gematric calculator (to be consulted for factoral values)

VERGIL ECLOGUE 4

III. The last sentence (62-63)

d) Structural Elements

This chapter continues the previous one.

QUI NON RISERE PARENTI,

NEC DEUS HUNC MENSA DEA NEC DIGNATA CUBILI EST.

Those who have not smiled at their parent,

Neither a GOD has considered him worthy of his table nor a GODDESS of her bed.

1. Each verse is a gematric unit. If a sentence begins before, the whole sentence is constructed as a wider unit. First the last line has to be examined:

	lett.	NS	FS	sm		lett.	NS	FS	sm
NEC	3	21	21	42	NEC	3	21	21	42
DEUS	4	47	26	73	DIGNATA	7	54	51	105
HUNC	4	44	31	75	CUBILI	6	54	37	91
MENSA	5	49	34	83	(E)ST	3	42	32	74
DEA	3	10	10	20
	19	171	122	293		19	171	141	312
312 = 24*13; 293+312 = 605 = 5*11² = 11*55

There are two parallel word groups, each introduced by NEC. Three things are most striking: First, the numeral sums (NS) are equal, second, the number of letters is equal too, third, 171 is the sum of numbers from 1-18.

2. There are more gematric parallelisms:

· Logically, without NEC each NS is 150.

· DEUS – MENSA and DEA – CUBILI are content parallelisms. Their NS are 96 and 64, forming the ratio 32*(3:2). The NS 96 is also obtained by DIGNATA EST or CUBILI EST.

· Twice NEC has the NS 42 like EST. (E is metrically elided.)

· DIGNATA CUBILI follow each other with the same NS 54, together 108. The two words form a NS-ratio 18*(6:13) with the other words. If HUNC is added, another ratio is 2*19*(4:5).

The 9 words are gematrically interconnected in such a way that all results are even.

3. In the previous chapter it has become evident that Vergil wanted to dedicate his poem to three persons put in the dative case: PUERO, MATRI, PARENTI. The 4values are once more presented:

	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
208 = 16*13
253:352 = 11*(23:32) = 11*55 = 5*11²

The coincidence of the 4value result 605 with the NS+FS of the last line suggests that the three persons are represented in the gematric construction. This can be shown with the NS of PUERO + PARENTI (150) and the NS+FS 108 of MATRI. 96 is the NS 57+FS 39 of PUER, 64 the NS of RISU.

312 forms with the NS 208 of the three persons the ratio 8*13*(2:3).

4. It is also possible to knit together the NS 208 of the three persons and the inverted sums 352 and 253:

NEC DEUS HUNC 21+47+44 = 112; CUBILI EST 54+42 = 96; 112:96 = 16*(7:6). 112+96 = 208.

	lett.	NS	FS	sm		lett.	NS	FS	sm
DEUS	4	47	26	73	NEC	3	21	21	42
HUNC	4	44	31	75	MENSA	5	49	34	83
DIGNATA	7	54	51	105	DEA	3	10	10	20
					NEC	3	21	21	42
					CUBILI	6	54	37	91
					(E)ST	3	42	32	74
	15	145	108	253		23	197	155	352
58*(2:3)

5. The NS+FS of the first part of the sentence are:

	lett.	NS	FS	sm
QUI	3	45	23	68
NON	3	40	35	75
RISERE	6	71	58	129
PARENTI	7	79	69	148
	19	235	185	420
l.63	38	342	263	605
	57	577	448	1025
185:235 = 5*(37:47)
1025 = 25*41

The first part of the sentence consists of 19 letters, half the letters of l. 63. 19 is also the cross sum of 577, a prime number. The three digits refer to the 7 points of the DR which represent 1+2 and 1+3 = 7 area units illustrated by the following figure:

25*41 refers to the 41 elements of a cross of double rhombi, whose hexagonal part consists of 25 elements, so 25:41 elements represent 1:3 area units of the two concentric tetractys circles:

Vergil does not always try to model a gematric construction on the elements of a geometrical figure so as to produce sensible proportions to by adequate placements. In this case he chooses the LINEAR option by an alternate count of the 13 NS+FS:

NS+FS1	68		129		42		75		20		105		74	513
NS+FS2		75		148		73		83		42		91		512
														1025

Here the principle of order consists of two consecutive and therefore constitutive numbers of their added sum. Divisibility by 25 is achieved by 3*150 NS, because RISERE PARENTI forms the third 150-unit. The ratio thus is 25*(18:23). If 23 is composed of 11+12, the FV are 11+7 = 18. 450 can be increased by the NS+FS 75 of NON so that now the NS+FS ratio is 525:500 = 25*(21:20).

