basis

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. A foundation upon which something rests.
2. n. The chief constituent; the fundamental ingredient: The basis for most liquids is water.
3. n. The fundamental principle.
4. n. A pattern or schedule for proceeding: on a weekly basis.
5. n. A condition for relating or proceeding: a first-name basis; a friendly basis. See Synonyms at base¹.

Century Dictionary and Cyclopedia

1. n. 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.
2. n. In architecture, same as base, 3.
3. n. A pedestal.
4. n. The principal constituent of a compound; a fundamental ingredient.
5. n. Milit., same as base, 15
6. n. . In crystallography and petrography, same as basal plane (which see, under basal).
7. n. In botany and conchology, same as base, 4.
8. n. [NL.] In anatomy, the base; the fundamental or basilar part of anything: as, basis cranii, the base of the skull.
9. n. In prosody, a trochee or its substitute preceding the dactyls of a logaœdic series. An apparent spondee or iambus, a long syllable of three times, or even a pyrrhic, tribrach, or anapest, may be used as a basis, and an anacrusis may be prefixed to it. The basis is sometimes double.
10. n. Same as basipodite.

Wiktionary

1. n. A starting point, base or foundation for an argument or hypothesis.
2. n. An underlying condition or circumstance.
3. n. regular frequency
4. n. linear algebra In a vector space, a linearly independent set of vectors spanning the whole vector space.
5. n. accounting Amount paid for an investment, including commissions and other expenses.
6. n. 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.

GNU Webster's 1913

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

WordNet 3.0

1. n. the most important or necessary part of something
2. n. the fundamental assumptions from which something is begun or developed or calculated or explained
3. n. a relation that provides the foundation for something