A-es sentence example

a-es
  • They were a well-traveled group for their uniformly young ages.
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  • Dean said, a little too loudly, just as the waitress arrived with the ginger ales.
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  • Aguilar "of the Frontier" was so named in the middle ages from its position on the border of the Moorish territories, which were defended by the castle of Anzur, now a ruin; but the spacious squares and modern houses of the existing town retain few vestiges of Moorish dominion.
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  • This is the reassertion of a principle which the middle ages had lost sight of - that knowledge, if it is to have any value, must be intelligence, and not erudition.
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  • The problem of the curves is solved by their reduction to a problem of straight lines; and the locus of any point is determined by its distance from two given straight lines - the axes of co-ordinates.
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  • The Roman emperors recognized it as a free state, and in the middle ages it was called Stampalia, and belonged to the noble Venetian family of Quirini.
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  • As a child she had already believed herself to have visions; these now became more frequent, and her records of these "revelations," which were tanslated into Latin by Matthias, canon of Linkoping, and by her confessor, Peter, prior of Alvastra, obtained a great vogue during the middle ages.
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  • The determination with which this remarkable race has maintained its mountain stronghold through a long series of ages has hitherto met with scant appreciation in the outside world.
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  • Avranches, an important military station of the Romans, was in the middle ages chief place of a county of the duchy of Normandy.
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  • Primary Inslruction.All primary public instruction is free and compulsory for children of both sexes between the ages of six and thirteen, but if a child can gain a certificate of primary studies at the age of eleven or after, he may be excused the rest of the period demanded by law.
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  • The intelligence was made known in April or May; and then began a rush of thousands, - men leaving their former employments in the bush or in the towns to search for the ore so greatly coveted in all ages.
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  • During the whole of the middle ages Tournai was styled the "seigneurie de Tournaisis," and possessed a charter and special privileges of its own.
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  • It was a popular opinion in the middle ages that extreme unction extinguishes all ties and links with this world, so that he who has received it must, if he recovers, renounce the eating of flesh and matrimonial relations.
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  • Yet he cannot deny that "he had some virtues which have caused the memory of some men in all ages to be celebrated"; and admits that "he was not a man of blood," and that he possessed "a wonderful understanding in the natures and humour of men," and "a great spirit, an admirable circumspection and sagacity and a most magnanimous resolution."
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  • It is situated on the canal from Bruges to Sluys (Ecluse), but in the middle ages a navigable channel or river called the Zwyn gave ships access to it from the North Sea.
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  • In the middle ages it was the seat of a large trade in linen.
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  • In the middle ages Teignmouth was a flourishing port, able to furnish 7 ships and 120 mariners to the Calais expedition of 1347, and depending chiefly on the fishing and salt industries.
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  • The Breisgau, originally a pagus or gau of the Frankish empire, was ruled during the middle ages by hereditary counts.
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  • The space thus included was known in ancient times as Venetia, a name applied in the middle ages to the well-known city; the eastern portion of it became known in the middle ages as the Frioul or Friuli.
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  • This constitution of the great mass of the central Apennines has in all ages exercised an important influence upon the character of this portion of Italy, which may be considered as divided by nature into two great regions, a cold and barren upland country, bordered on both sides by rich and fertile tracts, enjoying a warm but temperate climate.
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  • Unfortunately several of these fertile tracts suffer severely from malaria (q.v.), and especially the great plain adjoining the Gulf of Tarentum, which in the early ages of history was surrounded by a girdle of Greek cities—some of which attained to almost unexampled prosperity—has for centuries past been given up to almost complete desolation.
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  • This shows a considerable improvement, largely, but not entirely, in the diminution of infant mortality; the expectation of life at birth in 1882, it is true, was only 33 years and 6 months, and at three years of age 56 years I month; but the increase, both in the expectation of life and in its average duration, goes all through the different ages.
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  • above the sea, in a fertile but somewhat marshy district, which in the middle ages was very malarious.
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  • We can distinguish (I) digestive endoderm, in the stomach, often with special glandular elements; (2) circu-, latory endoderm, in the radial and ring canals; (3) supporting endoderm in the axes of the tentacles and in the endodermlamella; the latter is primitively a double layer of cells, produced by concrescence OC-- = w.?"
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  • Throughout the middle ages the sancta civitas Trevirorum abounded in religious foundations and was a great seat of monastic learning.
