pnugues/EB7 huggingface dataset:
RATIO, in Arithmetic and Geometry, is that relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.

The numbers, lines, or quantities, A and B, being proposed, their relation one to another may be considered under one or other of these two heads: 1. How much A exceeds B, or B exceeds A; which is found by taking A from B, or B from A, and is called arithmetical reason or rαtia. 2. How many times, or parts of a time, A contains B, or B contains A; which is called geometrical reason or ratio, or, as Euclid defines it, the mutual habitude, or respect, of two magnitudes of the same kind, according to quantity, that is, llow often the one contains or is contained in the other; and this is found by dividing A by B, or B by A. But observe, that that quantity which is referred to another quantity is called the antecedent e>f the ratio; and that to which the other is referred is called the consequent of the ratio. In the ratio of A to B, A is the antecedent, and B the consequent. Therefore any quantity as antecedent, divided by any quantity as a consequent, gives the ratio of that antecedent to the consequent.

Thus the ratio of A to B is ∙q r , but the ratio of B to A is B

B 12

—; and, in numbers, the ratio of 12 to 4 is — = 3, or tri-A ⅛

4 1

ple; but the ratio of 4 to 12 is — = -, or subtriple.

1 <~ «5

And here observe, that the quantities thus compared must be of the same kind; that is, such as by multiplication may be made the one to exceed the other, or as these quantities are said to have a ratio between them, which, being multiplied, may be made to exceed one another. Thus a line, how short soever, may be multiplied, that is, produced so as to exceed any given right line; and consequently these may be compared together, and the ratio expressed. But as a line can never, by any multiplication whatever, be made to have breadth, that is, to be equal to a superficies, however small, so these can never be compared together, and consequently have no ratio or respect to one another, according to quantity; that is, how often the one contains or is contained in the other.
RATION, in an army, a portion of ammunition, bread, drink, and forage, distributed to each soldier for his daily subsistence. The horse have rations of hay and oats when they cannot go out to forage.
RATIONALE, a solution or account of the principles of some opinion, action, hypothesis, or phenomenon.
RATIOS, of musical intervals. See articles Mnsic and Temperament.
RATISBON, or, as called by the Germans, Reosnb-
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burg, a city of the modern kingdom of Bavaria, the capital of the circle of that name. This city in ancient times, though under the protection of the elector of Bavaria, was considered as an imperial city, and the diets of the German empire were frequently held within it. It was then the see of an archbishop, and remarkable for its zealous adherence to the Catholic church. It was the scene of one of the most bloody conflicts during the Thirty Years’ War, when the army of the imperial general Wallenstein was intrenched before it, and the Swedish monarch Gustavus Adolphus made re-, peated but ultimately unsuccessful attempts to storm the works, and lost so many men that he was compelled to retreat. It suffered much during the war between the French and Austrians in 1809.

Ratisbon was a place of much greater relative importance in former times than it is at present, having then the exclusive right to all the trade by the river Danube, both upwards as far as Ulm, and downwards as far as Vienna.

The city stands on the river Danube, at the spot where the river Regen 1 from which its German name is derived, falls into that great stream. The bridge over the Danube connects the several parts of the city. It is still in an imperfect degree fortified, but is totally indefensible against any armed force. The buildings are of antique models, particularly the ancient council-house, in which the representatives of all the states of Germany were accustomed to assemble. The cathedral is a large Gothic building; as are the church of St Emeran and the Lutheran church of the Holy Trinity, the latter of which was the college of the Jesuits till the abolition of the order.

