gematric calculator

The Saviour's Smile: RISU in Eclogue 4 in the Names of MARIA IESUS

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

II. Vergil's Eclogue 4, 60-63: Gematric aspects

III. The last sentence (62-63)

IV. INCIPE PARVE PUER

 

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

nec deus hunc mensa, dea nec dignata cubili (e)st.

342

263

605

60-61: 72 letters; 62-63: 72 letters

1539

1176

2715

1539 = 81*19; 1176 = 48*49

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:

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

1.      What are the guidelines and principles for VERGIL to create his gematric constructions? It's the order of the decimal system, the tetrakys star with its two concentric circles and the SATOR square:

Supreme is the idea of a communion of three divine persons who are united as one GOD. This principle of 1:3/3:1 can be recognized from the area sizes of the two concentric circles.

The tetraktys star, developed from the hexagon, strives to its final form of octahedron. It is achieved by two double rhombi in the form of a cross:

2.      In trying to detect the main elements of a specific gematric construction, it is necessary to distinguish between more important and less important principles chosen by the poet. The highest gematric MOTIF is obviously contained in the first three words INCIPE PARVE PUER which I choose to demonstrate some varieties of structural sense in gematric creations:

 

lett.

NS

FS

SM

FV1

FV2

SM

TOT

INCIPE

6

54

41

95

11

41

52

147

PARVE

5

58

40

98

31

11

42

140

PUER

4

57

39

96

22

16

38

134

 

15

169

120

289

64

68

132

421

169 = 13² >26 ; 289 = 17² >34

The square number 169 is extended to 289 by the addition of the FS 120 achieved by three successive numbers 39-41. It's noteworthy that 120 is the sum of numbers 1-15. It corroborates letter P (PARVE PUER), the gematric equivalent of 15, as one of Vergil's key principles.

The two square numbers point to the cross of two double rhombi (DR) and the octahedron, which consists of 26 elements: 6 corners, 12 edges, 8 areas. The two pyramids can be seen as two halves of the octahedron, if 8 elements of its quadrate basis are attributed to each of them.

There are two more aspects in INCIPE:

·      The single digits of 54 and 41 show 5+4 elements of the DR-zigzagline and 4+1 elements of the hexagonal axis which represent 3:1 areas of the two circles:

·      The hexagon and its extension both consist of 24 symmetrical elements + central point, circle line and area, i.e. of 27+27 elements. The NS 54 of INCIPE can be divided up into twice 27.

3.      But why are the three words repeated? One reason is that the double rhombus contains twice two figures of 13 and 17 elements:

In the case of the double-triangle a second one comes about, if the two middle lines are folded and the two outer corners are joined.

A second reason is that a octahedron needs four double-triangles for its outer surface:

The third reason finally has to do with the SATOR square and almost everything revolves around the number 15: The NS of SATOR – Creator is 69 = 3*23. 6*9 = 54 is the FS of SATOR, and 54 is the NS of INCIPE. So a main starting point are the single-digits 6 and 9, and the combination of multiplication and addition leads to 6*9 = 54 + (6+9) = 69.

The word SATOR appears a second time in its inversion form ROTAS. So Vergil repeats the three words analogously.

4.      The frame of the double rhombus consists of 15 elements, 9 belonging to the hexagonal part, 6 to the extension part:

The 9 elements of the hexagonal part of the double rhombus fall into 5 points and 4 lines. This is the purpose of the 6, 5, 4 letters of INCIPE PARVE PUER.

5.      15 as 3*5 substantially refers to the three axes of the hexagon. Each axis consists of 2 radial lines and 3 points, together of 5 elements:

Any unit of measure needs being limited by two points, which leads to the double aspects of 5 uneven diametrical elements and 6 even radial elements. If these elements are numbered according the above grafic, the sum is 11+12 = 23.

The FV of 15 is 8, both together make 23 and 3*23 is the NS of SATOR. Further 3*11 = 33 of unnumbered elements is the NS of PEN, and put together the word PENSATOR comes about. The word refers to the act of weighing. Theologically it means that God rewards human beings after their earthly lives according to their merits.

The gematrical equivalent of 15 is the letter P. Now it becomes clear why it is used in each of the three words INCIPE PARVE PUER: 3*23 is the NS of SATOR.

6.      The very start of INCIPE is IN: The NV 9 and 13 characterise two geometrical figures of two and three axes, containing the 10 units of measure of the DECIMAL SYSTEM:

If a central point is counted for each axis, the sum of points increases from 12 to 15. These two aspects may be added to 27.

As the numbers 1-3 have trinitarian meaning, the two figures of two and three axes can be completed by a single axis (right figure). The result is 15 points and 12 measure lines, totalling 27. If we consider the total NS+FS-sum 2715, we might guess that it's a combination of 15 points + 12 measure units, and 5+7+3 points, including the single circle axis. However, I'm not sure whether Vergil considered this specific aspect.

