RAT 



We cannot extend onr remarks to a greater leiiffth in 

 this article ; we miift, therefore, refer the reader who wiflies 

 to fee thefe principles more completely developed, to Euler's 

 Analyfis Infinitorum, vol. i. ch. 2 and 1 1 ; to La Croix's 

 Algebra, and his Calcul Difl'erentiel et Calcul Integral. 

 See alfo Bonnycallle's Algebra, and Simpfoii's Fluxions. 



Rational or true bnr'rzon, is that wliofe plane is con- 

 ceived to pafs through the centre of the earth; and which 

 therefore divides the globe into two equal portions, or he- 

 mifpheres. See HoiuzoN. 



It is called the rational horizon, becaufe only conceived 

 by the underftanding ; in oppofition to the feti/i/i/e or appa- 

 rent horizon, which is vifible to the eye. 



Rational integer, or whole number, is that of which 

 unity is an aliquot part. See Number, and Aliquot />«;■/. 

 Rational tnixt number is that confiding of an integer, 

 and a fraftion ; or of unity, and a broken number. 



Commenfurable quantities are defined by being one to 

 another as one rational number to another. 



For unity is an aliquot part of a rational nvimber ; and 

 a fraftion has fome aliquot part common with unity ; in 

 things, therefore, that are as a rational to a rational number, 

 either the one is an aliquot part of the other, or there is 

 fome common aliquot part of both ; therefore they are com- 

 menfurable. 



Hence, if a rational number be divided by a rational, the 

 quotient is always a rational. 



Rational Phyfuians, in ancient medical hiftory, the phy- 

 ficians of the dogmatic fedt, who flood in oppofition to the 

 empiric feft ; the former appeahng to certain theoretical prin- 

 ciples in the application of remedies, while the latter refted 

 entirely upon experience, and difclaimed all knowledge of 

 firft principles. The tenets of both thefe fefts have been 

 handed down to us by a claflic author, Celfus, and have 

 been given at length under a former article. See Empiric. 

 Rational Quantity, or number, a quantity or number 

 commenfurable to unity. 



Suppofing any quantity to be i, there are infinite other 

 quantities, fome of which are commenfurable to it, either 

 fimply, or in power : thefe EucUd calls rational quantities. 

 Tiie reft, that are incommcnfurable to i, he calls irrational 

 quantities, or fur ds. 



Rational Ratio. See Ratio. 

 Rational Soul. See Soul. 



RATIONALE, a folution or account of the principles 

 of fome opinion, aftion, hypothefis, phenomenon, or the 

 like. Hence, 



Rationale is alfo the title of feveral books. The moft 

 confiderable is the " Rationale of Divine Offices," by Guil. 

 Durandus, a celebrated fchool-divine, bilhop of Mcnde, 

 finifhed in 1286, as he himfelf tells us. See Printing. 



Rationale alfo denotes an ancient facerdotal veftment, 

 worn by the high-prieit under the old law ; and called by the 

 Hebrews, 'jyrt' hhojchen ; by the Greeks, Xoyiov ; by the 

 Latins, rationale 3x\A peciorale ; and by the Englifh tranflators, 

 breajl-plate. 



The rationale was a piece of embroidered ftuff worn on 

 the breaft, about a fpan fquare. Du-Cange defcribes it as 

 a double fquare of four colours, interwoven with gold, 

 and fet with twelve precious ftones in four rows, on which 

 were engraven the names of the twelve tribes, and faltened 

 to the (houlder by two chains and two hooks of gold. The 

 form of the rationale was prefcribed by God himfelf, Exod. 

 xxviii. 15 — 29. 



A rationale appears alfo to have been anciently worn by 

 the bilhops under the new law. But authors are in doubt 



RAT 



about its form ; fome will have it referable that of the Jews ; 

 otiiers take it to be only the pallium. 



RATIONALIS, an officer mentioned in feveral ancient 



infcriptions. 



Lampridius, in the life of Alex. Severus, ufes rationalis 

 as fynoiiimous with procurator. 



The rationales were intendants or furveyors under the 

 emperors ; and though Lampridius pretends they were firft 

 cftablifhed by Severus, it is evident there were fome under 

 Auguftus. 



RATIONARIUM, among the Romans, a book which 

 contained the accounts of the empire. It was othervnfe 

 called hreviarium. Sec BllEVlARV. 

 RATIONIS Ens. See Ens. 

 Rationis DiJiinBio. See Distinctio. 

 Rationis Os, in Anatomy, the bone of the forehead, 

 othcrwife called os frontis. 



RATISBON, or Regenspeug, in Geography, an im- 

 perial city of Germany, in the circle of Bavaria, and capital 

 of a bifhopric of the fame name, fituated at the conflux of 

 tlie Regen and of the Danube. The town is large, populous, 

 and fortified ; and was anciently the capital of Bavaria, and 

 the refidence of its dukes. The emperor Frederic I. an- 

 nexed it to the empire. This town is a ftaple, but neither 

 its manufactures nor trade are very confiderable ; corn, 

 wood, and provifions, are fent by the Danube to Vienna. 

 The number of inhabitants is about 24,000 ; 62 miles N.E. 

 of Augfljurg. N. lat. 48^ 55'. E. long. 12° 50'. 



The bifhopric of Ratilbon comprehends about 1383 pa- 

 rifhes ; and was founded, as it has been fuppofed, by St. 

 Boniface, in the year 736. The feat of the bifliop is at 

 Ratifbon, where, however, he has no jurifdiftion. 



RATISKA, a town of Immeritia ; 35 miles N.E. of 

 Cotatis. 



RATKAI, George, in Biography, born in 1613, of a 

 noble family, in Hungary, entered into holy orders, and 

 was made canon of the church of Zagrab. He obtained 

 the efteera of the viceroy of Croatia, John Dralkovitz, 

 who engaged him to compofe the liiftory of that province, 

 and gave him free accefs to its archives. He accordingly 

 publilhed, in 1652, a very learned work, entitled " Me- 

 moria Regum et Banorum regnorum Dalmatiae, Crotiae, 

 Slavonias, inchoata ab origine fua ufque ad annum." Gen. 

 Biog. 



RATLINES, or, as the feamen call them, Rutlins, or 

 RattUngs, are certain fmall lines which traverfe the ilirouds 

 of a fliip horizontally, at regular diftances above the dead- 

 eyes upwards, and forming a variety of ladders, whereby 

 to climb to any of the mail -heads, or defcend from them. 

 Hence the term feems to be derived from rath, an ob- 

 folete word, fignifying a hill. In order to prevent the 

 rattling from flipping down by the weight of the failors, 

 they are firmly attached by a knot, called a clove-hitch, to 

 all the fhrouds, except the foremoft or aftmolt ; where one 

 of the ends, being fitted with an eye-fplice, is previoufly 

 fattened with twine -thread or pack-thread. Falconer. 



RATNO, in Geography, a town of Lithuania, in the 

 palatinate of Brzefc ; 50 miles S.E. of Brzefc. 



RATOATH, a poor village of the county of Meath, 

 Ireland, which, before the union, had its reprefentatives in 

 pai-liament. It gave name to a barony, and is 12^ miles 

 N.W. by N. from Dublin. 



RATOLY, a town of Hindooftan, in the circar of 

 Gohi'.d ; 25 miles S.E. of Raat. 



RATONES, a fmall ifland in the river La Plata, near 

 Monte Video. 



RATSCHA, 



