PARCERE SUBIECTIS ET DEBELLARE SUPERBOS

1.      Vergil, in Aeneis 6,853 pronounces Rome's political programme, starting with verse 851:

 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 = . 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, Rome's claim to ruling the whole world. The FS 273 has three meanings:

·     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 non-shared – 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 15th 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: 1-7 hexagonal points add up to 28, 8-13 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 SQUARE:

 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 SATOR SQUARE was held to be such an important religious monument that references are made to it in almost every gematric construction. It also applies to this line of Vergil's. It contains 7 of the 8 different letters of the SSQ, only N is missing. The following table shows the NS of the two parts of the line (without ET) according to frequency (frq) of the 7 letters:

 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 PARSpart. In constructing two equal NS, Vergil models on the word PENSATORs.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 1-14.

·     An octahedron consists of 6 corners and 8 areas.

·     From the two outer points a rhombus is extended to form a fish-shaped 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 fish-figures amounting to 68 elements.

·      86 is the NS of the word NOSTERour. The Latin word can be read as NOS TERwe 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 DR-frame. After 17 letters follow the remaining 6 letters from bottom to top on the inner elements. The horizontal DR contains the 12 non-SSQ 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 NOSTEROur 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 1-21.

The NV 313 refers to the 7 point-structure 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 OPUSwork 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 633-261 = 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 DR-cross 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 DR-crosses 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 DR-cross 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