The population, which in 1811 amounted to 18,843 persons, has much increased, and was found in 1837 to be 26,550. Of these, about one third are Lutherans; and two thirds, comprehending almost the whole of the labouring classes, are Roman Catholics. The former party have a gymnasium, and the latter a lyceum. There is a learned society, who have a botanical garden and a respectable library, with a museum of mathematical and philosophical instruments, and a picture-gallery. There are manufactures of morocco leather, many tanneries, soap-makers, wax and tallow chandlers, with large breweries and distilleries. On the banks of the Danube are some establishments for building barques and boats for navigating that river. The transit trade between eastern and western Germany gives employment to several respectable mercantile houses. A project, now considerably advanced, gives hope to the inhabitants of this city of a much greater portion of transit commerce. The Royal Bavarian Canal is hastening to its completion, and will open a communication by water between the Rhine and the Danube, the whole length being within the dominions of Bavaria. It commences at the river Mayn, which empties itself into the Rhine, and will terminate in the Danube, near this city. It is hoped that the timber of Bavaria will thus find a market in Hungary, and the surplus corn of that kingdom a constant vent on the banks of the Rhine, especially in Holland.
RATLINES, or, as the sailors call them, ratlins, those lines which make the ladder-steps to go up the shrouds and pattocks, hence called the ratlins of the shrouds.
RATTIBOR, a city, the capital of a circle of the same name, in the Prussian government of Oppeln, in Silesia. It stands on the left bank of the Oder, is surrounded with walls, and contains six Catholic and one Lutheran church, three hospitals, 4300 houses, and 4100 inhabitants. It has considerable trade in linen and woollen goods, in hosiery, and in timber, and has several distilleries and breweries.
RATTOLAW, a seaport of Hindustan, in the province of Gujerat, and gulf of Cambay, is situated on a navigable river. It was ceded to the East India Company by the Guicowar, the Mahratta chief, in 1803. It is forty-four miles south-west from the city of Cambay. Long. 72. 15. E. Lat 22. 3. N.
RAUJESHY, a district in Bengal, situated principally between the twenty-fourth and twenty-fifth degrees of north latitude. It is bounded on the north by Dinagepoor and Mymunsingh; on the south by Birbhoom and Kishenagur; on the east by Dacca, Jelalpoor, and Mymunsingh; and on the west by Monghir and Birbhoom. It is the most unwieldy zemindary in Bengal, comprehending an area of 12,909 square miles, and is intersected in its whole length by the Ganges and its lesser branches, with many navigable rivers and fertilizing streams. In answer to the inquiries of the Marquis Wellesley in the year 1801, the population was returned at 1.500,000.
RAUKOKE, one of the Kurile Islands, which is small and lofty, with a rocky shore.
RAUN, a town of some strength, situated upon the river Miza, and remarkable for a bloody skirmish between the Prussians and Austrians, in August 1744. The king of Prussia, intending to get possession of Beraun, sent thither six battalions, with eight cannon, and 800 hussars; but General Festititz being there with a great party of his corps, and M. Luchesi with 1000 horse, they not only repulsed the Prussians, but attacked them in their turn, and, after a warm dispute, obliged them to retire with considerable loss.
RAVA, a town of Asiatic Turkey, situated on the Euphrates, about half-way between Kerkesich and Anna. It contains about 200 houses in the midst of extensive ruins; but many of these houses are uninhabited. On the opposite side of the river are the ruins of a castle, on the summit of a rock.
RAVELIN, in Fortflcation, was anciently a flat bastion placed in the middle of a curtain; but it is now a detached work, composed only of two faces, which form a salient angle without any flanks, and are raised before the counterscarp of the place. See Fortification.
RAVENNA, a delegation of the States of the Church, in Italy, in the northern part of the ancient Romagna. It is 935 square miles in extent, and contains four cities, eight market-towns, many villages, and 123,760 inhabitants. It is a level district on the sea-coast, with numerous saline lakes, but towards the west there are some gentle undulations. It is moderately fertile, and is drained by the rivers La-mone, Lanterno, and their tributary streams. The capital is the city of the same name, which is of high antiquity. It was formerly on the sea-shore, but, by the recession of the water, is now three miles from it. It is in a marshy situation, surrounded by walls of no great strength. It is the see of a bishop, has a cathedral, twenty-one parish churches, twelve monasteries, five nunneries, a public library, an hospital, and some schools. It contains in the city 16,000 inhabitants, but, including the suburbs and some adjacent villages, the population amounts to 23,930. It was formerly the capital of the kingdom of the Ostrogoths, and, in later times, of an exarchate. There are now to be seen the remains of some old Gothic castles. Long. 12. 5.31. E. Lat. 44. 25. 5. N.