7.      The ratio of 1:3 area units of the two concentric tetraktys circles can be represented by 3 hexagonal radial elements and 5 radial elements for the total exterior circle as indicated in the zizag-line of the double-rhombus:

We can see the pattern 235 in the NS 58+57 = 115 = 23*5 of PARVE PUER. Significant are also the single-digit ratios of 5:8 radial elements of the zigzag-line and 5:7 points of the double rhombus, representing 3+4 = 7 and 1+3 = 4 area units:

8.      Vergil's amazing calculating faculties can be recognized in two gematrical constructions:

·      The double aspect of unnumbered and numbered diametrical and radial elements produced, as shown above, the sums 11 and 23 for one hexagonal axis. And 1123 is the FS of the NS and FS of the four lines:

line

NS

FS

SM

FV1

FV2

SM

TOT

60

398

295

693

201

64

265

958

61

395

313

708

84

313

397

1105

62

404

305

709

105

66

171

880

63

342

263

605

27

263

290

895

 

1539

1176

2715

417

706

1123

3838

·      The finite verbs of the four lines form part of the total NS+FS:

INCIPE

54

41

95

TULERUNT

124

102

226

INCIPE

54

41

95

RISERE

71

58

129

DIGNATA EST

96

83

179

36 letters

399

325

724

724 = 4*181

399 = 21*19; 325 = 13*25

The NS+FS of the finite verbs lead to the ratio 181*(4:11). 325 is the sum of the numbers 1-25 and so establishes a relationship to the SATOR-square.

9.      The single digits of the factor 181 again refer 10 units of measure, contained in the DR, 8 frame lines and 2 cross lines. This pattern is so important because a unit of measure needs two limiting points, and there are only 1-9 basic numbers as 0 in itself has no counting quality. So 9 points limit only 8 units of measure on a straight line:

However, in the DR 7 points limit 10 units of measure, and if the points are numbered in the form of a loop, it's 9 points:

The context of 9 points + 8+1+1 units of measure is also to be seen in the total NS 1539 = 81*19.

Vergil may have thought of the right figure as the NS of the 4 lines is 81*19 = 1539, containing 8+2 units of measure and 9 points. He considered this pattern 8+2 as so important that he repeated it in the summation of the NS+FS of the first and last lines: 693+605 = 11*(63+55) = 11*118. Here 11 means 7 points + 4 triangular areas, 118 2+8 units of measure.

10.        The two patterns of 4+6 and 8+2 units of measure correspond to the model of the SATOR square, second and fourth lines:

SATOR AREPO TENET OPERA ROTAS

The NS of the two models is 20+52 = 72 for each half, which is also the number of letters in lines 60-61 and 62-63.

The two axial figures and the DR can account for the total NS+FS 2715 though by rather a bold explanation. The following correspondence between PARVE (58) PUER (57) and the two models can be established:

number of pts

2axf.

number of el.

DR

real

12

21

33

extended (3*9)

15

27

42

 

27

48

75

12 and 15 points limit 20 units of measure, 27 limits 10 units of measure. 27 includes 12+15, so 27 may stand for 30 units and 15 for 10 units. The NS of PARVE PUER is 115, if two U = 40 units of measure are subtracted, 75 remains.

11.        Like in numerology gematric calculations consider letters whose NV are prime numbers or composite numbers. The palindrome character of the SATOR square becomes most cleary evident if you start in the middle and read by meandering in both directions

NET OPERA SATOR

THE CREATOR WEAVES HIS WORKS

Vergil's INCIPE PARVE PUER shares the NS+FS 289 = 17² of the SQ's two palindromic halves. Distinguishing between Prime Numbers and Composite Numbers: also the referential origin of the SATOR square, the multiplication table (from 3-7 without tens), should be included, as above shown:

 

SATOR

1x1-table

 

 

 

 

PN

CN

sm

PN

CN

sm

S-PN

S-CN

tot

NS

97

61

158

24

31

55

121

92

213

FS

97

34

131

24

23

57

121

57

178

sm

194

95

289

48

54

102

242

149

391

289:102 = 17*(17:6) = 17*23

The differenc between 178 and 213 is 35.

Vergil builds on the two results in the following way:

 

SATOR + 1x1

INCIPE

 

 

 

 

PN

CN

sm

PN

CN

sm

S-PN

S-CN

tot

NS

121

92

213

66

103

169

187

195

382

FS

121

57

178

66

54

120

187

111

298

sm

242

149

391

48

54

289

374

306

680

374:306 = 2*17*(11:9) = 34*20

187 = 11*17; 195 = 15*13

While the total results of the SQ and 1x1 are divisible by 17, Vergil achieves a ratio between the NS+FS of the prime numbers and the composite numbers.

Now, eventually, it has become clear why Vergil repeated INCIPE PARVE PUER: He imitates the two palindromic halves of the SATOR square and the multiplication table.

Vergil, furthermore, makes use of his models' FS 57 – which is the NS both of PUER and PATER – by adding 54, the NS of MATER and INCIPE.

12.        Vergil interweaves the main motif INCIPE PARVE PUER with the nouns of persons by repeating the factor 17 for the NS+FS: PUER (2) MATREM MATRI PARENTI DEUS DEA. The NS+FS is 374+289 = 663 = 17*(22:17) = 3*13*17. In this way PUER is used four times.

13.        It's an unusual and admirable coincidence that the NS+FS of the important word COGNOSCERE 99+79 = 178 is the same as MARIA (72) and IESUS (106). I tried to find two 5-letter words with the NS+FS 72 and 106: COGOC and SEREN. The first may be understood as a short form for COGIT OCCULTUMshe defeats the hidden evil, the second, completed to SERENUSserene characterises Jesus' constant disposition of mind.

 

Written: December 2021

VERGIL