PARCERE
SUBIECTIS ET DEBELLARE SUPERBOS
1. Vergil, in Aeneis 6,853 pronounces
MEMENTO
ROMANE … 
Remember,
Roman … 
PARCERE
SUBIECTIS
ET DEBELLARE SUPERBOS 
to spare the defeated and battle down
the proud. 
It is understood that
Vergil, before writing down a verse, converted all letters into number values (NV). The numerical constructions are related to the implications
of the decimal system with the hexagram as its central model. The numbers
themselves constitute a texture of higly condensed meaning. All sensibility for
artistic form derives from this knowledge of numeric relations. So this
investigation starts with aspects of structural form before the NV are established.
1. Verse 853 consists of two symmetrical parts of INFINITIVE + OBJECT, connected by ET. This parallel structure is
emphasised by shared letters, most strikingly by alliterating SU in SUBIECTIS SUPERBOS. The two pairs of words have 7 letters in common which are,
starting from the first word: PARE SUB expressing the meaning of the whole line: Obey under (Roman rule). Each phrase contains 3 exclusive letters: CIT and DLO. These 7+6 letters can be arranged on 7 hexagonal and 6 extension points of the hexagram:

Besides the NV
the factoral values (FV)
have to be considered. The NV and FV of the 13
letters are:

P 
A 
R 
E 
sm 
S 
U 
B 
sm 
tot. 
NV 
15 
1 
17 
5 
38 
18 
20 
2 
40 
78 
FV 
8 
1 
17 
5 
31 
8 
9 
2 
19 
50 
sm 




69 



59 
128 

C 
I 
T 
sm 
D 
L 
O 
sm 
tot. 
NV 
3 
9 
19 
31 
4 
11 
14 
29 
60 
FV 
3 
6 
19 
28 
4 
11 
9 
24 
52 
sm 



59 



53 
112 
The results yield
several ratios: 78:60 = 6*(13:10); 128:112 = 16*(8:7) = 240; 102:138 = 6*(17:23).
If the shared NV 78 is doubled the result of 20 letters is 156+60 =
216 = 6³. 6³ refers to the threedimensional figure of
octahedron with its 6 edges:

The octahedron can be
jointed together by folding a cross of double rhombi
of which there are three in the hexagram.
2. It's time now for the numeral sums
(NS) and factoral sums (FS) of the whole verse:

NS 
FS 
sm 

NS 
FS 
sm 

NS 
FS 
sm 
tot 
tot 
TOT 
PARCERE 
63 
56 
119 
ET 
24 
24 
48 
DEBELLARE 
61 
61 
122 



SUBIECTIS 
103 
66 
169 




SUPERBOS 
109 
66 
175 



sm 
166 
122 
288 

24 
24 


170 
127 
297 
360 
273 
633 
273 = 21*13; 633 = 3*211 = FV 214 = 2*107 
a(2) e(8) i(2) o(1) u(2) 
V 15 
114 
b(3) c(2) d(1) l(2) p(2) r(4) s(4) t(2) 
K 20 
246 
114:246
= 6*(19:41) 
The NS 360
suggests the degrees of a full circle and correspondingly the ORBIS TERRARUM,
·
The
single digits of 13 refer to the ratio 1:3 of the hexagonal circle field to the
hexagram circle, 21 to the ratio of 2 area units of the extended ring of the outer circle to 1 area unit of the hexagonal
circle:

The inverted ratio (2+1):1, written as 211
is the main prime factor of the NS+FS 633.
·
The
double rhombus consists of 21 elements, 13 of which belong to the hexagonal area. So 13:21 is equivalent to the area ratio 1:3 and 21:13
to 3:1.

