice 5 letters of MARIA and IESUS will have to be properly arranged on two tetraktyses.

An alternating pattern of the two names splits the numerical sum (NS) 110 into two halves:

 M A R I A I E S U S sm NS1 12 17 1 5 20 55 NS2 1 9 9 18 18 55 110

The count of values starts from the first letter of MARIA and proceeds in two groups of uneven and even numbers from 1-10.

This alternating pattern of uneven and even numbers with the same gematric results reveals the closest possible interrelation between MARIA and IESUS. It shows that MARIA puts her life totally in the service of her son and his work of salvation. It even seems that her share in the work of salvation is equal to her son's.

2.      The letters of MARIA and IESUS have proved to be intertwined in their regular juxtaposition. So it is most plausible to place the 5 letters of each name on the points of two tetraktyses as regularly as possible. The start for each name will be the cornerpoints of the two opposite tetraktyses, Mary's tetraktys running from top to bottom, Jesus' from bottom to top. The second to fifth letters occupy the 4 horizontal points of each tetraktys: Each tetraktys is now composed of 4 hexagonal and 3 extension letters. There is a relation of 4 inner to 6 outer letters (lts), whose numerical sum + factoral sum (FS) are:

 4 lts 6 lts sm NS FS sm NS 64 46 110 MARIA 40 32 72 FS 40 28 68 IESUS 70 36 106 sm 104 74 178 110 68 178

64 and 46 are inverted numbers, the digits showing accordance with the 4+6 letters. There are two ratios: 40:64 = 8*(5:8); 40:28 = 4*(10:7). The ratio 10:7 corresponds to the 10 points of the tetraktys and 7 points of the hexagon.

3.      The 4 hexagonal letters belong to both tetraktyses, so their values have to be counted twice: 46+64+64 = 174; 68+40+40 = 108. The two sums are to each other as 6*(18:29) = 6*47. The number 6 refers to 6 triangular sides of two tetraktyses, 47 to the ratio of part to whole, i.e. 4 points to the whole of (4 points + 3 lines) of one triangular side. The NS 108 in the product form 12*9 represents the initials of MARIA and IESUS.

These are the values of the two tetraktyses:

 Tetr. MARIA Tetr. IESUS NS FS sm NS FS sm 35 20 55 11 8 19 RISU 64 40 104 64 40 104 99 60 159 75 48 123 159:123 = 3*(53:41)

The ratio of the two FS 60:48 is 12*(5:4) = 12*9 , again confirming the initials of MARIA and IESUS.

4.      The four hexagonal letters, read clockwise, show a Latin noun form in the ablative case, derived from RISUSlaughter, smile. Two letters are taken from MARIA, two from IESUS. So the act of recognition and smile is a mutual one.

If one follows the outer points anticlockwise, starting from the A on the right, one can read AMASYou love. One may suppose a speaker inwardly addressing the Virgin Mary, as he observes her smiling at her child. The remaining letters IE may be complemented like this:

RISU AMAS IE(SUM)You show your love for Jesus by smiling at him.

The letters SUM, which are contained in the two names, complete the 13 points of the tetraktys star, occupying the missing points of the central axis: 5.      Love arises only between persons. It is engendered by acts of mutual recognition. Human love is a divine gift, and its eternal model is the loving relationship between the trinitarian persons of Father, Son, and Holy Spirit.

A SMILE starts from a person's mouth and expands over his whole face. So love transgresses all boundaries. Such a boundary is the hexagon that is expanded to form a hexagram including two tetraktyses. The hexagram is completed by a circle whose area is three times the size of the hexagon area. This expansion can be understood as self-manifestation of the trinitarian persons whose origin is the First person or God Father: The hexagon represents the unity of the Father with the Son and the Holy Spirit, the hexagram their loving relationship.

6.      The alternating pattern of uneven and even numbers in MARIA and IESUS resulted twice in the NS 55, which is the sum of the numbers 1-10. This corresponds to 2*10 points of two tetraktyses. So mother and son embody the perfect idea of the decimal system.

Besides, the tetraktys star contains three double rhombi: One double rhombus consists of 7 points, 4 triangular areas and 10 lines. These elements exactly characterise the NS of MARIA IESUS in the structure of the ratio 10*(4:7) = 10*11. This structure can be shown in the three tetraktys sides and on a straight distance:  Here again we can see that 3*4 = 12 points and 3*3 = 9 units of measure correlate to the the initials of MARIA and IESUS. It shows that Jesus was included in his mother's womb.

