21 Now this king of Egypt was a descendant from the loins of Ham, and was a partaker of the blood of the Canaanites by birth.
22 From this descent sprang all the Egyptians, and thus the blood of the Canaanites was preserved in the land.
23 The land of Egypt being first discovered by a woman, who was the daughter of Ham, and a daughter of Egyptus, which in the Chaldean signifies Egypt, which signifies that which is forbidden;
24 When this woman discovered the land it was under water, who afterward settled her sons in it; and thus, from Ham, sprang that race which preserved the curse in the land.
25 Now the first government of Egypt was established by Pharaoh, the eldest son of Egyptus, the daughter of Ham, and it was after the manner of the government of Ham, which was patriarchal.
26 Pharaoh, being a righteous man, established his kingdom and judged his people wisely and justly all his days, seeking earnestly to imitate that order established by the fathers in the first generations, in the days of the first patriarchal reign, even in the reign of Adam, and also of Noah, his father, who blessed him with the blessings of the earth, and with the blessings of wisdom, but cursed him as pertaining to the Priesthood.
27 Now, Pharaoh being of that lineage by which he could not have the right of Priesthood, notwithstanding the Pharaohs would fain claim it from Noah, through Ham, therefore my father was led away by their idolatry;
I hope you guys will indulge me as I try to figure out this mess.
So, according to Book of Abraham 1, Egypt's rulers:
1. Descended from Ham, the son of Noah
2. The rulers derive this lineage from a daughter of Ham who is also a daughter of Egyptus (presumably also a descendant of Ham).
3. She discovered Egypt when the Nile was flooded (presumably) and settled her sons on the land.
4. The first ruler of Egypt, Pharaoh, was "the eldest son of Egyptus, the daughter of Ham."
OK, it is at this point that I think to myself, "WTF?" How can the woman who discovered Egypt be a daughter of Egyptus, who is herself named Egyptus, who just a few lines later is no longer a daughter of Egyptus, but instead a daughter of Ham?
5. Pharaoh seeks to imitate the order of the priesthood, but he is cursed in respect to the priesthood by "his father" Noah.
Again, I am thinking, "WTF?" So, Pharaoh is now the son of Noah? How does this mess work?
Noah has a son Ham, who in turn has a daughter named Egyptus. Noah sleeps with his granddaughter Egyptus and then curses the offspring, Pharoah, with regards to the priesthood.
Now, it may very well be the case that the reference to Noah as Pharaoh's father is intended to convey the more general sense of patrilineal ancestor, in which case Noah did not have sexual relations with his granddaughter Egyptus (what a crazy name for a daughter of Ham), thereby begetting Pharaoh.
Here is a possible genealogical stemma:
Ham = Egyptus