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  • A closer scrutiny of the writers of all ages who preceded Charles Darwin, and, in particular, the light thrown back from Darwin on the earlier writings of Herbert Spencer, have made plain that without Darwin the world by this time might have come to a.
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  • Such a comparison is necessarily illogical, as the existing apes are separated from the common ancestor by at least as large a number of generations as separate it from any of the forms of existing man.
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  • of supporting axes from assimilating appendages, and as the body increases in size and becomes a solid mass of cells or interwoven threads, a corresponding differentiation of a superficial assimilative system from the deep-lying parts.
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  • Later, the axis branches by the formation of new growing-points, and in this way the complex system of axes forming the body of the ordinary vascular plant is built up. In the flowering plants the embryo, after developing up to a certain point, stopf growing and rests, enclosed within the seed.
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  • The middle ages saw geographical knowledge die out in Christendom, although it retained, through the Arabic translations of Ptolemy, a certain vitality in Islam.
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  • term which appears to have been introduced by Linnaeus, and was reinvented as a substitute for the cosmography of the middle ages by Professor Huxley.
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  • C. Geographical Distribution The study of the extinct organisms of any country leads to a proper appreciation of its existing flora and fauna; while, on the other hand, a due consideration of the plants and animals which may predominate within its bounds cannot fail to throw more or less light on the changes it has in the course of ages undergone.
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  • When Aaron himself is connected with the worship of the golden calf, and when to Moses is attributed a brazen serpent which the reforming king Hezekiah was the first to destroy, it is evident that religious conceptions developed in the course of ages.
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  • i) Moses received on Mount Sinai not only the written Law as set down in the Pentateuch, but also the Oral Law, which he communicated personally to the 70 elders and through them by a "chain of tradition" to succeeding ages.
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  • about 1136), was a mathematician, astronomer and philosopher much studied in the middle ages.
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  • Just below Mussaib there has been for all ages a great bifurcation of the river.
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  • Neither island has for ages been in any sense a Norman land, and the tongue which the Norman brought with him into both has not for ages been spoken in either.
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  • These works formed to a large extent the source from which the middle ages derived their knowledge of Aristotle.
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  • Whether he meant it so or not, the saint's argument became a programme and an apologia for the imperializing of the Western Church under the leadership of Rome during the middle ages.
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  • Moslems and Jews were applying Aristotelian philosophy to rigorously monotheistic faiths; Christianity had been encouraged by Platonism in teaching a trinity of divine persons, and Platonism of a certain order long dominated the middle ages as part of the Augustinian tradition.
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  • During the Russian Dark Ages certain clerical errors had crept into the liturgical books Reforms a nd certain peculiarities had been adopted in the ritual.
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  • Some attempt has been made to improve matters by macadamizing one of the principal thoroughfares, but it will be the labour of a Hercules to cleanse this vast city from the accumulated filth of ages of neglect.
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  • A poll tax is required of all males between the ages of 21 and 60 years, one half of which goes to the county in which it is collected and the rest to the state.
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  • Haloa, obviously connected with aces (" threshing-floor "), begun at Athens and finished at Eleusis, where there was a threshing-floor of Triptolemus, in the month Poseideon (December).
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  • The rotation of the planets on their axes is also explained as a consequence of the nebular theory, for at the time of the first formation of the planet it must have participated in the rotation of the whole nebula, and by the subsequent contraction of the planet the speed with which the rotation was performed must have been accelerated.
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  • The condensation of a nebula could be followed in the same manner as we can study the growth of the trees in the forest, by comparing the trees of various ages which the forest contains at the same time.
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  • - Biblical history previous to the separation of Judah and Israel holds a prominent place in current ideas, since over two-fifths of the entire Old Testament deals with these early ages.
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  • Frazer, Adonis, Attis, Osiris (1907), p. 67: " Prophecy of the Hebrew type has not been limited to Israel; it is indeed a phenomenon of almost world-wide occurrence; in many lands and in many ages the wild, whirling words of frenzied men and women have been accepted as the utterances of an in-dwelling deity.
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  • But though this defensive zeal led to active persecution, still in theory Judaism was a tolerated religion wherever the Church had sway, and many papal bulls of a friendly character were issued throughout the middle ages (Scherer, p. 32 seq.).
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  • from the south coast at Sphakia, in the middle ages the see of a bishop. On the N.