While the tetraktys emphasises the decimal system by the number of 10 points, it's in the double rhombus the 10 units of measure. 7 points + 4 triangular areas combine to represent 11 delimiting points for 10 units of measure: The figure shows the 9 different basic numbers delimiting 8 units of measure. So 2 units of measure have to be added, as represented in the cross lines of the double rhombus. If 8 units of measure and 9 points are read as 89, twice 89 is 178, the NS+FS of the MARIA and IESUS. Twice 89 also forms an axis cross numbered from 1-9 from the centre point: This axis cross can serve to support the idea of Mary's role as coredemptrixco-redeemer.

7.      The two names can be placed in various ways on the elements of the double rhombus of which I choose the following: The letters are placed loop-shaped, starting with MARIA below and continued by IES-, with the last two letters -US occupying the cross lines. The NS+FS of the lower and upper rhombi are:

 NS FS NS FS 5 lower 56 30 86 4 lower 36 21 57 5 upper 54 38 92 4 upper 36 30 66 110 38 178 72 51 123

56+54 are the constituents of their sum 110. 4 lower and 4 upper letters of the DR without the cross-line letters have the NS+FS 57+66, which are the FS+NS of the numbers 1-11, corresponding either to 11 elements of a single rhombus or to 7 points and 4 areas of the double rhombus. The NS+FS of -US is 38+17 = 55.

8.      The DR-zigzagline can be subdivided into 3 radial elements of the hexagonal part and 2 of the extension part. MARIA IESUS can be placed on these 10 radial elements from the central point: The NS+FS of the four parts are:

 hex. NS FS ext. NS FS MAR 30 25 55 IA 10 7 17 IES 32 19 51 US 38 17 55 62 44 106 48 24 72

The NS+FS 106 of the 6 letters of the hexagonal part is equal to the NS+FS of IESUS and the NS+FS 72 of the extension part to the NS+FS of MARIA. There are also two cross relations: 55+55 = 110 and 51+17 = 68 for the NS and FS of the two names. The cross-combined letters can be read als RAMUS | E(X) ISAIa branch from Isai, the father of king David, referring to the Book of Isaiah 11,1: "A shoot springs from the stock of Jesse", predicting the Messiah, who would be  born from a VIRGIN (Isaiah 7,14). The prophesy came true by the birth of IESUS from the Virgin MARIA.

The ratio 24:48 = 24*(1:2) shows one important meaning of 72: Without the central point the hexagon consists of 24 elements and the whole tetraktys star of 2*24 = 48 elements. So the ratio 1:2 elements means 1:3 area units of the two concentric circles.

9.      Similar to MARIA IESUS also CHRISTUS can be placed in loop form on the 8 lines of the frame of the double rhombus: The letters of RISU are segregated on the four left lines. The NS+FS of the 4+4 letters are:

 NS FS sm RISU 64 40 104 CHST 48 36 84 112 76 188 64:48 = 16*(4:3) 104:84 = 4*(26:21) = 4*47

47 is the NS of DEUSGod, 26 the FS and 21 the difference between FS and NS. So the NS+FS of DEUS is 47+26 = 73, which is the NS of FILIUSSon.

In this arrangement of letters CHRISTUS is recognised as the Saviour who looks at each human individual with a loving smile.

A special characteristic of this loop-shaped order is that the NS of the 4 hexagonal letters RU-TH (female figure of the Old Testament) is the same as the NS of RISU: 37+27 = 64.

#### II. Vergil's Eclogue 4, 60-63: Gematric aspects 12 Years after investigating into the last four lines of Vergil's eclogue 4 I've revised the original version but I'm far from claiming to have found the solution, given the immense complexity of gematric constructions. So my contribution should be regarded as an approach to plausible answers. I add a study on Vergil's main gematric principles.

1.      In his famous 4th eclogue the poet VIRGIL announces the birth of a boy who will bring peace to the world. In line 60 he says:

Incipe, parve puer, RISU cognoscere matrem

Begin, little boy, to recognise your mother with a SMILE

Virgil invites the little boy to reward his mother with a SMILE, while the tetraktys figure rather suggests MARIA is taking the initiative. Virgil wants to say that this child is so extraordinary that a smile is expected as a sign of his divine origin. In reality, however, babies do not smile after their birth at once. They are helpless bundles and have to be cared and caressed by their mothers until their human faculties are gradually elicited.

