The
Saviour's Smile in Eclogue 4
III. The last sentence
(6263)
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 434 and 424:

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:FSratios
in each word group with the common main NS+FSfactor 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:FSratio 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 434, 424 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 crosspoints 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 zigzaglines, 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 19
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 SATORSquare.
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 DRcross
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 DRframe.
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 twodigit
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 110 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 threedimensional 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 DRcross
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 19:

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 4digit 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 DRpoints 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 SATORSquare:
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 SATORSquare. 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