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2. The first star of Capricornus is according to my astronomy book Gredi (α), but we can see ξ is rising a few days earlier:

At the other end of Capricornus is Deneb Algiedi (the Tail of the Goat, δ), which is marking the last part of the constellation figure (although μ is a few days later).
 
Allen:

"Deneb Algedi is the transcription by Ulug Beg's translator of Al Dhanab al Jady, the Tail of the Goat; changed to Scheddi in some lists, - a name also found for γ."

"These [α¹ and α²] are the Prima and Secunda Giedi, or plain Algedi, from the Arabian constellation title Al Jady."

"In Persia it [Capricornus] was Bushgali, Bahi or Vahik, and Goi; in the Pahlavi tongue, Nahi; in Turkey Ughlak; in Syria, Gadjo; and in Arabia, Al Jady, usually written by us Giedi; all meaning the Goat, or, in the latter country, the Bādan, or Ibex, known to zoologists as Capra beden."

The name Deneb seems to be only a technical term for the end of a constellation; we can see it here evidently marks the tip of the right horn. The zodiacal sign of Aries is very similar to the head of the Ibex:

"Aratos called it Άιγοκέρως, the Horned Goat, to distinguish it from the Άιξ of Auriga, as did Ptolemy, but Ionic writers had Άιγοκέρευς; and this word, Latinized as Aegoceros, was in frequent use with all classical authors who wrote on astronomy.

The Arabo-Latin Almagest of 1515 turned this into Alcaucurus, explained by habens hirci; and Bayer mentioned Alcantarus.

Eratosthenes knew it as Πάν and Άιγι-Πãν, the Goat-Footed Pan, half fishified, Smyth said, by his plunge into the Nile in a panic at the approach of the monster Typhon; the same story being told of Bacchus, so that he, too, always was associated with its stars." (Allen)