The Merriam-Webster Online Dictionary, in an entry updated on Apr. 2, 2018 and available at defined "euthanasia" as:

“[T]he act or practice of killing or permitting the death of hopelessly sick or injured individuals (such as persons or domestic animals) in a relatively painless way for reasons of mercy…

The word comes from the Greek euthanatos, which means ‘easy death.’ In English, euthanasia has been used in exactly this sense since the early seventeenth century, when Francis Bacon described the phenomenon as ‘after the fashion and semblance of a kindly & pleasant sleepe.’ Nowadays, the word usually refers to the means of attaining such a death.”

Apr. 2, 2018