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If the floor of the ascending passage/grand gallery is extended at the same angle to the southern face of the pyramid, the ratio between the length of the ascending passage/grand gallery floor and the length of the extension, is the same as the ratio between the height and the half base of the pyramid. Proof as follows:

Petrie gives the position of the point where the floor of the ascending passage intersects the floor of the descending passage as 172.9 inches above ground level and 3016.3 inches north of the midline of the pyramid. Petrie gives the length from the intersection of the floors to the actual beginning of the floor of the ascending passage as 59.8 inches and he gives the angle for this part of the AP as 26 deg 12.5'. The sine of 26 deg 12.5' is .4416 and the cosine is .89719. Multiplied by the 59.8 inch sloping length of the extension gives 199.3 inches above ground level and 2962.65 inches north of the midline of the pyramid for the point of beginning of the actual floor of the ascending passage. Petrie gives 1658.92 inches for the height of the end of the floor of the grand gallery at the midline of the pyramid. 1658.92 minus 199.3 = 1459.62 inches for the vertical distance from the beginning of the floor of the ascending passage to the end of the floor of the grand gallery.

1459.62 squared plus 2962.65 squared equals 3302.69 squared. Petrie gives 3302.5 inches as his direct measurement for the sloping length of the floor of the ascending passage/grand gallery, so Pythagoras theory confirms Petrie's measurements within a margin of less than 2/10ths of one inch.

Given the sq rt phi ratio of 1.272/1 for the height and the half base of the pyramid, the vertical rise of the extension of the floor to the south face of the pyramid is

1459.62/1.272 = 1147.5

1147.5 plus 1658.92 = 2806.42 inches above ground level for the height above ground level the extension intersects the southern face of the pyramid.

Since the ratio between the horizontal section from the beginning of the AP to the midline of the pyramid and the horizontal section from the intersection point at the southern face of the pyramid to the midline of the pyramid is the same as the ratio between the height and the half base of the pyramid, the horizontal section from the beginning of the AP to the midline of the pyramid must be equal to the height of the pyramid up from the horizontal section of the extension, so:

2806.42 plus 2962.65 inches = 5769.07 inches for the height of the pyramd.

Petrie gives 9068.8 inches for the mean baselength of the pyramid, or 4534.4 inches for the half base:

4534.4 x 1.272 = 5767.85 inches. This is just slightly over one inch less than the height produced by the same ratio between the AP/GG floor and the extension. Since Petrie gives a possible margin of error of one to two inches in his calculation of the height of the end of the GG at the midline of the pyramid, the equality of the ratio between the height and the half base of the pyramid, and the length of the AP/GG floor and the extension to the southern face of the pyramid, is within the very small margins of error of Petrie's survey.

PS: 1.618 cubits for the vertical distance between the height of the end of the floor of the GG at the midline of the pyramid and the height of the floor of the KC is also within the small margins of error of Petrie's survey.