The seked was, of course, the unit of slope in AE, and expressed the horizontal run for a fixed vertical rise of one royal cubit (7 palms or 28 digits).

The seked is expressed in palms in the Rhind Mathematical Papyrus eg the seked of say 5 1/4 palms has a horizontal run of 5 1/4 palms for a vertical rise of 7 palms (one royal cubit).

The seked could have been expressed in royal cubits, for which the fixed vertical rise is 1 (royal cubit), or in digits for which the fixed vertical rise is 28 (digits). I called the latter 'the digit seked'. The example in RMP becomes the seked of 21 digits.

The lower Entrance Passage, in the bedrock, conforms to the seked of 14 palms. and this is a simple 1 in 2 slope which may be expressed as the digit seked as follows:
seked of 56 digits = 28 rise /56 horizontal run = 26 degrees 33 minutes 54 seconds

If I want the seked of 56 1/3 digits, then I type in my calculator:
56.333.. / 28 = 2.01190 inverse = 0.49704 shift tan = 26.429.. shift = 26 deg 25 min 46 secs

(What I call a digit, is not a Petrie digit, but an Edwards digit, with 4 digits in the palm and 7 palms in the royal cubit, that is 28 digits in the royal cubit)

The description of the build standard given by both Smyth and Petrie suggests that the rise and run would have been measured very precisely, probably accurate to better than 1 part in 1000, for which the as built slope should be within 3 arc minutes of the intended slope.

The slope of the upper Entrance Passage is approximately 26 degrees 27 minutes, and the intended slope was not the seked of 14 palms, if the build standard was 1 part in 1000.

Smyth described the microscopic perfection in relation to the level of the sides of the entrance floor, and Petrie could not detect any deviation from perfection in the azimuth of the passage, having taken measurements to 1/20th inch.

Is it not reasonable to assume that the builders were given a plan with rise and run, or a seked, given that the slope is so consistent?

If I had chosen a different unit of length, such as a Petrie digit or a Smyth Pyramid Inch, and then converted the rise of 1 royal cubit into that unit, then I would have got the same slope. Indeed that unit of length might be more convicing than my digit seked if it turned out to be a nice round number.
But I don't want to waste my time doing that, because I think I know the reason for the selected slope after contemplating the division of the royal cubit into 28 parts.

This topic is, of course, on the Ascending Passage, and I merely wanted to show that taking the width of the passage as the seked of the slope also highlights the slope of the Upper Entrance Passage.
I could have done it in palms, but the fractions would have been smaller.

Mark