REP 



REP 



Repetend, Sinj(le, is ihat where only one figure is repeat- 

 ed, aa in o. 3 3 ^, Sec. 



Repetend, Compound, is that where two or more fifrures 

 are repeated, as in 0.09 09, &c. or in o. 142857 142857, 

 &c. 



Decimals with repetends may always be reduced to vulgar 

 fraftions ;' for either the repetend begins with the decimal, 

 or not. 



If the repetend begins with the firft place of decimals, 

 or if the decimal is a pure circulate, make it the numerator 

 of a vulgar fraftion, and make the denominator conlill of 

 as many 9's as the repetend has figures ; or if there be 

 cyphers between the point and repetend, with as many cy- 

 phers to the right hand of the denominator, then will this 

 rulgar fraftion be equal to the decimal. 



Thus, if the repetend be fingle, as in o. 3 3 3 3, the vul- 

 gar fradlion equal to it will be = -J- = \. So if the repe- 

 tend be compound, as in o. 09 09, &c. the equivalent vul- 

 gar fraftion will = -^ = ^ = ^. 



And in hkc manner o. 142857 1428.57, &c. = -tA4^^r 



The reafon is obvious from this confideration, that the 

 decimal o. 3 3 3, &c. is = -rV + -rrn- + -n>'uTs» &c. the 

 fum of which will be equal to -i?j divided by i — Vo- = -i 

 = i ; and lo of the rert. 



If the repetend does not begin with the firft place of de- 

 cimals, but at fome place farther on towards the right, or 

 if it be a mixed circulate, as in the decimal o. 8 3 3 3, &c. 

 where the repetend does not begin till the fecond place of 

 decimals, obferve, that o. 8 3 3 5 + &c. = tV + ttu + 

 -n^ + &C. = -rV + rV X ,\ + A -■ + &C. But ^\ 

 + .,>r, 4. &c. = f = 4, as before: therefore the pro- 



... 24 -t- 1 

 pofed decimal is = -^- -[- Vr X -i = A + iV = 



IS — s 



"STT — ly' 



Thus alfo if the decimal o. 2 27 27, Sec. were propofed, 

 we ftiall find it = tV + tV X t'oV + toV' + Sec. And 

 -nrV + -tV-t.' + Sec. being t|- = -At the decimal will be — 



+ 



= tV + 



The reafon 



_22J-3 _ , 



of which is obvious from what has been faid. 



It may, perhaps, be worth while to obferve, that if tlie 

 numerator of a vulgar frattion be unity, and the denominator 

 any prime number, except 2 and 5, the decimal equal to the 

 propofed fradlion will always be a repetend, beginning at the 

 firft place of decimals ; and this repetend muft neceflarily be 

 a fubmultiple, or an aliquot part of a number exprefTed by 

 as many nines as the repetend has figures ; that is, if the 

 repetend have fix figures, it will be a fubmultiple of 999999 ; 

 if four figures, it will be a fubmultiple of 9999, &c. From 

 whence it follows, that if any prime number be called^, the 

 feries 9999, &c. produced as far as is neceflary, will always 

 be divifible by^, and the quotient will be the repetend of the 



decimal fraftion = — • For the manaprement of decimals 



P 

 of this kind, fee Malcolm's Arithmetic, book v. chap. 4. 



REPETITION, Repetitio, the reiterating of an ac- 

 tion. See Reiteration. 



Habits arc acqiured by the frequent repetition of aftions. 



School-philofoplicrs call the repetition of the fame nume- 

 rical effeft, in another place, the replication of that effe<S. 



Repetition. The Freixh make ufe of this word for a 

 rehearfal, which the Itahans call a pro'va. " Rehearfals 

 (fays Roufleau) are neceflary for compofitions that are 

 to be performed in public, in order to prove whether the 



feveral parts are correctly copied, and for aftertaiiiing tin- 

 entrances and tlic exits of the foveral charafters, as well at. 

 to fee that they fcizc the Ipirit of their parts, and of the 

 entire drama. Rehearfals are likewife of ufe even to the 

 compofer himlelt, to enable him to judge of effefts, and tO' 

 make fuch changes as may feem necetfary." 



