[Translation in progress; introduction to be added later.]
“When they signify eternity (aiṓn), they draw the Sun and the Moon, as being eternal elements.
“When they wish to write eternity in a different manner, they depict a snake which has its tail hidden under the rest of its body, and which the Egyptians call uraeus, which in Greek is basilískon, ‘little king’, which they make golden and bestow on the gods. And the Egyptians say that eternity is shown through this animal because, of the three kinds of snakes that there are, the rest are mortal, but this alone is immortal, and it kills any other animal by breathing upon it, even without biting. Therefore, because it seems to rule over life and death, on that account they place it upon the head of the gods.”
[Commentary to be added latter.]
“When they wish to write ‘cosmos’, they depict a snake eating its own tail (óphin … tḕn heautoû esthíonta ourán) and mark it with many scales, symbolizing the stars in the cosmos. The animal is the lowest, like the Earth, but also the smoothest, like water, [gap in the text?].
“Each year it puts away its age by sloughing off (its skin), on account of which it is also the annual time in the cosmos, and by making a change, it rejuvenates. And by using its own body for food, it signifies that all things which originate in the cosmos by divine providence also undergo, in turn, diminishment into themselves.”
This chapter seems to reflect some creative (“cryptographic”) use of hieroglyphs. […]
“Further, for ‘soul’, a falcon is placed, because of the translation of the name. For the falcon is called baiēth by the Egyptians, and when divided, this word signifies soul and heart; for baï is ‘soul’, and hēth is heart, and according to the Egyptians, the heart is the enclosure of the soul, so that the composition of the word signifies the soul within the heart. On account of which too the falcon, because of his sympathy with the soul, does not drink any water, but only blood, with which the soul is also nourished.”
Here, hēth (ἥθ) stands for Coptic hēt (ϩⲏⲧ), which does indeed mean heart, while baï (βαΐ = ⲃⲁⲓ) is a rare attestation of the native word for ‘soul’, which has been replaced by the Greek psyche (ψυχή = ⲯⲩⲭⲏ) in surviving the Coptic literature (in part, but not entirely, due to the influence of Christian terminology).
With baiēth, the case is a little more difficult. In consonantal Egyptian, the word is written byk, while in Coptic, it is bēc (ⲃⲏϭ). Horus Apollon is apparently using a vocalization that was archaic in his time, which we can fit into the consonantal skeleton as bayēk, but his pronunciation of the final consonant is in line with Bohairic Coptic. It must be something like sh or tch, for which the closest approximation in Greek at the time may indeed have been Theta (th, i.e. /θ/). Yet it requires transposition into Greek (where th is also an acceptable equivalent of Coptic t) to make baiēc seem to contain hēt.
As for the hieroglyph, Horus Apollon has half-preserved earlier tradition; the soul was indeed represented by a bird glyph, however not a falcon, but a human-headed one 𓅽 (G53 Gardiner):
The idea that the soul is fed by blood is not uncommon in ancient philosophy and medicine: even in late antiquity, the conception that the soul is incorporeal was far from universal.
[… 𓆣𓄿 / 𓄿𓆣]
“When they signify a god within the cosmos (‘encosmic god’), or fate (heimarménē), or the number five, they depict a star.
“God, because the providence of god ordains victory (? níkē), through which the motion of the stars and the entire cosmos is fulfilled; for it seems to them that nothing at all holds together without god.
“Fate, because it too subsists through the arrangement of the stars.
“The number five, because while there is a multitude (of stars) in heaven, only five of them bring about the arrangement of the cosmos by their motion.”