The Saviour's Smile: RISU in Eclogue 4 and the Names MARIA IESUS
The following study developed from a project on Shakespeare's Epitaph, in which, as I am convinced, the names of IESUS and MARIA play a
significant gematric role.
I. Aspects of the Decimal System in the names of MARIA and IESUS
II. Vergil's Eclogue
4, 6063: Gematric aspects
III. The last
sentence (6263)
Introduction into Eclogue 4, 60
1. The
numerical values (NV) of MARIA and IESUS are 40+70 = 110 = 2*55.
The sum of the numbers 110 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 110.
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 total relation of 4 inner to 6 outer letters (lts), whose numerical sum +
factoral sum (FS) are:

4 lts 
6 lts 

NS 
64 
46 
110 
FS 
40 
28 
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*(
These are the values of
the two tetraktyses:

Tetr. M 
Tetr. I 


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 RISUS – laughter,
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 AMAS
– You 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 selfmanifestation 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.
The noun form RISU
perfectly demonstrates the relationship between the two circle areas by the internal ratio (inr) and external ratio (exr) of its FS:NS:

FS 
diff. 
NS 


RISU 
40 
24 
64 
inr 
8*(5:3) 




exr 
8*(5:8) 
The two area sizes are
represented by the number of radial elements:

If the digits of the
two rations 5:3 and 5:8 are added up, a new ratio arises,

1.
In his famous 4^{th} 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 4^{th} eclogue consists of
lines 6063. 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 
nec deus hunc mensa, dea nec dignata cubilI (E)ST. 
342 
263 
605 

1539 
1176 
2715 
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.
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 19. 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
The total
result of NS+FS 2715 exactly reflects the last word of the poem (E)ST: Vergil extended the components 27+10 by another 5. Another meaning of 2715 is to be found further down.
5.
Having a look at the 9 words around RISU, we find that the
repetition of PARVE PUER and the references to his mother MATREM MATRI PARENTI consist of equally 18 letters, while RISU RISERE, serving as linking bond between Son and Mother, amounts
to 10 letters. So we should find out the values of these 10 letters first:

RISU 
RISERE 

NS 
64 
71 
135 
FS 
40 
58 
98 

104 
129 
233 
The number 135 especially refers to the 9 triangular areas of
the tetraktys, defined by 10 points:

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.
6.
The total results of the three groups (PRM) are:
P 
230 
158 
388 
M 
203 
175 
378 
R 
135 
98 
233 
621+378 = 999 


365 
256 
621 
621:378=27*( 
378 is the sum of the successive numbers 127.
The boy's mother is of mature perfection, which implies her smiling at him
first. It's only by his smiling back that her son lives up to the expectation
of his own perfection, represented by the added up result 388+233 = 621. There is a correspondence between the two ratio numbers 23 and 14, not only because
their digits have the sum 5, but because 23 is the sum of the NV 14 + its FV 9. The son embodies his mother's
nature and is further completed and enhanced by the nucleus of the factoral
value. It shows the selfless attitude of the mother, who serves her greater son
to fulfil his divine mission on earth.
7.
The number 27 has several meanings.
First, as the cube of 3 it has trinitarian relevance.
With regard to the two concentric circles of the tetraktys star, 13 points represent 3
area units, and 7+7 points 1+3 = 4 area units of the inner and outer
circle (each circle with a central point). Then it can refer to the 3*9 diametrical elements
of the doublerhombus, and finally to 9+9 lines and 9 triangles of the
tetraktys.
If the 10 points and 9 triangles of the
tetraktys form one unit and the 18 lines the second unit of 37 elements, the FV of 19+18 are 19+8 = 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, however, 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 6063.
8.
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

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*( 

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 doublerhombus:


9.
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. 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 perfect number 378 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 (621135):(378+135) = 486:513 = 27*(
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.
10.
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 as a 3digit 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*(

The
digits 243 refer to the the middle part of a doublerhombus: 2 crosslines, 4 triangles, 3 points. These 9 elements also apply to
the two diametrical zigzag lines so that the NS+FS result 999 shows 27 elements if the three parts are counted separately,
whereas as a united figure the doublerhombus consists of 21 elements.
Two groups of words provide divisibility by 37 and the result 333: First, the FS of the 7 motherson words (s.
table above), second the NS+FS of the words PUER (96) MATRI (108) RISERE (129), all divisible by 3. The ratio to the rest
of values is 1:2.
11.
The 9 words give some clues
to further gematrical constructions: First, the 4 words referring to the
Son (2x parve puer) and 3 to the Mother (matrem, matri,
parenti)
consist of equally 18 letters. The 10 letters of RISU RISERE add 5 letters to both sides. In fact, the NS+FS of each half of 23 letters is divisible
by 27 with the ratio

