gematric calculator

The Saviour's Smile in Eclogue 4

III. The last sentence (62-63)

c) The Underlying PRINCIPLES

d) Structure of last sentence

1.      In chapter b) 21 words proved to be a major gematric unit. At the end of the investigation emerged the underlying system which will be detailed here. The 21 words subdivided into 11+10 were attributed to the MOTHER and FATHER of the expected Saviour Boy:

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

 

MATREM

6

66

56

122

PARENTIS

8

97

77

174

163

133

296

 

MATRI

5

58

50

108

PARENTI

7

79

69

148

137

119

256

 

 

11

124

106

230

 

15

176

146

322

300

252

552

 

230:322 = 2*23*(5:7) = 46*12; 552 = 24*23

 

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

PUERO

5

71

48

119

PATRIIS

7

88

65

 

 

 

 

PUER

4

57

39

96

 

 

 

 

 

 

 

 

sm

9

128

87

215

 

7

88

65

153

216

152

368

368 = 16*23

 

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

ASPICE

6

51

31

82

ASPICE

6

51

31

82

 

 

 

INCIPE

6

54

41

95

INCIPE

6

54

41

95

 

 

 

PARVE

5

58

40

98

PARVE

5

58

40

98

 

 

 

PUER

4

57

39

96

PUER

4

57

39

96

 

 

 

RISU

4

64

40

104

RISERE

6

71

58

129

 

 

 

DEA

3

10

10

20

DEUS

4

47

26

73

 

 

 

CUBILI

6

54

37

91

MENSA

5

49

34

83

 

 

 

34

348

238

586

 

36

387

269

656

735

507

1242

1242 = 54*23

 

TOTAL RESULT of 21 words

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

mother

54

600

431

1031

father

58

651

480

82

1251

911

2162

2162 = 2*23*47 = 46*47

 

The 4 violet words belong to the first part of the poem:

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

PUERO

5

71

48

119

PATRIIS

7

88

65

 

 

 

 

PUER

4

57

39

96

PARENTIS

8

97

77

 

 

 

 

sm

9

128

87

215

 

15

185

142

327

313

229

542

542 = 2*271

The result of the shortened group of 17 words is:

 

lett.

NS

FS

sm

 

lett.

NS

FS

sm

SM

SM

GS

MATER

45

472

344

816

PATER

43

466

338

804

938

682

1620

816:804 = (8*102):(4*201); 1620 = 10*(9*18)

2.      The 21 words and 112 letters can be divided into 2 groups of 4-3-4 and 4-2-4:

 

lett

PUERO PUER PATRIIS PARENTIS

24

MATREM MATRI PARENTI

18

ASPICE INCIPE PARVE PUER

21

ASPICE INCIPE PARVE PUER

21

RISU RISERE

10

DEUS MENSA DEA CUBILI

18

There is a gematric correspondence of the two Groups between the two inner and 4 surrounding word Groups: First, there is a trinitarian ratio of 28:84 = 28*(1:3) letters, second, there are NS:FS-ratios in each word group with the common main NS+FS-factor 47:

 

NS

FS

sm

MATREM MATRI PARENTI

203

175

378

RISU RISERE

135

98

233

 

338

273

611

273:338 = 13*(21:26) = 13*47

 

 

NS

FS

sm

PUERO PUER PATRIIS PARENTIS

313

229

542

ASPICE INCIPE PARVE PUER

220

151

371

 

533

380

913

ASPICE INCIPE PARVE PUER

220

151

371

DEUS MENSA DEA CUBILI

160

107

267

 

380

258

638

 

913

638

1551

638:913 = 11*(58:83) = 11*141 = 3*11*47

The NS:FS-ratio 913:638 is repeated as NS+FS ratio 913:638 between the two upper and lower word Groups.

3.      The innermost PRINCIPLE of this gematric construction unit is contained in the NS+FS of the three words MATREM (l.60) MATRI (l.61) PARENTI (l.62): 203+175 = 378 = 7*(29:25) = 21*18. The geometric reference is the double rhombus (DR) with 4 triangular areas + 7 points and 10 lines:

 

 

 

 

sm

FW

sm

NS

4

7

10

21

10

31

FV

4

7

7

18

8

26

sm

 

 

 

39

18

57

57 is the NS of PUER, 39 the FS and 18 the difference between the FS and NS.

The four letters of PUER can be placed on the triangular areas:

The NS+FS of the inner two letters UE correspond to the FS, the outer two letters PR to the NS of the whole word. Morover, the first two letters have the NS+FS 52 = 4*13, the last two letters the NS+FS 44 = 4*11. The factors 13 and 11 are contained in the NS+FS results of the 2 inner and 4 surrounding word Groups. Out of 4 rhombi or 4 (hourglass shaped) double triangles a octahedron can be assembled, as can be seen below from two rhombi of the first two figures and two triangles of the right figure to be complemented by another two of each figure:

4.      One rhombus connects the hexagonal area with the extended area and so represents 3 area units:

One triangle consists of 7 elements, one rhombus of two triangles, but of 11 elements, three less than 2*7 = 14. If a ratio of elements of one triangle to one rhombus is established, this means 7:11 elements which is the number of letters of MATREM MATRI and PARENTI the triangle meant might belong to the hexagonal or the extended part of the tetraktys star. If the triangle belongs to hexagonal part, 7:11 elements represent the ratio 1:3 of circle area, if it is thought to belong to the extended part, the ratio is 2:3.