2.      It is from his overflowing love that God created the world. So the two concentric circles of the tetraktys star can be seen not only as an image of the trinitarian God himself, but also of his creation. Out of love God's Son, his own image, became a human being, and the loving smile between Mother and Son marks the beginning of hope for a future era of reconciliation and peace.

3.         The word RISU is one among 9 words which belong together. This last text unit of Vergil's 4th eclogue consists of lines 60-63. The following text is provided with the NS+FS of each line. The values of single words can be obtained by an online calculator:

 Incipe, PARVE PUER, RISU cognoscere MATREM: 398 295 693 MATRI longa decem tulerunt fastidia menses. 395 313 708 Incipe, PARVE PUER: qui non RISERE PARENTI: 404 305 709 1197 913 2110 nec deus hunc mensa, dea nec dignata cubilI (E)ST. 342 263 605 1539 1176 2715 1197:342 = 9*19*(7:2); 605 = 55*11; 2715 = 15*181

Translation:

Begin, little boy, to recognise your mother with a smile:

Ten months caused your mother long inconveniences.

Begin, little boy: Those who have not smiled at their parent (mother or father or both):

Neither a god has considered him worthy of his table nor a goddes of her bed.

4.         I have not found any scholarly answer to the prolonged 10 months of pregnancy the little boy's mother had to go through. From the point of view of the decimal system, the number ten is the completion of the basic numbers 1-9. In analogy, the announced extraordinary boy crowns and completes the history of mankind by his birth and the deeds of his life.

The tetraktys consists of units of 10 and 9: 10 points, 9 triangles, 18 lines, together of 37 elements. The poem ends with CUBILI (E)ST. Because of the preceding vowel I, E is dropped when the hexameter is read. The letter S corresponds to the 18 lines and T to the 10 points + 9 triangles. If an E (5) is added to ST, the elements of a single tetraktys are converted to the elements of two tetraktys FRAMES with 7 elements for each of the 6 sides (6*7 = 42).

5.         Having another look at the 9 words, we find that the repetition of PARVE PUER and the references to his mother MATREM MATRI PARENTI both consist of 18 letters, while RISU RISERE, serving as linking bond between Son and Mother, amounts to 10 letters. So let's find out the values of these 10 letters first:

 RISU RISERE NS 64 71 135 FS 40 58 98 104 129 233

The values of the 4+3 words follow:

 NS FS sm NS FS sm PARVE 58 40 98 MATREM 66 56 122 PUER 57 39 96 MATRI 58 50 108 sm 115 79 194 PARENTI 79 69 148 double 230 158 388 sm 203 175 378 230+203 = 433; 158+175 = 333

Son and Mother correspond to each other by the inverted NS 230 and 203. The digits of the sum 433, a prime number, show the structure of the 10 tetraktys points (4+3)+3. Also 433, a prime number, is the area size of an equiliteral triangle (exactly: 0.433).

6.         The total results of the three groups (PRM) are:

 P 230 158 388 2M+P 203 175 378 R 135 98 233 621+378 = 999 365 256 621 621:378=27*(23:14) = 27*37 365+203 = 568; 256+175 = 431 175:203 = 7*(25:29) = 7*54

378 is the sum of the successive numbers from 1-27. The ratio numbers 23+14 = 37 on the one hand represent 37 elements of the tetraktys, their digital sums on the other hand are two ways of representing twice 5 radial elements of the zigzag-line of the double rhombus: 7.         The product 27*37 is essential for the understanding of the four lines. The VESTA-cult based on the tetraktys star, was SECRET, open to those only who had been initiated. The formula and password for them was ST! imposing strict silence towards all who were not initiated to the cult. For VESTA can be read as VETAS meaning "you forbid", reminding the initiated of what the goddess expected from them. The formal logic behind this formula is that the tetraktys consists of 18 lines and 10 points + 9 triangular areas. The formula can be submitted to the 4-value calculation which means that FV can be obtained from NS and FS:

 P+A L sm FV sm NS 19 18 37 37 74 FV 19 8 27 9 36 sm 37 27 64 46 110

The result shows that the two inverted sums 64+46 = 110 provides twice the sums of the numbers 1-10 = 55 for the 10 points of two tetraktys. We can see the parallel to the NS 110 of MARIA IESUS: 64 is RISU on 4 hexagonal points and 46 for the letters on 6 extension points.