PARVE 
PUER 
RISU 
MATREM 
MATR 
sm 
I 
PARVE 
PUER 
RISERE 
PARENTI 
sm 
NS 
58 
57 
64 
66 
49 
294 
9 
58 
57 
71 
79 
274 
FS 
40 
39 
40 
56 
44 
219 
6 
40 
39 
58 
69 
212 

98 
96 
104 
122 
93 
513 
15 
98 
96 
129 
148 
486 
513:486
= 27*( 
Second, the numbers 5 and 18 are to be found in the numbered tetraktys, with 5 placed in the centre
and 1+7+10 = 18 in the corners. The 1+3 numbers (standing also
for 1:3 area units) were given a trinitarian meaning in the Roman system: The
letter equivalents are ES – You are. The 4+6 letter words RISU RISERE are chosen for this
purpose:

RISERE occupies the 6 hexagonal arc points.
The NS
of lines 6063 are 1539 = 81*19 >FV 31 and the FS 1176 = 24*49 >FV 23. The two FV 23+31 = 54 can be seen in
connection with the numbered tetraktys and the specific grouping of 4+6 numbers. The sum 54 as 2*27 relates to the tetraktys star
with its two concentric circles. On the assumption of each circle having its
own central point, both the hexagon and its extension part consist of 1+24 elements. The 2 other elements are the
circle
arc and
the circle area.
Third, if the frame of the doublerhombus is numbered
looplike, number 17 comes next to 1. The unoccupied middle part
consists of 6 elements so that there is room for 23 numbers or letters.
Twice 23 letters then call for a cross of doublerhombi:

The NS+FS of the left and upper
rhombi amount to 500, the bottom and right rhombi to 499. The two numbers are
constitutive of 999. Their FVs are 19+499 = 518.
12.
The four central letters of the figure read –
anticlockwise from left – VESV. If the last letter V
is replaced by TA, the word is VESTA, the goddess and code name of the
Roman gematric system.
The FV of double V (20) is 9 = I, the FV of ES (5+18) is 13 = N. In this way we get 3
13.
The ratio 3:1 has a natural basis in
3 elements of the middle
part of a rhombus + 1 central point. The four rhombi of the cross provide 12+4 elements. The NS of the 12 letters are divisible
by 13 and enable a ratio if two pairs of rhombi are joined, as the above
figure shows: 52:78 = 13*(4:6). The FS is 117 = 13*9, which gives a FS:NS ratio of 13*(
The
product of two NS (top and right rhombi) 37*41 is 1517, which comes about if
the FS 518 (from 500 and 499) is added to 999. The equivalent
letters for 1517 are PR, which can be aptly associated with the initials
of PUER and RISU.
If the NS of the 4 central
letters 63 and 247 are added, the result 310 is divisible by the inverted number 31. The FS of the central letters
is 31 itself, which gives a total result of 31*(1+10) =
341.
QUI non risere parenti: 
235 
185 
420 
nec deus HUNC mensa, dea nec dignata cubili
(E)ST. 
342 
263 
605 

577 
448 
1025 
1. The last
two lines show a grammatical anomaly that has caused much controversy in the
history of classical philology: The plural of the relative pronoun QUI is followed by
singular HUNC. The shift from plural to singular was considered so unusual that
later copyists changed QUI … PARENTI into CUI … PARENTES. Fortunately the two
lines are correctly quoted and commented by Quintilian 9,3,8.
What has
become clear so far is that the poet has no doubt that the little boy will
smile at his mother. So he expresses in negative terms what he means
positively: All children who show affection for her mothers will be rewarded in
some way. But the one little boy who is praised in the poem will rise far above
all the others, attaining divine honours for his merits.
The
motive why Vergil calls upon the boy to smile at his mother is not because he
is in any doubt about the boy, but because he loves and admires his mother. He
wants the boy to share his enthusiasm and to participate himself in the
relationship between mother and son.
2.
The imagery of the last line, as may be supposed by
now, serves special gematric concepts. Most striking is the parallelism DEUS
MENSA – DEA
CUBILI.
Both word pairs consist of 9 letters (4+5, 3+6), half the number of the
SonMother letters. The NS show a clear gematric relationship:

NS 
FS 
sm 

NS 
FS 
sm 
DEUS 
47 
26 
73 
DEA 
10 
10 
20 
MENSA 
49 
34 
83 
CUBILI 
54 
37 
91 

96 
60 
156 

64 
47 
111 
96:64 = 32*(3:2); 160+107=267=3*89 
The product 32*5 deserves some
attention. The natural constituents of 32 are 15+17 with the letter
equivalents of P+R and initials of PUER and RISU. The letter equivalent of 5 is E. The letter group PER, however, is the
repetitive component of the inner frame of the SATORSquare with the NS 37,
which is the main factor of 999:

The NS+FS of the initials of PARVE PUER (2x) and RISU RISERE
is also 160.