The first 6 FS and 7 last FS enable the ratio 232:216 = 8*(29:27), and by trial two exact halves can be obtained:

NS+FS1	23	35				26	31			21	51	37		224
NS+FS2			58	69	21			34	10				32	224
	232						216

If the NS of the 13 words are subsequently added up, it is remarkable that the calculation reaches the word DEUS at 303, which is the NS of the SATOR Square.

	Q	N	R	P	N	D	H	M	D	N	D	C	E
NS	45	40	71	79	21	47	44	49	10	21	54	54	42
	45	85	156	235	256	303	347	396	406	427	481	535	577

6. The total FS 448 can be understood as an equation of 4+4=8 that can be found in a cross of double rhombi with 8+8 frame lines. By the extension of the hexagon to the hexagram the two radial lines of each diameter are increased by two more radial lines but in such a way that they look in opposite directions. From the top point of the tetractys the eye follows the zigzag line till the bottom point (beyond the bottom line of the tetractys), and, recognizing the form of double rombus, moves on the other zigzag line BACK to the top point.

448 has occurred in lines 4 to 10 already where the letters RE – BACK, due to the respective content, are conspicuously more frequent than in the rest of the text. 25 E and 19 R in these lines equal 125+323 = 448.

The origin of the syllable RE can be seen in the circle axis with its 5 elements:

RE is here seen from the second half of the circle. In order to fulflill the condition of a full return the first half has to be covered for a second time. So RE in fact is a kind of shortform for ERE.

Vergil seems to have this circular model in mind as the the processing of the NS+FS of the last sentence may prove:

	NS	FS	sm	FW
	577	448	1025	51
FW	577	19	596	153
sm				204
51:153 = 51*(1:3)
596 = 4*149

A more developed form of RE can be derived from a numbered tetractys:

The tetractys is here divided into three parts, and the sums provide the equivalent letters S for the three corner points, P for the central hexagonal axis and ERE for the numbers on the double triangle. Here again 2 and 3 must be covered a second time to comply with the condition a full return. ERE is the fundamental model for palindromic numbers:

· It consists of three halves of a circle, the third half is identical with the first (51:15).

· The three palindromic parts coincide with three hexagonal axes.

· The returning principle is sanctified and objectivated by the numbered model of TETRACTYS.

448 can be obtained if 5 subsequent distances leading to the completion of the return movement are defined by two-digit composite numbers and if their FV are added:

						sm
	23	38	89	92	23	265
FV	23	21	89	27	23	183
						448

However, 448 can be the result of a more important concept which I haven't found so far.

In composite form PERE twice orbits the inner SATOR Square frame:

Vergil adopts this pattern in line 62 in inverted option: QUI NON RISERE PARENTI.

448 can also be understood as an additive result of two three-digit numbers which themselves are single digits originally: The NS 235 of the first half of the sentence in line 62 may give a hint. The 10 radial elements on a DR-zigzag line can be subdivided into 2+3+5:

The three radial elements represent 2+1+3 area units, so if the two groups of successive digits are made to two three-digit numbers their addition equals 448.

7. The 38 letters of the last line prove to be characterised by palindromic numbers, which convey the idea of returns to a new start. The first two have already been determined as two equal NS 171. The next two palindromic numbers come about by the prime (number) letters:

		NEC	DEUS	HUNC	MENSA	DEA	NEC	DIGNATA	CUBILI	EST
prime lett.	NS	21	9	16	19	10	21	45	16	24	181
letters		3	2	2	3	3	3	6	3	2	27
compos.lett.	NS	–	38	28	30	–	–	9	38	18	161

Another two palindromic numbers are achieved by the letters that belong to the SATOR-Square:

		NEC	DEUS	HUNC	MENSA	DEA	NEC	DIGNATA	CUBILI	EST
SQ-letters	NS	18	23	13	37	6	18	34		42	191
letters		2	2	1	4	2	2	4	–	3	20
	FS	18	13	13	27	6	18	34		32	161
	NS+FS										352
other lett.	NS	3	24	31	12	4	3	20	54		151

The NS+FS 352 forms the the ratio of the inverted sums 352:253 = 11*(32:23) already mentioned.