Repetition, in Muju, denotes a reiteration or playing 

 over again the fame part of a compofition, whether it be a 

 whole ftrain, or part of a ftrain, or a double ftrain. The 

 repetition is denoted by a charafter called a repeat ; which 

 is varied fo as to exprefs the various circumllances of the 

 repetition. 



Repetition, R'plyy is alfo ufed when, after a little 

 filence, one part repeats or runs over the fame notes, the 

 fame intervals, tTle fame motions ; in a word, the fame 

 fong, which a firft part had already gone over during the 

 filence of this. 



Repetition, Ripiy, is alfo a doubling or trebling, &c. 

 of ail interval, or reiteration of fome concord or difcord. 



Thus, a fifteenth is a repetition ot the otlave, ». e. a double 

 octave, or feoond oftave. 



Repetition of Pajfages. See Rosalia. 

 Repetition, in Rhetoric, is a figure by which the orator 

 rchcarfcs the fame words or phrafes over again. 



Of this there are two kinds. In the firft, the word is 

 repeated precifely iu the fame fenfe : as. Oh, Jerufalcm, Je- 

 rufalem, ivho k'dlejl the prophets, &c. My God, my God, ivhy 

 hnjl thru forfalen me? 



Such repetitions have the fame cfFedt in difcourfe, with 

 fecond ftrokes of the pencil in painting ; they render the 

 colours more ttrong and lively. 



Sometimes the orator begins again and again with the 

 fame word, of which we have an inftance in the beginning of 

 Cicero's firft oration againft Catiline : N'thUne noHurnum pm- 

 Jidium palatii, nihil urbis I'igilix, nihil timor populi, nihil con- 

 fenfus bonorum omnium, nihil hie miinitijjimus habendi fcnatus 

 locus, nihil horum ora •uultufque mo'veruni ? Where the word 

 tiihd fo often reiterated gives an admirable force and vehe- 

 mence to the difcourfe. Again, the fame author : Ouem 

 fenatus damndrit, quern populus R. damnarit, quern omnium ex- 

 yiimatio damndrit, eum "vcs Jententiis tiejlris abfolvetu '4 Again, 

 Non feram, non patiar, nonfinam. 



The fecond kind of repetition, called TOXoi<r, place, (which 

 fee,) is a repetition of the fame word in the fame phrafe ; 

 but in fuch a manner, as that fome new idea or charafter is 

 added to the word in the fecond, which it had not in the 

 firft. 



As, Cory don is always Cory don : E< illo Cory don Corydon 

 efl tempore nobis ; by which we fignify, that Corydon is no 

 ordinary perfon ; and that nothing can diftinguifh him but 

 the repetition of his own name : as if we fhould fay, he it 

 Corydon, that is enough. By the fame figure our Saviour 

 fpeaks, when he fays : Let your language be yea, yea ; and 

 nay. nay. See Recapitulation. 



REPETITUM, or Vetitum Namium, in La-ai. See 

 Namium. 



REPHAM, or Reepham, in Geography, a market-town 

 and parifh in the hundred of Eynsford, and county of Nors. 

 folk, England, is fituated at the diftance of 13 miles N.W. 

 by N. from Norwich, and 112 N.E. by N. from London. 

 The charter for its market, which is held on Saturday week- 

 ly, was obtained by fir John de Vaux, iu the fifth year of the 

 reign of king Edward V. An annual fair, on the 29th of 

 June, was granted at the fame time. At one period thk 

 parilb was remarkable for having three churches fituated 

 within one fepulchral inclofure ; -viz.. Reepham, Whitwefl, 

 and Hackford ; but only two of thefe are now ft.anding. 

 5 The 