RAVENSBURG, a city of the kingdom of Wirtemberg 1 in tile circle of the Danube, and the capital of a bailiwick of the same name. It stands on the river Schussen, and is surrounded with walls, defended by several ancient towers. It contains 870 houses, with 3760 inhabitants, one half Catholics and the other Protestants. It has several sawmills, and manufactories of cottons, hosiery, iron and wood ware; and it grows good wine. Long. 9.32. E. Lat. 47.46. 55. N.
RAVEY, the ancient Hydraotes, a celebrated river of Hindustan, and the third river of the Punjab. It rises in the eastern mountains of Cashmere, near a famous place of Hindu worship, not far from the sources of the Sutulege, the Chunaub, and the Beyah rivers. It afterwards runs in a south-westerly direction until it passes the city of Lahore, sixty miles above which it is 120 yards broad, and extremely rapid, yet navigable during the rains for boats of a considerable size. It flows in the same direction after passing the city of Lahore, and it is joined about twenty-eight miles above the city of Moultan by the Jhylum and the Chunaub rivers, forming a stream in some places several miles in breadth, and scarcely inferior to the Indus itself. Immediately after their junction it is one mile, one furlong, and eighty-five yards, but lower down the stream is contracted in its breadth to less than 350 yards. Seventy miles below Moultan the Ravey joins the Indus after a course, including its windings, of 500 miles. The water is light and wholesome.
RAVILPANDY, a large and populous town of Hindustan, in the district of the Punjab, situated about half way between the Indus and the Hydaspes rivers. The houses are flat-roofed, and the surrounding country is open and well cultivated. This place was visited by Mr Elphinstone in 1809. It belonged to Jewun Sing, a Sikh chief.
RAVREE, a town of Hindustan, in the Western Ghauts, and province of Bejapoor. It was the first stronghold seized by Sevajee, the great founder of the Mahratta power. It is forty-five miles south-south-west from Poonah. Long. 73. 32. E. Lat. 18. 2. N.
RAWAAD, a small town of Hindustan, in the province of Lahore, in the Sikh territories, 120 miles north-west from the city of Lahore. Long. 72. 12. E. Lat. 33. 5. N.
RAWAK, Isle, a small island in the Eastern Seas, off the north coast of Waygiou, with which it forms a harbour. The channel is here a mile broad, with a depth of from ten to fifteen fathoms, and a mud bottom. Sago, in cakes, is sold here in large quantities. Fish and turtle may also be had. Long. 131. 15. E. Lat. O. 3. N.
RAWANKRAD, a celebrated lake in the mountains of Thibet, on the north of the great Himalayah range. It is the source of the river Sutulege, and is connected with the lake Mansarowar. The lake is long and narrow, and is divided by an island. It derives its supplies from several small rivers that flow from the mountains, and also from the melting of the snows. The situation is about the thirty-first degree of north latitude, and near it may be seen Mount Cailas, a well-known scene of Hindu fable, covered with perpetual snow.
RAWCLIFFE, a town of the west riding of Yorkshire, in the parish of Snaith 1 and wapentake of Osgoldeross, 176 miles from London. It has some trade by the river Aire, which is navigable beyond it. The population amounted in 1801 to 920, in 1811 to 1143, in 1821 to 1496, and in 1831 to 1450.
RAWICZ or Rawitsch, a city of the Prussian province of Posen, in the circle of Kobben. It is surrounded with walls, is well built and paved, and, including the suburbs, contains 1100 houses, with 8640 inhabitants, who are occupied in making linen, woollen, and cotton goods, mostly by machinery, and in tanning and currying leather. Of the inhabitants, 1500 are Jews.
RAYLEIGH, a town of the county of Essex, in the hundred of Rochford, thirty-five miles from London. It stands on a creek of the Thames called Hadley Bay, in consequence of which it has a good trade in corn. The popu[7:19:79]Iation amounted in 1801 to 897, in 1811 to 1131, in 1821 to 1203, and in 1831 to 1339.
RAYPOOR, a town of Hindustan, in the Sikh territories, and province of Lahore, on the banks of the Beyah and Hydaspes. It is celebrated as the birthplace of Nanac, the founder of the Sikhs.
RAYSINGPOOR, a small village of Hindustan, in the Gujerat peninsula, near the Gulf of Cutch. It is situated on the banks of the Phooljee river, and in its vicinity are gardens in which cardamums are raised.
RAYUN, a town of Persia, in the province of Kerman, situated at the foot of lofty mountains, and surrounded by numerous gardens.
RE, an island on the coast of France, in the department of La V endée, and the arrondissement of Rochelle. It stands about seven miles from the mainland, has a very irregular shape, is eleven miles in length, and in the widest part three miles in breadth. The chief town is St Martins, which has 3000 inhabitants, and is defended by a strong citadel. The soil is fertile, yielding abundance of grapes, which are mostly used to make brandy; and on the shore much salt is made. There are two other towns, called La Flotte and Ars, of more than 3000 inhabitants each; and the whole population of the island amounts to 18,540. It was attacked by the English in the reign of Charles I., after the Duke of Buckingham’s unsuccessful attempt to relieve Rochelle in 1627, but was able to resist. Long. 1. 33. 25. E. Lat. 46. 14. 47. N.

