The
Saviour's Smile in Eclogue 4
III. The last sentence
(62-63)
c) The Underlying PRINCIPLES
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*21² |
|||||||||||
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*21². Two halves
can be achieved if the NS+FS of three PUER and of PATRIIS
are added: 288+153 = 441 = 21².
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*11² |
|||||||
208+181 = 389; 167+49 = 216 = 6³ |
|||||||
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 6³
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 6³ 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