4P 
2R 
sm 
NV 
60 
34 
94 
FV 
32 
34 
66 
sm 
92 
68 
160 
The
prefix RE means back, which in the present context refers to the boy's smiling
back at his mother. The letters ERE in RISERE coincide with the same
sequence of letters in the inner frame of the SATOR Square, representing
action (ER) and reaction (RE) of the mother's and son's smile.
In fact, it is a perpetual repetition of mutual affection that is symbolised by
the act of smiling. The NS of the 3 letters is 27,
contained as a factor in 999.
The next
point of interest should be the frequency of these three letters in the 9 words. There are 5 P, 8 E, and 10 R, 23 letters in all and
relatable to the 4 numbered tetraktys points whose some is 23: 5 for the centre, 8 as 1+7 and 10 for the corners. The NS+FS is the palindromical
number 535.
Of
course, we mustn't forget the 3 M of the mother. The NS+FS is 3*(12+7) = 57. The new sum 592 is divisible by 37
and provides the ratio of 26:20 letters = NS+FS 37*(
1.
We obtain the main syntactical structure of the
relative clause and the main clause if we connect QUI (3) and HUNC (4) with their finite
verb forms RISERE (6) and DIGNATA EST (10). The numbers of letters of each
pair correspond to each other according to the following equations: 1+2+3 = 6; 1+2+3+4 = 10.
The NS+FS of the pronominal
words are:

NS 
FS 
sm 
QUI 
45 
23 
68 
HUNC 
44 
31 
75 

89 
54 
143 
143=11*13 
The adjacing values 45+44 harmonise perfectly.
The model for 89 is a measure of 8 units

The FS 23+31
= 54 are
identical with the FV of the FS and NS of the total values 1176 and 1539, as explained above (with following figure).
The values of the verb
forms are:

NS 
FS 
sm 
RISERE 
71 
58 
129 
DIGNATA 
54 
51 
105 
EST 
42 
32 
74 
sm 
167 
141 
308 
308=11*28 
Both the NS+FS of the pronominal words
and verb forms are divisible by 11. The total result is 11*41.
The NS+FS of the whole sentence
is 1025 = 25*41. So the difference between the
two results is 14*41. The corresponding numbers of letters are 23+34 = 57, which is referable to
the 2+3 and 3+4 elements of a hexagon diameter and a tetraktys side. If they are
numbered, the diameter has the result 11 and the tetraktys side (according
to the right counting mode) 11 (

Finally,
the relative clause consists of 19, the main clause of 38 letters, forming the
ratio 1:2.
In
conclusion, the gematric evidence clearly excludes the text variant CUI RISERE
PARENTES
as Vergil's original version. Still, the internet offers four times more the
wrong
2.
If the poet proposes to the boy the privilege of
sharing the table with a god and the bed with a goddess as reward for smiling
at his mother, he is expected to give proof of such a blissful prospect by
performing a perfect gematric construction.
The precondition for
the boy's extraordinary reward is his smiling back at his mother. So the words RISU and RISERE should be assigned to
the twice 9 letters in the last line:
13 
NS 
FS 
sm 
15 
NS 
FS 
sm 
RISU 
64 
40 
104 
RISERE 
71 
58 
129 
DEUS MENSA 
96 
60 
156 
DEA CUBILI 
64 
47 
111 

160 
100 
260 

135 
105 
240 
260+240 = 500 = 20*( 

160:100 =20*(8:5); 135:105 =15*(9:7) 
The three
products gained by ratios are 20*25; 20*13, 15*16.
All
single values are divisible by 5. The model aimed at is especially the hexagon.
The ratio of letters of
the two word groups is

A NS/FS balance calculation
produces as a result the 37 elements of the tetraktys from the two constituent
numbers 19+18:


FV 
sm 
NS 
295 
64 

FS 
205 
46 


500 
110 

FV 
19 
18 
37 
3.
The NV of the NS+FS 500
(5*10*10)
is composed of 5+7+7 and so agrees in meaning with the NS 577 of the last sentence. The
three digits represent 1+3+3 area units (F) of the two
concentric circles of the tetraktys star, as is shown in the following figure:

The three
digits can be understood as 5+7 = 12 with FV 7. In this sense 500 and 577 refer to the letter M and the boy's mother (MATREM, MATRI).
The above
doublerhombus shows a
4.
There may be different reasons why Vergil chose
exactly 9896 hexameters for his epos AENEIS. But as the NS+FS of PARVE
PUER is 98 and 96, we may confidently
believe that he dedicated his great epic work to the longedfor saviour of the
world.
Written: March 2009
Last entry: December 2012