·
273 can be read
as 2*(7+3), referring to 2 tetractys, each consisting of 7 hexagonal points + 3
corner points.
3. The two parallel phrases are
related to each other by the NS+FS 188:297 = 9*(32:33)
= 9*65 = 45*13 =
FV 24. There is a
cross of axes consisting of 33+32
elements.
There is also a chiastic NS+FS
relation PARCERE
SUPERBOS to SUBIECTIS DEBELLARE of 294:291 = 3*(98:97).
The NS
relation of PARCERE DEBELLARE to SUBIECTIS SUPERBOS is 124:212
= 4*(31:53).
The single digits denote the area ratio 3:1
represented by 5:3
radial elements:

The radial elements occur twice on
the zigzag diameter of the double rhombus. The verse number 853 can mean just that.
4. After establishing the NS+FS of verse 853, another three ratios can be observed:
·
While
the ratio of the 20 letters – shared and
nonshared – to the 15 remaining letters is 5*(4:3)
the corresponding NS ratio is 216:144 = 72*(3:2). The two ratios refer to 4+3 elements of a
tetractys side and 3+2
elements of a hexagon axis:

72 has to be
related as 24 hexagonal elements to (24+24) hexagonal elements + extension elements,
representing the area ratio 1:3 of the
two concentric circles.
The same principle of 1:3 area units applies to the 7+7 shared letters and the 3+3 = 6 separate letters in considering them as 7:(7+6).
·
The
double rhombus consists of 15 frame
elements (7 points, 8 lines). The NS 24
of ET is the 15^{th}
part of 360 and so can logically be seen as
centre of the double rhombus.
·
The
FS of the 13
single letters to the 22 remaining letters
is 112:161 = 7*(16:23). The single digits of
13 and 22
can be interpreted as 1
area unit corresponding to 3 radial elements
of the hexagon and 2 area
units of the extension ring with 2 radial
elements:

5. It can be observed that the
corresponding words PARCERE DEBELLARE
and SUBIECTIS SUPERBOS have several letters in common.
Above, all different letters that occurred in each of the two syntactical pairs of words were counted only once, now in a
changed arrangement all same letters in each parallel word are counted; the letter P is eliminated:

A 
R 
E 
E 
sm 
S 
U 
B 
E 
S 
sm 
tot. 
NV 
1 
17 
5 
5 
28 
18 
20 
2 
5 
18 
63 
91 
FV 
1 
17 
5 
5 
28 
8 
9 
2 
5 
8 
32 
60 
sm 




56 





95 
151 
The NS 28 and 63 can be
related to 13 numerated
points of the hexagram: 17 hexagonal points
add up to 28, 813
extension points to 63:

The two sums represent
the area ratio 1:2. The NS 91 has to be doubled to 182
which is the NS of one half of the
SATOR 
OPERA 
TENET 
TENET 
OPERA 
ROTAS 
69 
52 
61 
61 
52 
69 
182 
182 
The NS+FS and prime number 151 refers
to the structure of the 7 points of the
double rhombus:

Twice 151 is referable to a cross of double rhombi to
form an octahedron as has been mentioned already.
Gematric constructions
quite frequently contain hidden religious messages. Here AERE SUBES
literally means You are hidden in the air. AERE may stand for the sky,
for the cosmos or for the invisible.
The hexagram with its
two concentric circles gives geometrical evidence of the one GOD in three persons. Trinitarian notions were developed
by the Romans in the secret cult of VESTA
some centuries before Christ.
6. The

both parts 
left 
right 


P 
A 
R 
S 

E 
T 

E 
O 

NV 
15 
1 
17 
18 
51 
5 
19 
24 
5 
14 
19 
frq 
1 
1 
2 
2 
6 
3 
1 
4 
4 
1 
5 
NS 
15 
1 
34 
36 
86 
15 
19 
34 
20 
14 
34 
FS 
8 
1 
34 
16 
59 
15 
19 
34 
20 
9 
29 
120+93
= 213; 120+88 = 208; 240+181 = 421 
These 7 SSQ
letters provide the NS 86+34 = 120 for both the left and right halves of the verse,
aptly rendering Latin PARS – part. In constructing two equal NS, Vergil models on the word PENSATOR – s.o. weighing, balancing, dispensing justice that
can be formed from the 8 different SSQ letters. The NS of each half is 51, and their
letters correlate in pairs to produce twice 51:
P 
E 
N 
S 
A 
T 
O 
R 
15 
5 
13 
18 
1 
19 
14 
17 
The model Vergil uses
is a double rhombus with its 8 frame lines which
can be marked by numbers or letters in a looping way:

Vergil devised the
elaborate palindromes 86+68+86 to obtain 240. Several meanings should be considered:
·
The
final aim of the hexagram is the construction of the octahedron. The 7 points of the double rhombus are reduced to 6 as the outer two points are joined, so the frame
of the double rhombus consists of 6+8 elements
now instead of 7+8.
86 is the FS
of the numbers 114.
·
An
octahedron consists of 6 corners and 8 areas.
·
From
the two outer points a rhombus is extended to form a fishshaped geometrical
figure consisting of 17 elements:

This figure is of
trinitarian significance because of its three triangular areas. In a cross of
double rhombi there are four fishfigures amounting to 68
elements.
·
86 is the NS of the word NOSTER
– our. The Latin word can be read as NOS TER – we thrice
denoting three divine persons.
Each half has 6 remaining letters:

C 
I 
B 
U 
sm 
D 
L 
B 
U 
sm 
tot 
NV 
3 
9 
2 
20 
34 
4 
11 
2 
20 
37 
71 
frq 
2 
2 
1 
1 
6 
1 
2 
2 
1 
6 
12 
NS 
6 
18 
2 
20 
46 
4 
22 
4 
20 
50 
96 
FS 
6 
12 
2 
9 
29 
4 
22 
4 
9 
39 
68 

42 
33 
75 
52 
37 
89 
164 
Two letters and BU occur twice
in each half, suggesting the elements of twice two rhombi. 164
= 4*41 refers to two double rhombi in each of which three geometrical
figures can be counted twice, from above and
from below:

7. As 24 is 15
times in 360, the three times NS 120 can be arranged on the 15 elements of the double rhombus:

Finally the (10+2+11)
+ (6+6) letters can be placed on the elements of a cross of double
rhombi (DR):

The vertical DR contains the 23
SSQ letters according to their order in the verse, starting from the bottom in
the looping way along the elements of the DRframe.
After 17 letters follow the remaining 6 letters from bottom to top on the inner
elements. The horizontal DR contains the 12 nonSSQ letters, again in looping
from, moving from left to right, again in verse order.
There are three
remarkable results:
·
The
joint values of the lower and left rhombi and the corresponding upper and right
rombi produce the constituent numbers 179+181
of their sum 360. The NS+FS 312+321 are
reversal numbers, 133:140 is 7*(19:20).
·
The
NS ratio of the lower to the upper rhombus is 121:143 = 11*(11:13) = 264.
This ratio corresponds to the FS 121 and NS 143 of PATER NOSTER – Our
Father which can be formed from each half of the SSQ. The FS 273 of the verse is the NS of two PATERNOSTER in an axis system with one N as centre letter. Without ET the NS – and
with them the FV – of three of the four
words are prime numbers, totalling 273,
which is given a second N
by the FV 13:

NS 
FV 
sm 
SUBIECTIS 
103 
103 
206 
DEBELLARE 
61 
61 
122 
SUPERBOS 
109 
109 
218 

273 
273 
546 
PARCERE 
63 
13 
76 

336 
286 
622 
622
= 2*311 >
313 
The axis systems of the SSQ are
recognizable in the FV of the NS of the two pairs or words without ET: DEBELLARE
consists only of prime numbers like TENET with
the same NS 61:

Without one centre N the NS of the
cross is 109, with two 109+13
= 122, together 231 = 21*11, the NS of 121.
The NV 313 refers to the 7
pointstructure of the double rhombus.
·
The
joint NS+FS
of the left rhombus and the lower inner
letters and correspondingly of the other two rhombi are equal:

left 
inn. 
sm 
right 
inn. 
sm 
tot 
NS 
58 
38 
96 
38 
49 
87 
183 
FS 
36 
21 
57 
32 
34 
66 
123 

94 
59 
153 
70 
83 
153 
306 
123:183 = 3*(41:61) 
The most probable reference is the
sum of the unnumbered elements of the cross of
double rhombi and two numbered versions :