Re, in Grammar, an inseparable particle prefixed to the beginning of words, to double or otherwise modify their meaning; as in re-action, re-move, re-export, and the like.
RE-ACTION, in Physiology, is the resistance made by all bodies to the action or impulse of others which endeavour to change their state, whether of motion or rest.
RE-AGGRAVATION, in the Roman ecclesiastical law, the last monitory, published after three admonitions, and before the final excommunication. Previous to fulminating the last excommunication, they publish an aggravation and a re-aggravation. Fevret observes, that in France the minister is not allowed to come to re-aggravation, without the permission of the bishop or official, as well as that of the lay judge.
REALISTS, a sect of scholastic philosophers formed in opposition to the Nominalists. Under the realists are included the Scotists, Thomists, and all excepting the followers of Ocham. Their distinguishing tenet is, that uni-versals are realities, and have an actual existence out of idea or imagination, or, as they express it in the schools, a parte rei; whereas the nominalists contend that they exist only in the mind, and are merely ideas, or manners of conceiving things. Odo, or Oudard, a native of Orleans, afterwards abbot of St Martin de Tournay, was the chief of the sect of the Realists. He wrote three books of dialectics, in which, on the principles of Boethius and the ancients, he maintained that the object of that art was things, not words, and hence the sect took its rise and name.
REALITY, in the schools, a diminutive of res, thing, was first used by the Scotists, to denote a thing which may exist of itself; or which has a full and absolute being of itself, and is not considered as a part of any other.
REALM, a country which gives its head or governor the denomination of a hing.
RE-ANIMATION, means the reviving or restoring to life those who are apparently dead. Sudden death is dreaded by every human being, and it is one of those evils against which the Church of England prays in her litany. Accidents, however, cannot always be prevented; but, after they have happened, it is often possible to prevent their effects. By the establishment of what has with great propriety been called the Humane Society, this has been abundantly proved; for, in the course of twelve years immediately after its institution, it was the means of saving the lives of 850 persons, who otherwise would in all human probability have been lost to the community. Since that period it has saved many more; and various persons, even in the most distant parts of the kingdom, have done the same by following the directions prescribed. To preserve one human being from premature death, we must consider as of the utmost consequence, both as citizens and Christians; and how much more the preservation of thousands? It appears from the writings of Mead, Winslow, Bruhier, Fothergill, Haller, Lecat, Tissot, Van Engelen, Gummer, and others, that they had prepared the way for institutions similar to the Humane Society; for in their works they have elucidated the principles on which such institutions proceed, and furnished directions for the practice they favour.
REAR, a term frequently used in composition to denote something behind or backwards in respect of another. It is used in opposition to van. Rear of an Army signifies, in general, the hindmost part of an army, battalion, regiment, or squadron; and also the ground behind either.

