RE C 



REC 



philosophers, that Genus and Species are 

 some real Things, existing independ- 

 ently of our conceptions and expressions ; 

 and that, as in the case of Singular terms 

 there is some real individual correspond- 

 ing to each, so, in Common terms also, 

 there is some Thing corresponding to 

 each ; which is the object of our thoughts 

 when we employ any term. This doc- 

 trine, though attributed to Aristotle, is 

 by him expressly contradicted. See 

 Nominalists. 



REASON. Whately has pointed out 

 several of the ambiguities to which this 

 word is liable. It is used to signify, 



1, all the intellectual powers collectively; 



2, those intellectual powers exclusively 

 in which man differs from brutes ; 3, the 

 faculty of carrying on the operation of 

 the mind, which logicians call reason- 

 ing ; 4, the premiss or premises of an 

 argument, especially the minor premiss ; 

 and it is from Reason in this sense 

 that the word *' Reasoning" is derived; 

 5, lastly, it is often used to signify a 

 cause, as when we say, in popular lan- 

 guage, that the " Reason of an eclipse 

 of the sun is, that the moon is inter- 

 posed between it and the earth." This 

 should be strictly called the cause. 



" "What adds to the confusion is, that 

 the Cause is often employed as a Proof of 

 the effect : as when we infer, from a 

 great fall of rain, that there is, or will 

 be, a flood ; which is at once the physical 

 effect, and the logical conclusion. The 

 case is just reversed, when from a flood 

 we infer that the rain has fallen." 



REASONING IN A CIRCLE. A 

 fallacious mode of reasoning, in which 

 the truth of a proposition is asserted by 

 adducing the conclusion. The following 

 is Whately's illustration : — " To allow 

 every man an unbounded freedom of 

 speech must always be, on the whole, 

 advantageous to the state ; for it is highly 

 conducive to the interests of the com- 

 munity, that each individual should en- 

 joy liberty, perfectly unlimited, of ex- 

 pressing his sentiments." 



RECEIVER. A glass vessel employed 

 in pneumatical experiments for contain- 

 ing the object on which an experiment 

 is to be exhibited by means of the air- 

 pump. In Chemistry, the term denotes 

 a vessel fitted to the neck of a retort, 

 alembic, &c., for the purpose of receiving 

 the products of distillation. 



RECE'PTACLE. In Botany, the di- 

 lated and depressed axis of the inflores- 

 cence termed capitulum, constituting the 

 284 



seat of the artichoke, &c. The receptacle 

 is called torus or thalamus, and in Greek 

 compounds has the name of clinium. To 

 this part may be referred the gynophore, 

 the polyphore, and the gynobase of bo- 

 tanical writers. 



RECI'PROCAL {reciprocus, mutual; 

 flowing backward or forward). A term 

 employed in mathematics to denote a 

 fraction which is formed by inverting 

 another fraction ; thus ^ is the reciprocal 

 of 1 ; and j, the reciprocal of 7 or ^. A 

 reciprocal property is that which each of 

 two things has with reference to the 

 other; thus, if A and B are what is 

 called conjugate diameters of a conic 

 section, the tangent at either extremity 

 of A is parallel to B, and that at either 

 extremity of B is parallel to A. Hence, 

 these lines are reciprocally connected 

 with each other, and are therefore called 

 conjugate ; for the term conjugate, which 

 denotes joined, generally means joined 

 by a reciprocal property. 



RECTA'NGLE {rectum unguium ha- 

 bens). A geometrical term, denoting a 

 right-angled parallelogram, or any figure 

 of which all the angles are right angles. 

 A rectangle is said to be contained by any 

 two of its adjoining sides. The areas of 

 all figures whatever, whether bounded by 

 straight lines or curves, are expressed by 

 those of equivalent rectangles. 



RECTIFICATION. In Chemistry, 

 the repeating of a distillation or a sub- 

 limation several times, in order to ren- 

 der the substance purer and finer. 



RECTIFICATION (in Mathematics). 

 The finding of a right line equal in length 

 to an arc of a curve. The term is thus 

 analogous to that of quadrature, as ap- 

 plied to the finding of its area; for as an 

 area is considered to be found when a 

 square equal to it has been exhibited, so 

 the length of an arc is known when a 

 straight line equal to it has been found. 



RECTI LI'NEAL {recta linea, aright 

 line). A term applied in Geometry to all 

 figures which are contained by right lines, 

 as a triangle, a square, &c. 



RECURRING DECIMAL. Circula- 

 ting Decimal. For the exact expression 

 of a vulgar fraction by a decimal, the 

 former must either have, or be capable of 

 being reduced to another which has 10 

 or some power of 10 for its denominator. 

 Otherwise, the decimal will go on inter- 

 minably, the same figure or figures recur- 

 ring in the same order. These are called 

 recurring, repeating, or circulating deci- 

 mals, and the part repeated is called the 



