Etymology
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Words related to anesthesiology

anesthesia (n.)

1721, "loss of feeling," medical Latin, from Greek anaisthēsia "want of feeling or perception, lack of sensation (to pleasure or pain)," abstract noun from an- "without" (see an- (1)) + aisthēsis "feeling," from PIE root *au- "to perceive." For the abstract noun ending, see -ia. As "a procedure for the prevention of pain in surgical operations," from 1846. Aesthesia "capacity for feeling" is attested in English from 1853, perhaps a back-formation.

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-ology 

word-forming element indicating "branch of knowledge, science," now the usual form of -logy. Originally used c. 1800 in nonce formations (commonsensology, etc.), it gained legitimacy by influence of the proper formation in geology, mythology, etc., where the -o- is a stem vowel in the previous element.

The second element is prop[erly] -logy (-logue, etc.), the -o- belonging to the preceding element; but the accent makes the apparent element in E[nglish] to be -ology, which is hence often used as an independent word. [Century Dictionary] 
anaesthesiology (n.)
alternative spelling of anesthesiology (q.v.). See æ (1).
anesthesiologist (n.)
1943, American English, from anesthesiology + -ist.