alternately

Etymology

alternate + -ly

adv

1. In reciprocal succession; succeeding by turns; in alternate order.
   Tired with the heat and my walk, I threw myself down on the grass in the shadow of the house, where I lay half-asleep enjoying a quiet rest, when I was startled by an unpleasant clamour, the jarring voice of a woman, who was trying by alternately scolding and using pet names to pacify a litter of grunting pigs on the farm. 1886, Peter Christen Asbjørnsen, translated by H.L. Brækstad, Folk and Fairy Tales, page 278
   Well, I can't help noticing that you insult me and then you're polite to me alternately. 1970, “The Butcher Who is Alternately Rude and Polite”, in Monty Python's Flying Circus, season 2, episode 5, spoken by Customer (Michael Palin)
2. (mathematics) By alternation; when, in a proportion, the antecedent term is compared with antecedent, and consequent.
3. (chiefly Canada, US, sometimes proscribed) Alternatively.
   Downstairs, he was informed. That is, down the escalators, where there is both a women’s room (often with a line) and a men’s room (almost never with a line). Or alternately, he could ask the station master to buzz him into the “family” bathroom. He opted to go downstairs. 2008-07-18, Jennifer 8. Lee, “A ‘Women Only’ Restroom Renovation Tips the Balance at Grand Central”, in New York Times