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  • Shrines of the Double Axes have been found in the palace of Cnossus itself, at Hagia Triada, and in a small palace at Gournia, and many specimens of the sacred emblem occurred in the Cave Sanctuary of Dicte, the mythical birthplace of the Cretan Zeus.
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  • Complete scenes of worship in which libations are poured before the Sacred Axes are, moreover, given on a fine painted sarcophagus found at Hagia Triada.
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  • In the counties there is a board of education and there is also a local school committee of three in each township. The compulsory attendance at school of children between the ages of eight and fourteen for sixteen weeks each year by a state law is optional with each county.
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  • His followers held a progressive revelation of God in the ages of the Father, Son, and Holy Spirit.
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  • Clerical immunities, of course, differed largely at different times and in different countries, the extent of them having been gradually curtailed from a period a little earlier than the close of the middle ages.
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  • And in regard to Reid's favourite proof of the principles in question by reference to "the consent of ages and nations, of the learned and unlearned," it is only fair to observe that this argument assumes a much more scientific form in the Essays, where it is almost identified with an appeal to "the structure and grammar of all languages."
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  • This " intensive " culture in a more or less developed form was practised by the great nations of antiquity, and little decided advance was made till after the middle ages.
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  • Under the later empire agriculture sank into a condition of neglect, in which it remained throughout the Dark Ages.
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  • During the middle ages cattle and sheep were the chief farm animals, but the intermixture of stock consequent on the common-field system was a barrier to improvement in the breed and conduced to the propagation of disease.
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  • The fact that the growth of a leguminous crop, such as red clover, leaves the soil in a higher condition for the subsequent growth of a grain crop - that, indeed, the growth of such a leguminous crop is to a great extent equivalent to the application of a nitrogenous manure for the cereal crop - was in effect known ages ago.
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  • In the middle ages this differentiation of the industrial, municipal and political life had not taken place, and in order to understand the working of at first sight purely economic regulations it is necessary to make a close study of the functions of local government.
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  • Alger's History of the Doctrine of a Future Life, as it has prevailed in all Nations and Ages (1862), and published separately in 1864.
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  • In later ages the representations of birds of one sort or another in Egyptian paintings and sculptures become countless, and the bassi-rilievi of Assyrian monuments, though mostly belonging of course to a subsequent period, are not without them.
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  • Henceforward it was to be the serious study of the workings of nature in producing the beings we see around us from beings more or less unlike them, that had existed in bygone ages and had been the parents of a varied and varying offspring - our fellow-creatures of to-day.
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  • on muscular anatomy, making the two major divisions of Aves (his Homalogonatae and Anomalogonatae, depend in the first instance on the presence or absence of a peculiar muscular slip in the leg, known as the ambiens, although indeed he expressly stated that this was not on account of the intrinsic importance of the muscle in question, but because of its invariable association with other peculiarities.
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  • This burlesquing of things universally held sacred, though condemned by serious-minded theologians, conveyed to the child-like popular mind of the middle ages no suggestion of contempt, though when belief in the doctrines and rites of the medieval Church was shaken it became a ready instrument in the hands of those who sought to destroy them.
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  • This naive temper of the middle ages is nowhere more conspicuously displayed than in the Feast of the Ass, which under various forms was celebrated in a large number of churches throughout the West.
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  • Till recently these apes have been generally included in the same family (Simiidae) with the chimpanzee, gorilla and orang-utan, but they are now regarded by several naturalists as representing a family by themselves - the Hylobatidae.
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  • The substratum of the plain is a bed of boulders, covered during the lapse of ages by a deposit of rich alluvial soil.
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  • In the middle ages it was a strong fortress defending the confines of Piedmont towards Liguria, but the fortifications on the rock above the town were demolished in 1800 by the French, to whom it had been ceded in 1796.
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  • It is certain that in previous geological ages Lake Baikal had a much greater extension.
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  • The fauna, explored by Dybowski and Godlewski, and in 1900-2 by Korotnev, is much richer than it was supposed to be, and has quite an original character; but hypotheses as to a direct communication having existed between Lake Baikal and the Arctic Ocean during the Post-Tertiary or Tertiary ages are not proved.
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  • They protected Europe from the new revival of Mahommedanism under the Turks; they gave it a time of rest in which the Western civilization of the middle ages developed.
