[W/K] :: Theorem of Pappus

  Theorem \The"o*rem\, n. [L. theorema, Gr. ? a sight,
     speculation, theory, theorem, fr. ? to look at, ? a
     spectator: cf. F. th['e]or[`e]me. See Theory.]
     1. That which is considered and established as a principle;
        hence, sometimes, a rule.
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              Not theories, but theorems (?), the intelligible
              products of contemplation, intellectual objects in
              the mind, and of and for the mind exclusively.
                                                    --Coleridge.
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              By the theorems,
              Which your polite and terser gallants practice,
              I re-refine the court, and civilize
              Their barbarous natures.              --Massinger.
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     2. (Math.) A statement of a principle to be demonstrated.
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     Note: A theorem is something to be proved, and is thus
           distinguished from a problem, which is something to be
           solved. In analysis, the term is sometimes applied to a
           rule, especially a rule or statement of relations
           expressed in a formula or by symbols; as, the binomial
           theorem; Taylor's theorem. See the Note under
           Proposition, n., 5.
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     Binomial theorem. (Math.) See under Binomial.
  
     Negative theorem, a theorem which expresses the
        impossibility of any assertion.
  
     Particular theorem (Math.), a theorem which extends only to
        a particular quantity.
  
     Theorem of Pappus. (Math.) See Centrobaric method, under
        Centrobaric.
  
     Universal theorem (Math.), a theorem which extends to any
        quantity without restriction.
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  Centrobaric \Cen`tro*bar"ic\, a. [Gr. (?) ? a treatise of
     Archimedes on finding the center of gravity, fr. ?
     gravitating toward the center; ? center + ? weight.]
     Relating to the center of gravity, or to the process of
     finding it.
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     Centrobaric method (Math.), a process invented for the
        purpose of measuring the area or the volume generated by
        the rotation of a line or surface about a fixed axis,
        depending upon the principle that every figure formed by
        the revolution of a line or surface about such an axis has
        for measure the product of the line or surface by the
        length of the path of its center of gravity; -- sometimes
        called theorem of Pappus, also, incorrectly, Guldinus's
        properties. See Barycentric calculus, under Calculus.
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