Alternatively

a choice limited to one of two or more possibilities, as of things, propositions, or courses of action, the selection of which precludes any other possibility:
You have the alternative of riding or walking.
one of the things, propositions, or courses of action that can be chosen:
The alternative to riding is walking.
a possible or remaining course or choice:
There was no alternative but to walk.
affording a choice of two or more things, propositions, or courses of action.
(of two things, propositions, or courses) mutually exclusive so that if one is chosen the other must be rejected:
The alternative possibilities are neutrality and war.
employing or following nontraditional or unconventional ideas, methods, etc.; existing outside the establishment:
an alternative newspaper; alternative lifestyles.
Logic. (of a proposition) asserting two or more choices, at least one of which is true.
Contemporary Examples

alternatively, there is an informal proposal to set up a special inquiry into atrocities in Syria.
U.S.: Assad’s ‘Machinery of Death’ Worst Since the Nazis Josh Rogin July 6, 2014

alternatively, they argue, she could become a lady-in-waiting to her sister and step inside the protective caress of the Palace.
Pippa in Peril Tom Sykes March 4, 2012

alternatively, one can consult facts—and it’s no wonder, when you do, why Berman and Davenport don’t mention any numbers.
Not-Crippling-Enough Sanctions? Ali Gharib September 26, 2012

alternatively, he has been described by Egyptian officials as a disillusioned radical, on his way to meet Hamas in Gaza.
Mysterious American Man Found Dead In Egyptian Jail Sophia Jones October 13, 2013

alternatively, he gets caught in a lie and does that nervous laugh thing, which America is onto by now.
Mitt Romney’s Game-Change Moment in the Denver Presidential Debate Michael Tomasky October 1, 2012

Historical Examples

The year begins in April-May and comprises twelve lunar months of thirty and twenty-nine days alternatively.
Indo-China and Its Primitive People Henry Baudesson

The piers of the Nave are alternatively circular and octagonal.
The Cathedrals of Great Britain P. H. Ditchfield

Extend and push him forward, passing one while from the Walk to that of the Trot, and so alternatively.
A New System of Horsemanship Claude Bourgelat

“Or alternatively, by the act of party or parties unknown,” interpolated Warriner.
In Jeopardy Van Tassel Sutphen

Damaraland is alternatively known as Hereroland, both names being derived from the tribes inhabiting the region.
Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 9 Various

noun
a possibility of choice, esp between two things, courses of action, etc
either of such choices: we took the alternative of walking
adjective
presenting a choice, esp between two possibilities only
(of two things) mutually exclusive
denoting a lifestyle, culture, art form, etc, regarded by its adherents as preferable to that of contemporary society because it is less conventional, materialistic, or institutionalized, and, often, more in harmony with nature
(logic) another word for disjunctive (sense 3)
adj.

1580s, “offering one or the other of two,” from Medieval Latin alternativus, from Latin alternatus, past participle of alternare (see alternate (v.)). Meaning “purporting to be a superior choice to what is in general use” was current by 1970 (earliest reference is to the media); e.g. alternative energy (1975). Related: Alternatively.
n.

1620s, in rhetoric, from Medieval Latin alternativus (see alternative (adj.)). Of courses of action, from 1814. Of objects, etc., “the other of two which may be chosen,” by 1838.