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  • geography more studied; the Crusades gave a great impulse to the writing of history, and produced, besides innumerable other works, the greatest historical work of the middle ages - the Historia transmarina of William of Tyre.
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  • The ages were not dark in which Christianity could gather itself together in a common cause, and carry the flag of its faith to the grave of its Redeemer; nor can we but give thanks for their memory, even if for us religion is of the spirit, and Jerusalem in the heart of every man who believes in Christ.
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  • [During the middle ages his work was current in a French translation, known as the Chronique d'outremer, or the Livre or Roman d'Eracles (so called from the reference at the beginning to the emperor Heraclius).
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  • If a current is passed through the fixed coil and movable coil in series with one another, the movable coil tends to displace itself so as to bring the axes of the coils, which are normally at right angles, more into the same direction.
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  • But " alchemy " was something more than a particularly vain and deluded manifestation of the thirst for gold, as it is sometimes represented; in its wider and truer significance it stands for the chemistry of the middle ages.
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  • 14.6), preservation of the temple is due to its conversion into a church in the middle ages.
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  • In the middle ages Zutphen was the seat of a line of counts, which became extinct in the 12th century.
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  • It is the seat of a court of justice and of an archbishop. During the middle ages it was for a time a fief of the Villehardouins.
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  • To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters' (x, ?i, w), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules.
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  • In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.
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  • 6), be the axes of temperature and pressure, and A corresponds to the transition point (95.6°) of rhombic sulphur, we may follow out the line AB which shows the elevation of the transition point with increasing pressure.
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  • At various periods in the history of the middle ages we encounter sudden outbreaks of millennarianism, sometimes as the tenet of a small sect, sometimes as a far-reaching movement.
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  • He may be reckoned the most illustrious pope since Benedict XIV., and under him the papacy acquired a prestige unknown since the middle ages.
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  • Before each of these ages there is a period of incubation, or initiation: the first age begins with Abraham, but the period of initiation with the first man Adam.
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  • During the middle ages it was the chief town of the district of Beauce, and gave its name to a countship which was held by the counts of Blois and Champagne and afterwards by the house of Chatillon, a member of which in 1286 sold it to the crown.
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  • In virtue of the enactments of May 1880, of November 1886, of February 1888 and of December 1903, military service had been obligatory on all Mussulmans, Christians having been excluded but under obligation of paying a " military exoneration tax " of T50 for 135 males between the ages of 15 and 75.
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  • The duties are estimated to produce £T393,107; other professional duties £T110,887 - together £T503,994 A " Military Exoneration tax " is levied on male Ottoman subjects between the ages of 15 and 75 to the amount of £T50 for 135 persons - certain exceptions such as priests, religious orders, &c., are allowed.
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  • Aeetes required of Jason that he should first yoke to a plough his bulls, given him by Hephaestus, which snorted fire and had hoofs of brass, and with them plough the field of Ares.
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  • Though clad, armed and organized in European fashion, the soldiers retained in a marked degree the traditions of their Mongolian forerunners, their transport wagons were in type the survival of ages of experience, and their care for their animals equally the result of hereditary habit.
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  • In the middle ages Romford was rather a meetingplace for merchants than an industrial centre.
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  • In the course of the middle ages the northern parts of Thrace and some other districts of that country were occupied by a Bulgarian population; and in 1361 the Turks made themselves masters of Adrianople, which for a time became the Turkish capital.
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  • The real greatness of the town dates from the time when Constantinople became the metropolis of the Roman world: then its geographical situation raised it to a position of importance which it retained throughout the middle ages.
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  • It should be noted that this name occurs again in the middle ages in Burgundy, not far from Dijon; in all probability a detachment of this people had settled in that spot in the 5th or 6th century.
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  • The efforts of the kings to minimize this evil, and of the old jurisprudence to deal with the matter, resulted in two expedients: (1) the reversion of the appanage to the crown was secured as far as possible, being declared inalienable and transmissible only to male descendants in the male line of the person appanaged; (2) originally the person appanaged had possessed all the rights of a duke or count - that is to say, in the middle ages nearly all the attributes of sovereignty; the more important of these attributes were now gradually reserved to the monarch, including public authority over the inhabitants of the appanage in all essential matters.
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  • In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.
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  • Or, instead of looking upon a linear substitution as replacing a pencil of lines by a projectively corresponding pencil retaining the same axes of co-ordinates, we may look upon the substitution as changing the axes of co-ordinates retaining the same pencil.
