I am led to believe from study of the plan, and consideration of the whole numbers in this 20, 21, 29 triangle, that the R.B. cubit, like the Memphis cubit, was divided into 280 parts.
The whole numbers of radius, sine, and co-sine divided by 280, give a very pretty measure and series in R.B. cubits, viz., 43½, 30, and 31½, or 87, 60, and 63, or 174, 120 and 126;—all exceedingly useful in right-angled measurements. Notice that the right-angled triangle 174, 120, 126, in the sum of its sides amounts to 420.
Figure 33 illustrates the 20, 21, 29 triangle. Figure 34 shows the 5·2 and 7·3 triangles built up on the sine and co-sine of the 20, 21, 29 triangle.
The 5·2 triangle contains 21° 48′ 5·08″ and the 7·3 triangle 23° 11′ 54·98″.
Figure 35 shows how these two triangles are combined with the 20, 21, 29 triangle on the circumference, and Figure 36 gives a general view and identification of these six triangles which occupied an important position in the trigonometry of a people who did all their work by right angles and proportional lines.
Fig. 36. Ratios of Leading Triangles.
§ 8. GENERAL OBSERVATIONS.
It must be admitted that in the details of the building of the Pyramids of Gïzeh there are traces of other measures than R. B. cubits, but that the original cubit of the plan was 1·685 British feet I feel no doubt. It is a perfect and beautiful measure, fit for such a noble design, and, representing as it does the sixtieth part of a second of the Earth's polar circumference, it is and was a measure for all time.