Apollodorus Library 2.3

[1]
  Bellerophon, son of Glaucus, son of Sisyphus, having accidentally killed his brother Deliades or, as some say, Piren, or, as others will have it, Alcimenes, came to Proetus and was purified. ¹ And Stheneboea fell in love with him, ² and sent him proposals for a meeting; and when he rejected them, she told Proetus that Bellerophon had sent her a vicious proposal. Proetus believed her, and gave him a letter to take to Iobates, in which it was written that he was to kill Bellerophon. Having read the letter, Iobates ordered him to kill the Chimera, believing that he would be destroyed by the beast, for it was more than a match for many, let alone one; it had the fore part of a lion, the tail of a dragon, and its third head, the middle one, was that of a goat, through which it belched fire. And it devastated the country and harried the cattle; for it was a single creature with the power of three beasts. It is said, too, that this Chimera was bred by Amisodarus, as Homer also affirms, ³ and that it was begotten by Typhon on Echidna, as Hesiod relates. ⁴

[2] So Bellerophon mounted his winged steed Pegasus, offspring of Medusa and Poseidon, and soaring on high shot down the Chimera from the height. ⁵ After that contest Iobates ordered him to fight the Solymi, and when he had finished that task also, he commanded him to combat the Amazons. And when he had killed them also, he picked out the reputed bravest of the Lycians and bade them lay an ambush and slay him. But when Bellerophon had killed them also to a man, Iobates, in admiration of his prowess, showed him the letter and begged him to stay with him; moreover he gave him his daughter Philonoe, ⁶ and dying bequeathed to him the kingdom.