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The Collaborative International Dictionary of English v.0.48:

Theory \The"o*ry\, n.; pl. Theories. [F. th['e]orie, L. theoria, Gr. ? a beholding, spectacle, contemplation, speculation, fr. ? a spectator, ? to see, view. See Theater.] 1. A doctrine, or scheme of things, which terminates in speculation or contemplation, without a view to practice; hypothesis; speculation. [1913 Webster] Note: "This word is employed by English writers in a very loose and improper sense. It is with them usually convertible into hypothesis, and hypothesis is commonly used as another term for conjecture. The terms theory and theoretical are properly used in opposition to the terms practice and practical. In this sense, they were exclusively employed by the ancients; and in this sense, they are almost exclusively employed by the Continental philosophers." --Sir W. Hamilton. [1913 Webster] 2. An exposition of the general or abstract principles of any science; as, the theory of music. [1913 Webster] 3. The science, as distinguished from the art; as, the theory and practice of medicine. [1913 Webster] 4. The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments. [1913 Webster] Atomic theory, Binary theory, etc. See under Atomic, Binary, etc. [1913 Webster] Syn: Hypothesis, speculation. Usage: Theory, Hypothesis. A theory is a scheme of the relations subsisting between the parts of a systematic whole; an hypothesis is a tentative conjecture respecting a cause of phenomena. [1913 Webster] Theosoph
The Collaborative International Dictionary of English v.0.48:

Binary \Bi"na*ry\, a. [L. binarius, fr. bini two by two, two at a time, fr. root of bis twice; akin to E. two: cf. F. binaire.] Compounded or consisting of two things or parts; characterized by two (things). [1913 Webster] Binary arithmetic, that in which numbers are expressed according to the binary scale, or in which two figures only, 0 and 1, are used, in lieu of ten; the cipher multiplying everything by two, as in common arithmetic by ten. Thus, 1 is one; 10 is two; 11 is three; 100 is four, etc. --Davies & Peck. Binary compound (Chem.), a compound of two elements, or of an element and a compound performing the function of an element, or of two compounds performing the function of elements. Binary logarithms, a system of logarithms devised by Euler for facilitating musical calculations, in which 1 is the logarithm of 2, instead of 10, as in the common logarithms, and the modulus 1.442695 instead of .43429448. Binary measure (Mus.), measure divisible by two or four; common time. Binary nomenclature (Nat. Hist.), nomenclature in which the names designate both genus and species. Binary scale (Arith.), a uniform scale of notation whose ratio is two. Binary star (Astron.), a double star whose members have a revolution round their common center of gravity. Binary theory (Chem.), the theory that all chemical compounds consist of two constituents of opposite and unlike qualities. [1913 Webster]