An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.
In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. One day, a poisonous arrow shot at him was lodged in his heel, killing him shortly afterwards.
Although the death of Achilles is predicted by Hector in Homer's Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a heel wound which was the result of an arrow--possibly poisoned--shot by Paris.
Classical myths attribute Achilles's invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him--that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.
The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called "the cord of Achilles." As an expression meaning "area of weakness, vulnerable spot," the use of "Achilles heel" dates only to 1840, with implied use in Samuel Taylor Coleridge's "Ireland, that vulnerable heel of the British Achilles!" from 1810 (Oxford English Dictionary).
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The large and prominent tendon of the gastrocnemius, soleus, and plantaris muscles of the calf is called the tendo achilleus or Achilles tendon. This is commonly associated with the site of Achilles' death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the Lernaean Hydra.
A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his posterior tibial artery behind the medial malleolus, in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in Thetis's grip.
Vocatum passim chorda Achillis, & ab Hippocrate tendo magnus. (Appendix, caput XII. De musculis pedii et antipedii, p. 269)