WordNet

(logic) an inference that follows directly from the proof of another proposition
a practical consequence that follows naturally; "blind jealousy is a frequent corollary of passionate love"
issue or terminate (in a specified way, state, etc.); end; "result in tragedy" (同)ensue
come about or follow as a consequence; "nothing will result from this meeting"
something that results; "he listened for the results on the radio" (同)resultant, final result, outcome, termination
take as a given; assume as a postulate or axiom; "He posited three basic laws of nature" (同)posit
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning (同)posit
reason by deduction; establish by deduction (同)infer, deduct, derive
conclude by reasoning; in logic (同)infer
the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation (同)illation
the final point in a process (同)end_point
(botany) the whorl of petals of a flower that collectively form an inner floral envelope or layer of the perianth; "we cultivate the flower for its corolla"

PrepTutorEJDIC

(数学で)系 / 《文》必然的結果,帰結
〈C〉〈U〉『結果』,結末;成果,効果 / 《複数形で》(試験・競技などの)『成績』 / (…の)『結果起こる』(『生じる』)《+『from』+『名』(do『ing』)》 / (…という)『結果になる』,(…に)終わる(end)《+『in』+『名』(do『ing』)》
(自明のこととして)…‘を'仮定する;…‘だと'仮定する《+『that節』》 / (推論の基礎となる)仮説,仮定;(数学の)公理
…'を'導き出す,推論する
〈U〉推量,推論,推測 / 〈C〉推量の結果,結論
結果として起こる / (力などが)合成の / 結果 / (物理学で)合力
花冠

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/10/03 05:37:41」(JST)

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A corollary (/ˈkɒrəˌlɛri/ KORR-əl-er-ee or UK: /kɒˈrɒləri/ ko-ROL-ər-ee) is a statement that follows readily from a previous statement.

Overview

In mathematics a corollary typically follows a theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. Proposition B is a corollary of proposition A if B can be readily deduced from A or is self-evident from its proof. The importance of the corollary is often considered secondary to that of the initial theorem; B is unlikely to be termed a corollary if its mathematical consequences are as significant as those of A. Sometimes a corollary has a proof that explains the derivation; sometimes the derivation is considered self-evident.

Peirce's theory of deductive reasoning

Charles Sanders Peirce held that the most important division of kinds of deductive reasoning is that between corollarial and theorematic. He argued that, while finally all deduction depends in one way or another on mental experimentation on schemata or diagrams,^[1] still in corollarial deduction "it is only necessary to imagine any case in which the premises are true in order to perceive immediately that the conclusion holds in that case", whereas theorematic deduction "is deduction in which it is necessary to experiment in the imagination upon the image of the premise in order from the result of such experiment to make corollarial deductions to the truth of the conclusion."^[2] He held that corollarial deduction matches Aristotle's conception of direct demonstration, which Aristotle regarded as the only thoroughly satisfactory demonstration, while theorematic deduction (A) is the kind more prized by mathematicians, (B) is peculiar to mathematics,^[1] and (C) involves in its course the introduction of a lemma or at least a definition uncontemplated in the thesis (the proposition that is to be proved); in remarkable cases that definition is of an abstraction that "ought to be supported by a proper postulate."^[3]

Notes

^ ^a ^b Peirce, C. S., from section dated 1902 by editors in the "Minute Logic" manuscript, Collected Papers v. 4, paragraph 233, quoted in part in "Corollarial Reasoning" in the Commons Dictionary of Peirce's Terms, 2003–present, Mats Bergman and Sami Paavola, editors, University of Helsinki.
^ Peirce, C. S., the 1902 Carnegie Application, published in The New Elements of Mathematics, Carolyn Eisele, editor, also transcribed by Joseph M. Ransdell, see "From Draft A – MS L75.35–39" in Memoir 19 (once there, scroll down).
^ Peirce, C. S., 1901 manuscript "On the Logic of Drawing History from Ancient Documents, Especially from Testimonies', The Essential Peirce v. 2, see p. 96. See quote in "Corollarial Reasoning" in the Commens Dictionary of Peirce's Terms.

References

Weisstein, Eric W. "Corollary". MathWorld.

corollary at dictionary.com
Chambers's Encyclopaedia. Volume 3, Appleton 1864, p. 260 (online copy, p. 260, at Google Books)

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