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  • If now the nti c denote a given pencil of lines, an invariant is the criterion of the pencil possessing some particular property which is independent alike of the axes and of the multiples, and a covariant expresses that the pencil of lines which it denotes is a fixed pencil whatever be the axes or the multiples.
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  • Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.
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  • They then reigned over the two dioceses of Lescar and Oloron; but their capital was Morlaas, where they had a mint which was famous throughout the middle ages.
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  • A wire or rod in this condition is said to be circularly magnetized; it may be regarded as consisting of an indefinite number of elementary ring-magnets, having their axes coincident with the axis of the wire and their planes at right angles to it.
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  • 4 S'N' is a small magnet of moment M', and SN a distant fixed magnet of moment M; the axes of SN and S'N' make angles of 0 and 4 respectively with the line through their middle points.
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  • If the magnetization is parallel to the major axis, and the lengths of the major and minor axes are 2a and 2C, the poles are situated at a distance equal to 3a from the centre, and the magnet will behave externally like a simple solenoid of length 3a.
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  • The internal force F is opposite to the direction of the magnetization, and equal to NI, where N is a coefficient depending only on the ratio of the axes.
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  • If each of these axes successively is placed parallel to the lines of force in a uniform field H, we shall have = 12 = 13=K3H, the three susceptibilities being in general unequal, though in some cases two of them may have the same value.
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  • On the other hand, the form of the third curve, with its large intercepts on the axes of H and B, denotes that the specimen to which it relates possesses both retentiveness and coercive force in a high degree; such a metal would be chosen for making good permanent magnets.
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  • Weber's theory, the molecules of a ferromagnetic metal are small permanent magnets, the axes of which under ordinary conditions are turned indifferently in every direction, so that no magnetic polarity is exhibited by the metal as a whole; a magnetic force acting upon the metal tends to turn the axes of the little magnets in one direction, and thus the entire piece acquires the properties of a magnet.
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  • The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).
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  • It was on this spot, on the Appian way, that was built the basilica of St Sebastian, which was a popular place of pilgrimage in the middle ages.
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  • In the middle ages it fell into the hands of the Venetians, who fortified it so strongly that in 1477 it successfully resisted a four months' siege by a Turkish army thirty thousand strong; in 1499, however, it was taken by Bayezid II.
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  • The naval strength of the republic consisted in 1906 of a collection of armoured and wooden vessels of various ages and types of construction, of which three armoured vessels (including the two designed for coast defence), four protected cruisers, five destroyers and torpedo-cruisers, and half a dozen torpedo boats represented what may be termed the effective fighting force.
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  • By a law passed in 1868 attendance at school is obligatory on all children between the ages of 6 and 12 years.
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  • They brought from their native Italy a thorough knowledge of the science of government as the middle ages understood it, and the decimation of the Hungarian magnates during the civil wars enabled them to re-create the noble hierarchy on a feudal basis, in which full allowance was made for Magyar idiosyncracies.
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  • It continued to be a place of some importance, the situation being favourable and the region fertile, and does not seem to have been wholly abandoned till the middle ages.
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  • A quaternion is best defined as a symbol of the type q = Za s e s = aoeo + ales = ale, + a3e3, where eo, ...
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  • The motive was avowedly the same which in the Middle Ages led a medixval garrison to drive the civil population of a town into the camp of its would-be deliverers.
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  • (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz
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  • His son was smitten by Ares in battle; his daughter Laodameia was slain by Artemis; he himself, flung from his horse, lamed or blinded, became a wanderer over the face of the earth until his death (Pindar, Isthmia, vi.
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  • A complex of igneous rocks of different ages covers immense areas in the central Transvaal.
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  • Rank has accounted for much, and ceremonial dress - the apparel Romans, naturally left its mark, and there have been ages of increasing luxury followed by periods of reaction, with a general levelling and nationalization on religious grounds (Judaism, Islam).
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  • 12), and when in the middle ages they marked out the Jew for persecution they were transferred to a small under-garment (the little talith), the proper talith being worn over the head in the synagogue.
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  • Ranking as a papal cathedral, this became a much-favoured place of assembly for ecclesiastical councils both in antiquity (313, 487) and more especially during the middle ages.