303 is the NS
of the SSQ, with three centre points of the horizontal DR
the total is 306. So the average NV+FV for twice 9
letters is 17.
8. The originally 21 letters of the Latin alphabet
contain 11 composite numbers with a
difference between NV and FV:
Lt. 
F 
H 
I 
K 
M 
O 
P 
Q 
S 
V 
X 

NV 
6 
8 
9 
10 
12 
14 
15 
16 
18 
20 
21 
149 
FV 
5 
6 
6 
7 
7 
9 
8 
8 
8 
9 
10 
83 
A 
B 
C 
D 
E 
G 
L 
N 
R 
T 

1 
2 
3 
4 
5 
7 
11 
13 
17 
19 
82 
1 
2 
3 
4 
5 
7 
11 
13 
17 
19 
82 
The difference between the FS 83 and NS 149
is 66. If 4 is shifted to the composite numbers, the two FS are reversal numbers 78:87.
The difference between the FS 273 to the NS 360 is 87:

P 
I 
U 
S 
sm 
S 
U 
P 
O 
sm 
tot 
NV 
15 
9 
20 
18 
62 
18 
20 
15 
14 
67 
129 
frq 
1 
2 
1 
2 
6 
2 
1 
1 
1 
5 
11 
NS 
15 
18 
20 
36 
89 
36 
20 
15 
14 
85 
174 
FS 
8 
12 
9 
16 
45 
16 
9 
8 
9 
42 
87 

The reverse reading of
SUPO is OPUS
– work which is neuter so that the masculine
PIUS can refer to the addressed Roman
(Romane memento) who generously spares the defeated enemy, but is always
resolved to face an enemy with fierceness.
The FS:NS ratio is 87*(1:2), or – if the FV is regarded as part of the NV – the ratio is 1:1. The geometrical reference point is the two
concentric circles of the hexagram. Without the centre point the number of smmetrical
hexagonal and extension elements are equal,
but the corresponding areas are 1:2. Behind
these two ratios there is much speculation about the divine persons: The second
divine person is the image of the first, but the terms second
and two include a third
person. In the hexagon there are two constellations of geometrical figures
which throw light to this reality:

The left grafic shows
equal figures, the right two rhombic figures united by the middle figure. So
the 11 composite numbers presumably refer to
the second person and (13+11) numbers the
other two persons. The number 35 is connected
to 29 by the letters VI
with the NV 20+9
and the number signs 5+1.
The 24 letters based on prime numbers have the NS+FS 633261 = 372 =
12*31 = 2*186. The single digits of the product numbers
represent the two area ratios of the hexagram circles 1:2 and 3:1.
9. 29 is especially made up by the
letters OP (cf. OPERA in the SSQ) and their gematric equivalents 14+15, whose FV are 9+8 = 17. The two numbers bear important
trinitarian relevance: The frame of the DRcross consists of 29 elements, of which 17 belong to the hexagonal field:

The ratio 17:29 represents 1:3 area units of the two concentric
circles. As there are three DR in the
hexagram, three DRcrosses are required if
each DR is combined with each. This is the
meaning of 87 = 3*29.
The NS
of OPUS is 67
which is inverted by I = NV 9 to 76. The NS of the
five letters can be divided up into 2*38:

P 
I 
O 
sm 
S 
U 
sm 
tot 
NV 
15 
9 
14 
38 
18 
20 
38 
76 
FV 
8 
6 
9 
23 
8 
9 
17 
40 
116 = 4*29 
116 
Again 29 is the main factor of the NS+FS 116.
21 letters of twice PATERNOSTER in the SSQ
can be placed in a DRcross and the
remaining A and O
on the crosslines:

The NS of the three letters TAS and EOT is 38 each. 38 is obtained by 18
frame elements (9 points + 9 lines) of two tetractys and two centre points:

The crosslines and the limiting
points form the middle basis for two pyramids of the hexahedron. The three
parts of the hexadron are:

Remarkably the NS+FS of the
middle basis of Vergil's verse is 115+71 = 186, the
same as the NS or the FS
of the 24 prime numbers.
written: April
2019