8. The single digits of the two palindromic sums 181 and 191 represent 1+8+1 units of measure and 1+9+1 delimiting points, according to a circular and a linear model:

The circular model shows that units of measure have first to be delimited by points and second, only the basic numbers from 1 to 9 are countable and what is beyond belongs to the DIVINE sphere outside the categories of space and time. The circular model starts with point 0 and returns to it whereas the linear model goes on with a another point so that 21 and the 21 letters of the Latin alphabet are the perfect manifestation of the decimal system and especially based on these two palindromic models. The numbers 1-21 can be placed on a circular line for illustration:

VERGIL took the pains to model the last 4 lines on this described basis of the decimal system. He did so in the following way:

· The prime letters of line 62 amount to 191 as a parallel to palindromic 181 of line 63:

line 62		INCIPE	PARVE	PUER	QUI	NON	RISERE	PARENTI
SQ-letters	NS	21	23	22		26	44	55	191
letters		3	3	2		2	4	5	19

· The prime letters of ll. 60 and 61 are:

line 60		INCIPE	PARVE	PUER	RISU	COGNOSCERE	MATREM
SQ-letters	NS	21	23	22	17	53	42	178
letters		3	3	2	1	7	4	20

Vergil chose 178 to match the NS+FS 99+79 of COGNOSCERE.

line 61		MATRI	LONGA	DECEM	TULERUNT	FASTIDIA	MENSES
SQ-letters	NS	37	32	17	84	25	23	218
letters		3	4	4	6	4	3	24

The sum of the first two lines 178+218 is the same as the NS+FS 231+165 = 396 = 36*11 of the numbers 1-21. The prime NS of ll. 60/61 and ll. 62/63 form the ratio 396:372 = 12*(33:31) = 12*64 = 768 = 3*256 = 3*16².

The number of letters of the 4 lines is 20+24 = 44; 19+27 = 46; 44+46 = 90; 90:54 = 18*(5:3) = 144, which is the total number of letters of ll. 60-63. 144 is the NS of the OPERA-grate in the SQ:

The 54 letters left correspond to twice the NS of ERE.

9. The SQ-letters of the four lines are:

	A	E	N	R	T		O	P	S		sm
NV	1	5	13	17	19	55	14	15	18	47	102
frequ.	12	23	14	12	8	69	4	7	9	20	89
NS	12	115	182	204	152	665	56	105	162	323	988
FS						665	36	56	72	164	829
						1330				487	1817
665:323 = 19*(35:17) = 19*52 = 4*13*19; 323-164 = 159
1817 = 79*23 = FW 102

159 is the difference between the FS 164 and the NS 323 of the three composite NV, it coincides with the NS of the 9 letters of the SQ which occupy the uneven positions between 1 and 5.

52 = 4*13 is the NS of OPERA, 4 double triangles contained in a DR-cross can be used to put together an octahedron. It also sums up the elements of one double triangle + two rhombi and one fish figure:

The three figures containing 9 triangles and multiplied with 7 elements equal 63. In this way 52+63 results in 115 = 23*5, which is the sum of 23 E. 2+3+5 has been explained as 10 radial elements further above.

4*13*19 refers to the central N of the SQ and 4 T. Combined with E the word NET – He weaves can be read 4 times from the centre. The number of 89 letters can be derived from the 5 central letters: 4*19+13 = 89.

The NS of the 4 lines is 1539 = 81*19. So the ratio of the NS of 89 to 55 letters is 19*(52:29) = FV 36+48 = 84. 19 may be so important in the last 4 lines because of PUER with the NS 57 = 3*19.

14 N have the NS 182 of SATOR OPERA TENET, which is one half of the SQ.

The total NS+FS 1817 can be understood as 18+17 and the letters SR, initials of SATOR ROTAS. 23 is one main factor of the NS+FS 552 = 24*23 of the SQ. 102 is the NS of PENSATOR, composed of the 8 different letters of the SQ .

Written: January 2022

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