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  • The loss of an eye will be followed by atrophy of the optic nerve; the tissues in a stump of an amputated limb show atrophic changes; a paralysed limb from long disuse shows much wasting; and one finds at great depths of the sea fishes and marine animals, which have almost completely lost the organs of sight, having been cut off for long ages from the stimuli (light) essential for these organs, and so brought into an atrophic condition from disuse.
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  • These poor compilations, together with Latin translations of certain works of Galen and Hippocrates, formed a medical literature, meagre and unprogressive indeed, but of which a great part survived through the middle ages till the discovery of printing and revival of learning.
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  • A continuous thread of learning and practice must have connected the last period of Roman medicine already mentioned with the dawn of science in the middle ages.
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  • A conspicuous example of the incalculable evil wrought by lack of integration is well seen in the radical divorce of surgery from medicine, which is one of the most mischievous legacies of the middle ages - one whose mischief is scarcely yet fully recognized, and yet which is so deeply rooted in our institutions, in the United Kingdom at any rate, as to be hard to obliterate.
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  • Quicherat, he developed a strong inclination to the study of the middle ages.
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  • To his own age Voltaire was pre-eminently a poet and a philosopher; the unkindness of succeeding ages has sometimes questioned whether he had any title to either name, and especially to the latter.
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  • In the middle ages there was a constant succession of pageants, processions and tournaments.
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  • They likewise display a much higher degree of intelligence than any of the other man-like apes.
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  • Some of the Roman artificers in glass no doubt migrated to Constantinople, and it is certain that the art was practised there to a very great extent during the middle ages.
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  • iravaeaa, all-healing, from 7ras, all, and ae€iveac, to heal), a universal remedy, or cure for all diseases, a term applied in the middle ages to a mythical herb supposed to possess this quality.
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  • (9) Turning the axes to make them coincide with the principal axes of the area A, thus making f f xydA = o, xh = - a 2 cos a, y h = - b 2 sin a, (io) where ffx2dA=Aa2, ffy 2 dA= Ab 2, (II) a and b denoting the semi-axes of the momental ellipse of the area.
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  • In particular, with sh a =1, the cross-section of n = a is x 4 +6x 2 y 2 4= 2c 4, or x 4 -{-y =c 4 (20) when the axes are turned through 45°.
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  • The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.
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  • Beginning with a single body in liquid extending to infinity, and denoting by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest.
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  • These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-mP. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox, Oy, Oz through 0, and denoting by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed.
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  • The Apocalyptic literature of Judaism and Christianity embraces a considerable period, from the centuries following the exile down to the close of the middle ages.
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  • In the middle ages Venice was the great European centre of the sugar trade, and towards the end of the 15th century a Venetian citizen received a reward of ioo,000 crowns for the invention of the art of making loaf sugar.
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  • It became the capital of the pagus Constantinus (Cotentin), and in the middle ages was the seat of a viscount.
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  • The same needs produce in different ages associations which have striking resemblances, but those of each age have peculiarities which indicate a spontaneous growth.
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  • They are important because they played a prominent role in the social life of England, especially as eleemosynary institutions, down to the time of their suppression in 1547 Religious gilds, closely resembling those of England, also flourished on the continent during the middle ages.
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  • In the middle ages Ivrea was the capital of a Lombard duchy, and later of a marquisate; both Berengar II.
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  • We have traced a definite line of descent for feudal institutions from Roman days through the Merovingian and Carolingian ages to the 10th century.
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  • At the moment, however, when feudalism was disappearing as the organization of society, it gave rise to results which in a sense continued it into after ages and even to our own day.
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  • The Versus practically reproduce in outline Bwda's account of Ca dmon's dream, without mentioning the dream, but describing the poet as a herdsman, and adding that his poems, beginning with the creation, relate the history of the five ages of the world down to the coming of Christ.
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  • On the old clearings of another village Mr Bates himself, although he did not see a gorilla, saw the fresh tracks of these great apes and the torn stems and discarded fruit rinds of the "mejoms," as well as the broken stalks of the latter, which had been used for beds.
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  • 1278) wrote a Biographical Dictionary of the Worthies of the First Ages of Islam.
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  • In 1003 we find records of a war between Pisa and Lucca, which, according to Muratori, was the first waged between Italian cities in the middle ages.
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  • In the later middle ages he is represented as fighting with giants, dragons and dwarfs, and finally disappears on a black horse.
