History of the star: Alpha is actually two stars, 4 minutes apart, in the right horn of the Goat in Capricornus. Alpha¹ (Giedi Prima), double, 3.2 and 4.2, yellow. Alpha²  (this star Giedi Secunda), triple, 3, 11.5, and 11.5, pale yellow, ash, and lilac.

These are the Prima and Secunda Giedi, or plain Algedi, from the Arabian constellation title Al Jady "The goat".

Other titles, Dabih and the degenerated Dschabbe and Dshabeh, applied to them, but more commonly to beta, have been traced by some to Al Jabbah, "the Forehead", although the stars are nearer the tip of the horn; but the names undoubtedly come from Al Sa'd al Dhabih, "the Lucky One of the Slaughterers", the title of the Arabic 20th manzil (of which these alphas and betas were the determinant point), manifestly referring to the sacrifice celebrated by the Arabs at the heliacal rising of Capricorn.

And of similar signification was the Euphratean Shak-shadi and the Coptic Eupeutos, or Opeutus, for the same lunar asterism of those peoples.

It was thought that alpha, then seen only as a single star, with beta and nu was known by the Akkadians as Uz, the Goat; and as Enzu in the astronomy of their descendants; while Epping is authority for the statement that this, or perhaps beta, marked the 26th ecliptic asterism of the Babylonians, Qarnu Shahu, "the Horn of the Goat".

Alpha is said to have represented the 8th antediluvian king Amar Sin.

[Star Names, Their Lore and Meaning, Richard Hinchley Allen, 1889].

Influences of the Arabic 20th manzil: Helps the escape of servants and captives and the curing of diseases. With Moon transiting here; take medicine, travel, but do not lend money or marry.  (Robson*).

The astrological influences of the constellation: The Goat is associated with the Hebrew letter Yod and the 10th Tarot Trump, The Wheel of Fortune". (Robson*). 

The astrological influences of the constellation given by Manilius:

In her shrine Vesta tends your fires, Capricorn : and from her you derive your skills and callings. For whatever needs fire to function and demands a renewal of flame for its work must be counted as of your domain. To pry for hidden metals, to smelt out riches deposited in the veins of the earth, to fold sure-handed the malleable mass—these skills will come from you, as will aught which is fashioned of silver or gold. That hot furnaces melt iron and bronze, and ovens give to the wheat its final form, will come as gifts from you. You also give a fondness for clothes and wares which dispel the cold, since your lot falls for all 241 time in winter's season, wherein you shorten the nights you have brought to their greatest length and give birth to a new year by enlarging the daylight hours. Hence comes a restless quality in their lives and a mind which is often changed and floats this way and that; the first half of the sign is the slave of Venus, and that with guilt involved, but a more virtuous old age is promised by the conjoined fish below. [Astronomica, Manilius, 1st century AD, book 4, p.241.]

The general astrological influences of the star: Associated with piety and self-sacrifice. (Larousse Encyclopedia of Astrology).

*(Fixed Stars and Constellations in Astrology , Vivian E. Robson, 1923)