basis

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A foundation upon which something rests.
• noun The chief constituent; the fundamental ingredient.
• noun The fundamental principle.
• noun An underlying circumstance or condition: synonym: base.
• noun A pattern or schedule for proceeding.
• noun A condition for relating or proceeding.

from The Century Dictionary.

• noun Same as basipodite.
• noun The foundation of anything; that on which a thing stands or on which anything is reared; a foundation, groundwork, or supporting principle: now most commonly used of immaterial things.
• noun In architecture, same as base, 3.
• noun A pedestal.
• noun The principal constituent of a compound; a fundamental ingredient.
• noun Milit., same as base, 15
• noun . In crystallography and petrography, same as basal plane (which see, under basal).
• noun In botany and conchology, same as base, 4.
• noun [NL.] In anatomy, the base; the fundamental or basilar part of anything: as, basis cranii, the base of the skull.
• noun In prosody, a trochee or its substitute preceding the dactyls of a logaœdic series.

from the GNU version of the Collaborative International Dictionary of English.

• noun The foundation of anything; that on which a thing rests.
• noun obsolete The pedestal of a column, pillar, or statue.
• noun The groundwork; the first or fundamental principle; that which supports.
• noun The principal component part of a thing.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A starting point, base or foundation for an argument or hypothesis.
• noun An underlying condition or circumstance.
• noun regular frequency
• noun linear algebra In a vector space, a linearly independent set of vectors spanning the whole vector space.
• noun accounting Amount paid for an investment, including commissions and other expenses.
• noun topology A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun the most important or necessary part of something
• noun the fundamental assumptions from which something is begun or developed or calculated or explained
• noun a relation that provides the foundation for something