REAR-Guard is that body of an army which marches after the main body. The march of an army is always composed of an advanced guard, a main body, and a rearguard; the first and last commanded by a general.

REAR Half-files are the three hindmost ranks of the battalion when it is drawn up six deep.

REAR-Line of an army encamped, is always twelve hundred feet at least from the centre line, both of which run parallel to the front line, as also to the reserve.

REAR-Ranh is the last rank of a battalion when drawn up, and generally sixteen or eighteen feet from the centre line when drawn up in order.
REASON, a faculty or power of the mind. See the article Metaphysics.
REASONING, Ratiocination, the exercise of that faculty of the mind which is called reason; or it is an act or operation of the mind, deducing some unknown proposition from other previous ones that are evident and known. See the article Logic.
REBATE or Rebatement, in Commerce, a term much used at Amsterdam for an abatement in the price of seve-

VOL. XIX.

ral commodities, when the buyer, instead of taking time, advances ready money.

Rebatement, in Heraldry, a diminution or abatement of the bearings in a coat of arms.
REBELLION, Rebellio, amongst the Romans, was where those who had been formerly overcome in battle, and yielded to their subjection, made a second resistance. But with us it is generally used for the taking up of arms traitorously against the king, whether by natural subjects or others when once subdued; and the word rebel is sometimes applied to him who wilfidly breaks a law, as also to a villein disobeying his lord.

There is a difference between enemies and rebels. Enemies are those who are out of the king’s allegiance; and therefore subjects of the king, either in open war or rebellion, are not the king’s enemies, but traitors. Thus David prince of Wales, who levied war against Edward L 1 because he was within the allegiance of the king, had sentence pronounced against him as a traitor and a rebel. Private persons may arm themselves to suppress rebels.
REBUS, an enigmatical representation of some name or thing, by using figures or pictures instead of words or parts of words. Camden mentions an instance of this kind of wit in a gallant who expressed his love to a woman named Rose Hill, by painting in the border of his gown a rose, a hill, an eye, a loaf, and a well; which, in the style of the rebus, reads, “Rose Hill I lave well.” This kind of wit was long practised by the great, who took the pains to find devices for their names. It was, however, happily ridiculed by Ben Jonson in the humorous description of AbelDrug-ger’s device in the Alchemist, by the Spectator in the device of Jack of Newberry, at which time the rebus, being raised to sign-posts, was grown out of fashion at court.

Rebus is also used by the chemical writers, sometimes to signify sour milk, and sometimes for what they call the ultimate matter of which all bodies are composed. Rebus, in Heraldry, is a coat of arms which bears an allusion to the name of the person; as three castles for Castleton, three cups for Butler, three conics for Conisby; a kind of bearings which are of great antiquity.
RECANATI, a city of Italy, in the delegation of Macerata, in the papal dominions. It is situated on a mountain overlooking the Adriatic Sea. It is the seat of a bishop in union with the city of Loretto, and has a cathedral, eight parish churches, eight monasteries, and four nunneries. It is well built, and has a haven at the mouth of the Potenza, with a population of 5990 persons. Long. 13. 27. 48. E. Lat. 43. 25. 40. N.
RECENSIO, was an account taken by the censors, every lustrum, of all the Roman people. It was a general survey, at which the equites, as well as the rest of the people, were required to appear. New names were now put upon the censor’s list, and old ones cancelled. The recensio, in short, was a more solemn and accurate sort of probatio, and answered the purpose of a review, by showing who were fit for military service.
RECHABITES, a kind of religious order amongst the ancient Jews, instituted by Jonadab the son of Rechab, comprehending only his own family and posterity. Their founder prescribed them three things: first, not to drink any wine; secondly, not to build any houses, but to dwell in tents; and, thirdly, not to sow any corn or plant vines.
RECHEAT, in hunting, a lesson which the huntsman plays on the horn, when the hounds have lost their game, to call them back from pursuing a counter scent.
RECHERCHE, Archipelago, agroup of islands stretching about 126 miles along the south coast of New Holland, between the thirty-third and thirty-fourth degrees of south latitude. Several of them are naked rocks; and from the coast of New Holland the access is extremely difficult, owing to the rocks and shoals that are interspersed.
RECIPROCAL, in general, is something that is mutual, or which ls returned equally on both sides, or affects both parties alike.

. Reciprocal, in Mathematics, is applied to quantities which, multiplied together, make unity. Thus - and x, y and -, are reciprocal quantities. Likewise - is said to be y % reciprocal of x, which is again the reciprocal of X

in Geometry, those which have the antecedents and consequents of the same ratio in both figures.

is when, in four numbers, the fourth is less than the second by as much as the third is greater than the first, and vice versa. Great use is made of this reciprocal proportion by Sir Isaac Newton and others, in demonstrating the laws of motion.

amongst logicians, are those which have the same signification, and consequently are convertible, or may be used for each other.