A double triangle + another triangle form a fish shaped figure, 4 more elements add a fourth triangle:

17:4 elements mean a trinitarian ratio of 3:1 triangles. This accounts for the 4 words of the first half of the poem and 17 of the second half.

5.      On a smaller scale FATHER, MOTHER and CHILD have to be looked at more closely gematrically:

 

line

lett.

NS

FS

sm

 

line

lett.

NS

FS

sm

PATRIIS

17

7

88

65

153

PUERO

8

5

71

48

119

PARENTIS

26

8

97

77

174

PUER

18

4

57

39

96

PARENTI

62

7

79

69

148

PUER

60

4

57

39

96

 

 

 

 

 

 

PUER

62

4

57

39

96

 

105

22

264

211

475

 

148

21

242

165

407

475+407 = 882 = 2*21

264:242 = 22*(12:11) = 22*23 = 506; 211+165 = 376 = 8*47

153+97 = 250; 250:225 = 25*(9:10); 165:242 = 11*(15:22) = 11*37

71+57+57+57 = 185; 185:222 = 37*(5:6)

105+148 = 253 = 11*23

23 and 47 are the main factors in the total NS+FS result 2162 = 2*23*47. One reason for number 23 is that the NV+FV of P, the initials of PATER and PUER, is 15+8. One can see this when adding 105+60 = 165; 165:88 = 11*(15:8).

25 and 37 refer to the number of elements of the hexagon and the tetraktys, representing area ratio 1:3 of the two tetraktys circles.

The two NS+FS 475+407 equal 882 = 2*21. Two halves can be achieved if the NS+FS of three PUER and of PATRIIS are added: 288+153 = 441 = 21.

There is finally to be added MATREM MATRI RISU RISERE:

 

line

lett.

NS

FS

sm

7 words

253

43

506

376

882

MATREM

60

6

66

56

122

MATRI

61

5

58

50

108

 

374

54

630

482

1112

RISU

60

4

64

40

104

RISERE

62

6

71

58

129

 

122

10

135

98

233

total

496

64

765

580

1345

1345 = 5*269

630:135 = 45*(14:3) = 45*17

269 is the sum of the 4values of PATER MATER:

 

NS

FS

sm

FV1

FV2

sm

GS

PATER

57

50

107

22

12

34

141

MATER

54

49

103

11

14

25

128

 

111

99

210

33

26

59

269

The result shows an ideal family relationship because father, mother and child love each other by smiling at each other.

6.      The pattern 4-3-4, 4-2-4 explained above fits perfectly for placing the 21 letters on the 21 elements of the DR. How Vergil carried out this task, however, is not easy to find out. After testing different possibilities, I think to have reached a satisfactory solution. It consists of two principles here: First, the letters are placed in a continuous movement from below to top and from top to bottom. Second, the NS and FS are separated and placed in a cross of double rhombi so that the lower rhombus can be combined with the right rhombus:

According to the above pattern there are 6 up and down movements. The placement starts with PUERO on the 4 cross-points and goes down the 3 central points and up again on 4 triangular areas. The second part of the pattern starts from above down on 4 zigzag-lines, then up again on 2 cross lines and finally down on the 4 other zigzag lines.

The surprising result is that the NS+FS of the lower + right and left + upper rhombi are equally 1027 = 79*13 = FW 92 = 4*23 if MATRI in the central point is omitted. 1027 can be referred to the TETRAKTYS and understood as 10 points, 18 lines + 9 triangular areas. On the scale of the basic numbers 1-9 the digits 7 and 9 are complementary to 3 and 1 and so have equally trinitarian meaning. 79 and 97 are the NS of PARENTI (l.62) and PARENTIS (l.26). 7 signifies the number of hexagonal points, 9 the number of points of the tetraktys frame:

In this context 7 to 9 points represent the ratio of 1 to 3 area units of the two concentric circles.

Without MATRI the 8 words of the longitudinal axis have the NS+FS 874 = 19*46. The ratio of 8:13 words in this way is 46*(19:28) = 2162.

The NS+FS 108 of MATRI added to 536 equals 644 = 28*23, thus forming a ratio of 46*(14:33) for the 21 words.

The FS 92 = 4*23 can be associated to a square whose 4 sides consist of 2 units of measure and 3 points. It can be constructed by shifting two angles of an axis cross against each other:

The frame of the square is part of OPERA in the SATOR Square:

The word OPERA work contains 3 letters of PUER and 4 letters of PUERO. The NS+FS of OPERA is 52+40 = 92. The two equal sums of 1027 coincide with twice OPERA/AREPO of the SATOR-Square.

92 is the NS of SANCTUS HOLY to which PATRIIS shows a certain resemblance of its 4values:

 

NS

FS

sm

FV1

FV2

sm

GS

SANCTUS

92

61

153

27

61

88

241

PATRIIS

88

65

153

17

18

35

188

The axis cross above consists of 1+8+8 = 17 elements.

