You seem to be asking how the AE surveyors could have determined the altitude of a star at it its highest point due south or north, and then build the shafts accordingly.


Dyn 4 pyramids were oriented reasonably accurately to the cardinal directions, especially Khufu's pyramid and Sneferu's northern pyramid at Dahshur which were oriented to the cardinal directions extremely accurately. The general consensus is that the AE were either using stars as an aid in the establishment of the main N / S axis of the pyramid, or the sun for the east / west axis, but the extreme accuracy of some of the orientations and the probable precessionally induced skew over time of the orientations, indicate that stars which are points of light were sighted to.

The most obvious candidate, is the North or Pole Star, Thuban either alone or with another circumpolar star using a vertical straight edge, set up using a plumb line. Another candidate, is a vertical alignment of two bright stars (Betelgeuse and Alnitak) in Orion due south.


"The astronomical knowledge of the Egyptian priests and architects at this time is indicated by early examples of the ceremony of pedj shes ('stretching the cord'), first attested on a granite block of the reign of the 2nd-Dynasty king Khasekhemwy (c.2686 BC). This method relied on sightings of the Great Bear and Orion (see SAH) constellations, using an 'instrument of knowing' (merkhet) which was similar in function to an astrolabe, and a sighting tool made from the central rib of a palm leaf, thus aligning the foundations of the pyramids and sun temples with the cardinal points, usually achieving an error of less than half a degree." (British Museum Dictionary of AE, 1995, Ian Shaw, and Paul Nicholson)


The French Egyptologist, Georges Goyon, in his book 'Le Secret Des Batisseurs Des Grandes Pyramides' 1977: 90, suggested Khufu's pyramid was aligned with Khem, 16.6 km to the north, using the North / Pole Star, Thuban.


Once due north and south are known, then its a question of waiting until the relevant star or vertical alignment of two stars, is 'eclipsed' by the vertical straight edge set up with a backsight pointing due north or south and the point where it was eclipsed, marked. Its then a simple matter of measuring the rise and run of a right angled triangle that defines the incline. A wooden template can be constructed in the form of a right angled triangle which can then be used together with a plumb line by the masons to check the slope of an inclined passage or the shafts.


The northern sky and earth had a special meaning to the AE - the king stood up in the north of the sky and also of the earth, and took possession of the Two Lands as king (of the gods) (PT 439 §814). The 'Two Lands' (tAwi) were the united Upper (southern), and Lower (northern delta region) Egypt - the north side of the sky associated with Lower (northern) Egypt. The southern sky was associated with Upper (southern) Egypt, where the large distinctive constellation of Orion (sAH) was Foremost of Upper Egypt). (PT 477 §959)


Two large distinctive star patterns are mentioned together in this MK text: "A sweet breeze to your nose! Sah (sAH, 'Orion') says to the 'Plough' / 'Big Dipper' (msxtiw)........ CT 611


From the Early Dynastic Period up to early OK, an AE sky watcher looking at the northern sky, could not have failed to realize over time that the 'Plough' / 'Big Dipper' (msxtiw) made a complete circle every 24 hours, around a point in the sky closely marked by the North or Pole Star, Thuban.

During the longest night of the year, it appeared to revolve on a circular path around the NCP from a 1 o'clock position in the sky to a 7 o'clock position during the course of the night - half a circle circling anti clockwise - in the process it turned upside down further highlighting its circular path. During the shortest night, the 'Plough' / 'Big Dipper' went from a 7 o'clock position to a 3 o'clock position.

Its clearly apparent from these observations that the Big Dipper circled around an invisible point in the sky closely 'marked' by a single star, Thuban


It was as if msxtiw was 'tethered' to a pole unable to break free, circling endlessly round and round. The ancient Egyptians may have alluded to this in their depictions of the northern sky, for example, msxtiw is depicted as an oval shaped bovine tethered from its tail to a small circle at the top of a high 'mooring' pole on Senmut's ceiling.The Pyramid Texts mention the 'Mooring Post' (mint) and 'Moorer' (smntt) that J.P. Allen describes as "two unidentified constellations of the northern or northwestern sky, envisioned as a mooring post and a hippopotamus driving it into the ground."


This 'mooring pole' may be an indication of how the AE saw this unique area of the sky - a fixed centre point around which stars revolved.


This region of the sky was probably the celestial sxt Htp (Marsh of Rest / Field of Offerings). According to an inscription in the pyramid of Pepy I, the sxt Htp was laid out by a potter - laid out for the king in the god's limit (with the help(?) of the gods).

According to the corresponding inscription in the pyramids of Merenre and Pepi II, a plumb-line / measuring cord was used.

Its interesting a potter was involved, as pots revolve on a wheel as they are made, and this revolving theme is very apparent in the northern sky. A plumb-line / measuring cord was used to lay out this celestial region just as fields were laid out after the waters of the inundation had receded.

The word for 'potter' is qd, and in PT 518 is written: Aa 28 (phono. qd, 'build', 'fashion pots') D46 (d) G43 (w) + W14 (a tall pot with horizontal line through it). 'Potter', qd, was pronounced the same as 'builder', qd.


J.P. Allen: "Pepi is the Potter of the Dual Ennead (psDti), who laid out the Marsh of Rest (sxt Htp)." P 466"Nemtiemzaf Merenre is the measuring cord of the Dual Ennead with which the Marsh of Rest was laid out." M 358 (N 546)


R.O. Faulkner: "I am the plumb-line of the Two Enneads by means of which the Field of Offerings (sxt Htp) was founded. (Var. P: "I am the potter of the Two Enneads who founded the Field of Offerings")


The king went to the big island in the midst of the Marsh of Rest on which the gods and the swallows landed - the Imperishable Stars were the swallows - The king was to be the greatest official of the akhs, the northern Imperishable Stars of the sky. (P 467; PT 519 §1216, 1220)

Allen: This Pepi has come to you, Horus, Geb's heir of whom Atum says "All is yours," of whom the Dual Ennead say "All is yours," that you might say that this Pepi will be among them, the gods in the sky, for you have assembled those in the (sky's) arcs and banded together those who are the Imperishable Stars. Turn Pepi around - ah! ah! - day from day, night from night. (Allen's note: i.e. transfer the deceased from day to night and night to day). Day after day will [he] exist, forever. Night after night will he exist, forever. P 516; PT 574 §1489-91


These texts clearly indicate the AE were interested in the region of the northern sky where the circumpolar stars are found, to the extent they incorporated them into their afterlife beliefs, and the laying out of this region with a plumb line / measuring cord resonates with the laying out of the royal funerary complexes.

CT