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The following account of the foundation of Alexandria is not historical. It comes from The Life of Alexander of Macedon (Longmans, Green and Co. 1955) by an unknown author named Pseudo-Callisthenes.
According to the translator, Elizabeth Hazelton Haight, the Life was written around c. AD 300 although it is likely based on much a much older text dating, it seems, to just after Alexander’s death.
Now they began to construct Alexandria from the plain of Mesos and the district took its name from the fact that the building of the city began there…
[Alexander] directed that the digging of the foundations should proceed only in one place, namely exactly where a great hill appeared which is called Kopria. And when he had prepared the foundations of the greatest part of the city and planned it, he inscribed five letters Α Β Γ Δ Ε, Α for Alexander, Β for βασιλεύς (king), Γ for γἐνος, (son), Δ for Δίος (of a god), and E for the initial of the phrase beginning ἔκτισε (built the city).
… [Alexander] constructed a very great altar in front of the Heroon, which is now called the Altar of Alexander. Then he made a sumptuous sacrifice, and offered this prayer: “Whatever god thou art who dost protect this land and dost survey the boundless world, accept the sacrifice and be my helper against my foes.” With these words, he placed the sacrifice on the altar. Then suddenly a great eagle, swooping down, seized the viscera of the offering and bearing them through the air put them down upon another altar… [Alexander] went… in haste and saw the viscera lying on the altar and a temple built in antiquity and a seated wooden image inside, which mortal tongue could not describe… Now he made enquiries of the natives there as to who the god was…
The mysterious god turned out to be Sarapis. He appeared to Alexander in a dream and prophesied the rise of Alexandria to him, and the Macedian king’s destiny:
…
By my authority, you in your youth
Shall all the tribes barbarian subdue.
And have a longed-for city, queen of the world.
And, after many seasons and times pass,
It shall be famed among the brave, adorned
By many temples, many varied shrines,
Famed for its beauty, size, inhabitants.
And every traveller shall come to stay,
Forgetful of the land where he was born.
And of this city I shall be the god
…
… everywhere and always in your life
Shall mortals reverence you as if a god,
And dying you shall be a god indeed,
Receive obeisance and the gifts of kings.
Here in this city always you shall dwell
In life and death. The city which you built.
Shall be your tomb. This I, your sire, swear,
O Alexander…
The Second Achilles 