7.      MATRI is justified to occupy the centre of the DR-cross because its NS+FS 108 is connected with the NS+FS 1620 of 17 words by the ratio 108*(1:14), so it is rightly the centre of 15 frame elements of the DR.

The FS of the NS+FS of the 21 words and the 3 subsums again lead to the prime number 269, the 4values of PATER MATER:

 

 

 

 

sm

FV

NS

1027

1027

108

2168

72

FV

92

92

13

197

197

sm

 

 

 

 

269

An NS+FS ratio of the two zigzag lines is obtained if MATRI is assigned to the right zigzag line:

728:560 = 7*8*(13:10). 7*8 is related to 7 points and 8 lines of the DR-frame. 13:10 could mean 13 points of the tetraktys star and 10 points of the tetraktys. But it could specially refer to the DI, the plural of DEUS. The NV of the two letters are 4+9 = 13 and their FV 4+6 = 10. 13 can be seen in a trinitarian sense as One God in Three Persons. As a two-digit number 49 is the sum of elements of the tetraktys star. Vergil's Eclogue 4 consists of 409 words.

8.      PUERO (l.8), MATRI (l.60) and PARENTI (l.62) are three dative cases which, as we confidently imagine, the poet Vergil chose to dedicate his poem to these unique venerable divine persons by whom mankind would be presented with a felicitous future. He did not do so without making sure of their combined special gematric properties. Besides the NS+FS their FV are necessary:

 

NS

FS

sm

FV1

FV2

sm

GS

PUERO

71

48

119

71

11

82

201

MATRI

58

50

108

31

12

43

151

sm

129

98

227

102

23

125

352

PARENTI

79

69

148

79

26

105

253

total

208

167

375

181

49

230

605

253:352 = 11*(23:32) = 11*55 = 5*11

208+181 = 389; 167+49 = 216 = 6

208 = 16*13

605 is the NS+FS of line 63, the last line of the poem.

The inverted sums 253 and 352 show the relationship between father, mother and child: A mother conceives her child by a father and carries him in her womb until he is born. In the numerated tetractys the sum of numbers 1-10 can be grouped to sums of 23 and 32:

The digits of 216 can describe the structure of points on the tetraktys frame: 2 bottom corner points, 1 top corner point, 6 hexagonal points. In this context 6 can mean 3*6 elements of the tetractys frame: 9 points, 9 lines. On the other hand each tetractys side consists of 4 points and 3 lines, 7 elements together. If the points are numerated with 2 and the lines with 3, the sum is 8+9, for three sides 3*(8+9), which could be read as the prime number 389:

Equally or more important are three geometrical "fish figures" (cf. above) in the tetractys, each consisting of 17 elements:

The cube number 6 also points to the three-dimensional figure of hexahedron with its 6 corners. This context is indicated by the prime numbers 151 and 181 both contained in the DR which in the form of a DR-cross is a construction element for the octahedron. 151 refers to the structure of DR points: 5 hexagonal points and 2 extension points, 181 to 10 units of measure, 2 cross lines 8 frame lines. 181 is of DIVINE significance as it shows 2 units of measure limited by uncountable 0 in a circular circumference beyond the basic numbers 1-9:

This above model is characterised by 3+17 elements leading to the following calculation: 3+17 = 20; 17*3 = 51; 20+51 = 71. 3, 17 and 71 are factors of the NS of the whole poem: 25347 = 3*7*17*71. 181 is also the main NS+FS factor of the 4 last lines: 2715 = 15*181.

This basic circular model can be represented in linear extension:

The linear model ends with a second point so that the calculation is 2+17+2 in contrast to the circular model 2+17+1. As a 4-digit number 2172 = 12*181 the linear model points to the circular model of 1+8+1 units of measure.

The circular model substantiates a special numeration of the DR-points in loop shape so that 9 positions delimit 8 units of measure including the two cross lines:

The right DR is an attempt to illustrate the palindromic number 181.

Vergil obviously also considered the verse numbers of the three names 8+60+62 = 130 which turns attention to the SATOR-Square: SATOR TENET The Creator Holds has the NS 69+61 = 130 = 2*65 = FV 20. NS+FV equal 150 = 6*25. The single digits of the two multiplication numbers are the same, they represent the elements of a double triangle with 2 triangular areas (F), 6 lines and 5 points:

The three lines lead to 181 again:

 

 

 

 

sm

NS

8

60

62

130

FV

6

12

33

51

sm

 

 

 

181

In the SATOR Square 181 is the sum of the prime number NS:

 

T

E

R

N

A

sm

NV

19

5

17

13

1

55

frequ.

4

4

4

1

4

17

NS

76

20

68

13

4

181

TERNA is neuter in the plural meaning a Set of Three, which can be theologically applied to the three divine persons. The 5 letters have the average NS 11. Another anagram is ENTRA Enter! expressing an invitation to learn about the wisdom of the SATOR-Square. A third anagram is REANT they shall calculate, expressing a wish to recognize the numeral system behind the 25 lettes of the square.

 

Written: January 2022

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