The Solution of the Pyramid Problem; or, Pyramid Discoveries / With a New Theory as to their Ancient Use - Robert Ballard

ANGLE OF PRIMARY			PRIMARY			SATELLITE.		ANGLE OF SATELLITE
DEG.	MIN.	SEC.	RAD.	CO.-S.	SINE.	SATELLITE.		DEG.	MIN.	SEC.
2	47	39·70	841	840	41	41	1	1	23	49·85
6	43	58·62	145	144	17	17	1	3	21	59·31
8	47	50·69	85	84	13	13	1	4	23	55·34
10	23	19·89	61	60	11	11	1	5	11	39·94
12	40	49·37	41	40	9	9	1	6	20	24·68
14	14	59·10	65	63	16	8	1	7	7	29·55
16	15	36·73	25	24	7	7	1	8	7	48·36
18	55	28·71	37	35	12	6	1	9	27	44·35
22	37	11·51	13	12	5	5	1	11	18	35·75
25	3	27·27	85	77	36	9	2	12	31	43·63
25	59	21·22	89	80	39	13	3	12	59	40·61
28	4	20·94	17	15	8	4	1	14	2	10·47
30	30	36·49	65	56	33	11	3	15	15	18·24
31	53	26·85	53	45	28	7	2	15	56	43·42
36	52	11·65	5	4	3	3	1	18	26	5·82
41	6	43·52	73	55	48	8	3	20	33	21·76
42	4	30·08	97	72	65	13	5	21	2	15·04
43	36	10·15	29	21	20	5	2	21	48	5·07
46	23	49·85	29	20	21	7	3	23	11	54·92
47	55	29·92	97	65	72	9	4	23	57	44·96
48	53	16·48	73	48	55	11	5	24	26	38·24
53	7	48·35	5	3	4	2	1	26	33	54·17
58	6	33·15	53	28	45	9	5	29	3	16·57
59	29	23·51	65	33	56	7	4	29	44	41·75
61	55	39·06	17	8	15	5	3	30	57	49·53
64	0	38·78	89	39	80	8	5	32	0	19·39
64	56	32·73	85	36	77	11	7	32	28	16·36
67	22	48·49	13	5	12	3	2	33	41	24·24
71	4	31·29	37	12	35	7	5	35	32	15·64
73	44	23·27	25	7	24	4	3	36	52	11·63
75	45	0·90	65	16	63	9	7	37	52	30·45
77	19	10·63	41	9	40	5	4	38	39	35·31
79	36	40·11	61	11	60	6	5	39	48	20·05
81	12	9·31	85	13	84	7	6	40	36	4·65
83	16	1·38	145	17	144	9	8	41	38	0·69
87	12	20·30	841	41	840	21	20	43	36	10·15

Reference to the plan ratio table at the commencement, and to the tables here introduced, will shew that most of the primary triangles mentioned are indicated on the plan ratio table principally by the lines corresponding to the ratios of the satellites. Thus—

PRIMARY TRIANGLE	INDICATED BY
17, 144, 145.	Triangle FP, PA, AF on plan.
13, 84, 85.	Plan ratio of SJ to SU, 7 to 6.
11, 60, 61.	Plan ratio BC to FB, 6 to 5, and DN to NR, 61 to 60.
12, 35, 37.	Plan ratio EO to AY, 37 to 12, and EA to AY, 35 to 12.
5, 12, 13.	Plan ratio CY to BC, 3 to 2; JE to EX, 3 to 2; CA to YA, 5 to 1; and NZ to ZA, 12 to 5.
8, 15, 17.	Plan ratio FB to BY, 5 to 3, and AC to BC, 15 to 8.
33, 56, 55.	Plan ratio YX to AY, 7 to 4; AB to BO, 7 to 4; and EA to AZ, 7 to 4.
28, 45, 53.	Exists on plan, AB, BJ, JA.
3, 4, 5.	Pervades the plan, and is also indicated by plan ratio GX to DG, 2 to 1; SU to SV, 2 to 1; and CY to YZ, 3 to 1.
48, 55, 73.	Exists on plan, FW, WV, VF—and is also indicated by plan ratio FO to OZ, 8 to 3.
65, 72, 97.	Plan ratio AC to CH, 9 to 4; MY to YZ, 9 to 4.
20, 21, 29.	Exists on plan FB, BA, AF; and plan ratio, GU to DG, 5 to 2.

It seems probable that could I add to my pyramid plan the lines and triangles that the missing eleven pyramids would supply, it would comprise a complete table on which would appear indications of all the ratios and triangles made use of in right-angled trigonometry, a "ratiometer" in fact.

I firmly believe that so far as I have gone it is correct—and it is possible, therefore, with the start that I have made, for others to continue the work, and add the eleven pyramids to the plan in their correct geometrical position. By continuing the system of evolution by which I defined the position of Cephren, and the little pyramid to the south-east of Cheops, after I had obtained Cheops and Mycerinus, may be rebuilt, at one and the same time, a skeleton of the trigonometrical tables of a forgotten civilization, and the plan of those pyramids which are its only link with the present age.

§ 13. THE SIZE AND SHAPE OF THE PYRAMIDS INDICATED BY THE PLAN.

I pursued my investigations into the slopes and altitudes of the pyramids without reference to the plan, after once deciding their exact bases.

Now it will be interesting to note some of the ways in which the plan hints at the shape and size of these pyramids, and corroborates my work.

The dimensions of Cheops are indicated on the plan by the lines EA to YA, measuring 840 and 288 R.B. cubits respectively, being the half periphery of its horizontal section at the level of Cephren's base, and its own altitude from its own base. (See Fig. 5.)

The line EA, in fact, represents in R.B. cubits the half periphery of the bases of either Cheops or Cephren measured at the level which I have set forth as the plan level, viz., base of Cephren.