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  • The Archbishopric Of Mainz, one of the seven electorates of the Holy Roman Empire, became a powerful state during the middle ages and retained some of its importance until the dissolution of the empire in 1806.
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  • The sea-coast, like the rest of the south shore of the Euxine, was studded with Greek colonies founded from the 6th century onwards: Amisus, a colony of Miletus, which in the 5th century received a body of Athenian settlers, now the port of Samsun; Cotyora, now Ordu; Cerasus, the later Pharnacia, now Kerasund; and Trapezus (Trebizond), a famous city from Xenophon's time till the end of the middle ages.
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  • Chabeuf, Dijon a travers les ages (Dijon, 1897), and Dijon, monuments et souvenirs (Dijon, 1894).
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  • On the one hand there were during the middle ages sects, like the Catharists and Albigenses, whose "opposition as a rule developed itself from dualistic or pantheistic premises (surviving effects of old Gnostic or Manichaean views)" and who "stood outside of ordinary Christendom, and while no doubt affecting many individual members within it, had no influence on church doctrine."
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  • The Priestly Writer in the Pentateuch also a p pears to be acquainted with this doctrine; it is the first of four ages which begins with the Creation and ends with the Deluge.
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  • A far more probable explanation of their name "Chretiens" is to be found in the fact that in medieval times all lepers were known as pauperes Christi, and that, Goths or not, these Cagots were affected in the middle ages with a particular form of leprosy or a condition resembling it.
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  • 2 Consider then an ellipsoidal shell the axes of whose bounding surfaces are (a, b, c) and (a+da), (b+db), (c+dc), where da/a =db b =dc/c =,u.
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  • The above expressions for the capacity of an ellipsoid of three unequal axes are in general elliptic integrals, but they can be evaluated for the reduced cases when the ellipsoid is one of revolution, and hence in the limit either takes the form of a long rod or of a circular disk.
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  • The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and v for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.
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  • Since there is no example of the archbishop of York exercising or being reputed to have such disciplinary jurisdiction over his suffragans,' and this right could, according to the canon law cited above, in the middle ages only be exercised normally in concert with the provincial synod, it would seem to be a survival of the special jurisdiction enjoyed by the pre-Reformation archbishop as legatus natus of the pope.
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  • The book appears to have been known in the ages immediately succeeding his own; and, though there is no contemporary manuscript in existence, there are some half-dozen which appear to date from the end of the 13th or the course of the 14th century, while one at least appears to be a copy made from his own work in that spirit of unintelligent faithfulness which is much more valuable to posterity than more pragmatical editing.
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  • GOLD [[[symbol]] Au, atomic weight 1 95.7(11 = I),197 2(O =16)], a metallic chemical element, valued from the earliest ages on account of the permanency of its colour and lustre.
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  • (a) On population: immigration, of course, is a direct addition to the population of new countries, and greatly accelerates the growth by natural increase, especially as the immigrants are in the most productive ages of manhood and womanhood.
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  • In the middle ages they were known to Ratherius of Verona (loth century), who quotes a passage from i.
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  • The question appeared to be worthy of such a consultation, especially in view of the number of persons of all ages and ranks, and of both sexes, who were imperilled.
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  • These were formed in different geological ages by the gulf, which had in historical times receded to a distance of 14 m.
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  • It is a common practice in the magic of all ages and countries to acquire control and influence over men and animals by making images of them.
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  • 11 a art in cult; they may equally explain its genesis and rise in certain ages and countries.
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  • Events which greatly affected the physical condition of the human race, or were of a nature to make a deep impression on the minds of the rude inhabitants of the earth, might be vaguely transmitted through several ages by traditional narrative; but intervals of time, expressed by abstract numbers, and these constantly varying besides, would soon escape the memory.
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  • A volume of supplemental notes to his Middle Ages was published in 1848.
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  • The Middle Ages is described by Hallam himself as a series of historical dissertations, a comprehensive survey of the chief circumstances that can interest a philosophical inquirer during the period from the 5th to the 15th century.
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  • In the cliffs opposite the town on the south is the rock-cut church of the Madonna del Parto, developed, no doubt, out of an Etruscan tomb, of which there are many here; and close by is a rock-hewn amphitheatre of the Roman period, with axes of 55 and 44 yds., now most picturesque.
