R. B. CUBITS. {Base 420 Base angle 51° 49′ 37-42/471″ {Altitude 267·1239849 &c. {Apothem 339·7875153 &c. But the builder practically carries out _both_ plans when he builds to my templates of 34 to 21 with-- R. B. CUBITS. {Base 420 Base angle 51° 51′ 20″ {Altitude 267·394839 &c. {Apothem 340 and neither king nor architect could detect error in the work. The reader will remember that I have previously advanced that the level of Cephren's base was the plan level of the Gïzeh pyramids, and that at this level the base of Cheops measures 420 R.B. cubits--same as the base of Cephren. This hypothesis is supported by the revelations of the pentangle, in which the ratio of 34 to 21 = apothem 340 to half-base 210 R.B. cubits, is so nearly approached. Showing how proportional lines were the order of the pyramids of Gïzeh, we will summarise the proportions of the three main pyramids as shewn by my dimensions and ratios, very nearly, viz.:-- _Mycerinus. Base : Apothem :: Altitude : Half-Base._ as shown by the ratios, (_Fig_. 13), 40 : 32 :: 25 : 20. _Cephren. Diagonal of Base : Edge :: Edge : Altitude._ as shown by ratios, (_Fig_. 12), 862 : 588 :: 588 : 400. _Cheops. (Apothem + Half Base): Apoth. :: Apoth. : Half Base._ as shown by the ratios, (_Fig_. 9), 55 : 34 :: 34 : 21. and--_Apothem : Altitude :: Altitude : Half-B._ Similar close relations to other stars may be found in other pyramids. Thus:--_Suppose NHO of figure 69 to be the NHO of a heptangle instead of a pentangle_, then does NH represent apothem, and NO represent base of the pyramid Mycerinus, while the co-sine of the angle NHM (being MH minus versed sine) will be equal to the altitude of the pyramid. The angle NHM in the heptangle is, 38° 34′ 17·142″, and according to my plan of the pyramid Mycerinus, the corresponding angle is 38° 40′ 56″. (_See Fig_. 19.) This angular difference of 0° 6′ 39″ would only make a difference in the apothem of the pyramid of _eight inches_, and of _ten inches_ in its altitude (apothem being 283 ft. 1 inch, and altitude 221 ft.). § 17. THE MANNER IN WHICH THE SLOPE RATIOS OF THE PYRAMIDS WERE ARRIVED AT. The manner in which I arrived at the Slope Ratios of the Pyramids, viz., 32 _to_ 20, 33 _to_ 20, and 34 _to_ 21, for _Mycerinus_, _Cephren_, and _Cheops_, respectively (_see Figures_ 8, 7 _and_ 6), was as follows:-- First, believing in the connection between the relative positions of the Pyramids on plan (_see Fig_. 3, 4 _or_ 5), and their slopes, I viewed their positions thus:-- Mycerinus, situate at the angle of the 3, 4, 5 triangle ADC, is likely to be connected with that "primary" in his slopes.