From Wikipedia.
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Mythology
The constellation, which originally formed part of the scorpion's claws, is the youngest of the Zodiac and the only one not to represent a living being. In Greek mythology, the constellation depicts the scales held by Astraea (the Virgin), the goddess of justice.
Astrology
The astrological sign Libra (September 23 - October 22) is associated with the constellation.
In some cosmologies, Libra is associated with the classical element Air, and thus called an Air Sign (with Aquarius and Gemini). It is also one of the four cardinal signs (along with Aries, Cancer, and Capricorn). Its polar opposite is Aries. Each astrological sign is assigned a part of the body, viewed as the seat of its power. Libra rules the lower back and internal reproductive organs. The symbol for Libra is the Scales. Libran qualities include physical beauty, strong sensuality, artistic sensibilities, tact and diplomacy, and an innate sense of fairness and balance.
Libra, the Scales, can be found between Scorpius and Virgo, Libra is the age old symbol of justice, harmony and balance.
It is interesting that to the Italians, French, Germans, Anglo-Saxons, and Romans the constellation was the scales.
The early Greeks did not recognize Libra as the scales, but included it as the claws of the scorpion. Credit is usually given to the Romans for creating this constellation as a sign of the autumnal equinox. The constellation first appeared in the Julian calendar in 46 B.C. The constellation appears again in 43 B.C. in which a comet appeared during the same year as Caesar's assassination, the writing indicates the comet took his soul to heaven, this comet may very well be the same one seen in 531, 1106 and 1680; its next apparition will be 2255.
However, the Egyptians, Hebrews, Persians and Syrians all had it on their planetspheres and called the constellation the 'weigh beam' or scale beam. The Arabs followed the greeks including it as part of the scorpions claws.