The word RISU itself can be divided up into RU = 17+20 = 37 and IS = 9+18 = 27. 9 and 18 are the result of theological speculation: The first 3 numbers 1+2+3 add up to 6. If there is belief in 3 divine persons, the calculation runs 6+3 = 9 and 6*3 = 18.

The NS+FS 37+26 = 63 of UR is also of importance: 63 is achieved, if the elements of the 3 levels of the tetraktys are added up: 63 means 7 elements for each of the nine triangular areas. Vergil may have considered 63 in the ZS+FS 693 = 11*63 of line 60.

8.         If the 18 lines of the tetraktys form one unit and the 10 points and 9 triangles the second unit of 37 elements, the FV of 18+19, meaning ST, are 8+19 = 27. So the product 27*37 = 999 represents the FS+NS of the two groups of elements.

The meaning of 27, as specifically relevant in the present context, consists in the NV of P+M = 15+12 = 27, the initials of PUER and MATER. The FV of the two numbers are 8+7 = 15. So it seems plausible to associate these two numbers with the total NS+FS 2715 of lines 60-63. A plain, but plausible exlanation could be that 2715 unites the initials of (PATER+MATER) + PUER.

9.         If 27 is composed of the values of P+M, Vergil will have spent special attention to the 9 initials. We can group them into two pairs of P+M, three further P, and two R:

 2(P+M) 3 P sm 2 R tot NV 54 45 99 34 133 FV 30 24 54 34 88 sm 84 69 153 68 221 54:99 = 9*(6:11) = 9*17 153:68 = 17*(9:4) = 17*13

The trinitarian number 153 forms a ratio with the NS+FS of the 2 R 68, which shows that the mutual smile between Mother and Son flows from their common and united nature. The numbers 11, 13, 17 refer to the number of elements of 3 geometrical figures to be found both in the tetraktys and the double-rhombus:  10.    The poet attributes great significance to the little boy's smile. Two aspects already mentioned have to be considered: The son has his own nature and has adopted that of his mother, in whom his body was formed. It seems he strongly claims his life as his own at the expense of his mother's. It's perhaps for this reason that the poet calls upon the boy to smile at his mother in order to give her something back as his due.

The number 378 = 14*27 suggests that his mother smiles at him first. The NS of RISU and RISERE is 135 = 5*27. If he answers her smile, he gives her 135 of his values so that the NS+FS ratio between Son and Mother is now (621-135):(378+135) = 486:513 = 27*(18:19). In this way the 37 elements of the tetraktys are most equally and justly divided up.

The numbers 18+19 are the NV of ST, the last two letters of the poem. Furthermore, the NS of the last line is 18*19 = 342.

11.    Also divisible by 27 are the NS+FS of the first two + the last three of the nine words so that successive groups of 2+4+3 words come about which, assembled to the 3-digit number 243, is 9*27.

 NS FS sm NS FS sm PUER 57 39 96 PARVE 58 40 98 RISERE 71 58 129 PUER 57 39 96 PARENTI 79 69 148 sm 115 79 194 sm 208 177 373 194+373 = 567 = 21*27

The 5:4 words thus have the NS+FS ratio 27*(21:16). The ratio can refer to the frame of a double-rhombus numbered with 1, 2 and 3, 21 being the sum of the hexagonal part, and the 2*8 = 16 the sum of the extension part: The digits 243 refer to the the middle elements of a double-rhombus: 2 crosslines, 4 triangles, 3 points. These 9 elements also apply to the two diametrical zig-zag lines of 9 elements each so that the NS+FS result 999 shows 27 elements if the three parts are counted separately, whereas as a united figure the double-rhombus consists of 21 elements.

Two groups of 3:6 words provide divisibility by 9*37 = 333: the NS+FS of the words PUER (96) MATRI (108) RISERE (129). So both the ratio of words and gematric values is 1:2.

12.         The relation of the first three lines to the last becomes clear if we subtract 2110-999 = 1111 = 101*11. The NS+FS 605 of the last line is 55*11, together 1716 = 12*11*13. Written: March 2009

Last entry: December 2021