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  • Although it was a slave state, the majority of the people of Delaware opposed secession in 1861, and the legislature promptly answered President Lincoln's call to arms; yet, while 14,000 of the 40,000 males between the ages of fourteen and sixty served in the Union army, there were many sympathizers with the Confederacy in the southern part of the state.
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  • This was built by the Capuchins, who in the middle ages chose Syra as the headquarters of a mission in the East.
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  • Avallon (Aballo) was in the middle ages the seat of a viscounty dependent on the duchy of Burgundy, and on the death of Charles the Bold passed under the royal authority.
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  • &prtos, even, and &Lktvxos, a finger or toe, "even-toed"), the suborder of ungulate mammals in which the central (and in some cases the only) pair of toes in each foot are arranged symmetrically on each side of a vertical line running through the axes of the limbs.
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  • In appearance the town is quaint and romantic, presenting almost as faithful a picture of a town of the early middle ages as Nuremberg does of the later.
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  • The revenue for schools in 1907-08 was $8,020,229, of which $2,761,651 was from the state tax, $2,080,159 from the local tax, $1,640,969 from the one dollar poll tax on males between the ages of twenty-one and sixty, $481,899 from a state occupation tax, $4 2 9,3 6 5 from county funds, and $105,806 from tuition fees.
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  • However, there are laws requiring that each school be taught at least six months in a year, and that children between the ages of seven and fourteen attend for at least twelve consecutive weeks, and for a total of sixteen weeks in every year.
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  • The state established a university at Iowa City in 1847, a State Agricultural College and Model Farm in 1858 (opened at Ames in 1869 as the Iowa State College of Agriculture and the Mechanic Arts), an Agricultural Experiment Station in 1887, an Engineering Experiment Station in 1904, and a normal school at Cedar Falls in 1876.
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  • In the middle ages Aire belonged to the counts of Flanders, from whom in 1188 it received a charter, which is still extant.
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  • Now if the atoms are regarded as points or spherical bodies oscillating about positions of equilibrium, the value of n+3 is precisely six, for we can express the energy of the atom in the form (9 2 v a 2 v a2v E = z(mu 2 +mv 2 +mw 2 +x 2 ax2 + y2ay2-fz2az2), where V is the potential and x, y, z are the displacements of the atom referred to a certain set of orthogonal axes.
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  • The Stoics divided XoytK17 (logic) into rhetoric and dialectic, and from their time till the end of the middle ages dialectic was either synonymous with, or a part of, logic.
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  • This is covered to a considerable extent by rocks of recent and late Tertiary ages.
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  • The work was a complete encyclopaedia of the liberal culture of the time, and was in high repute during the middle ages.
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  • BIDPAI (or [[Pilpay), Fables Of]], the name given in the middle ages (from Sanskrit Vidya-pati, chief scholar) to a famous collection of Hindu stories.
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  • This site, which in the middle ages appears to have been lost - Gilgal being shown farther north - was in 1865 recovered by a German traveller (Hermann Zschokke), and fixed by the English survey party, though not beyond dispute.
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  • In the middle ages Phaedrus exercised a considerable influence through the prose versions of his fables which were current, though his own works and even his name were forgotten.
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  • The consecration of material objects and in general their use in religion and cult was consistently avoided by the Manicheans; not because they failed to share the universal belief of earlier ages that spirits can be inducted by means of fitting prayers and incantations into inanimate things, but because the external material world was held to be the creation of an evil demiurge and so incapable of harbouring a pure spirit.
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  • It was not until 1789 that the French Church of the middle ages lost its vast possessions and was subjected to a fundamental reconstruction by the Civil Constitution of the Clergy (1791).
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  • Apart from one or two of the greatest minds, notably Dante, what appealed to the thinkers of the middle ages was not the idea of reality as a progressive self-revelation of an inner principle working through nature and human life, but the formal principles of classification which it seemed to offer for a material of thought and action given from another source.
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  • Oude Trecht or Old Ford, rendered in Latin documents Vetus Trajectum) is a city of great antiquity and much historic interest, especially as illustrating the growth of civic liberties during the middle ages.
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  • Douai, the site of which was occupied by a castle (Castrum Duacense) as early as the 7th century, belonged in the middle ages to the counts of Flanders, passed in 1384 to the dukes of Burgundy, and so in 1477 with the rest of the Netherlands to Spain.
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  • The counts of Armagnac possessed a castle in the city, which was the capital of Armagnac in the middle ages.
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  • This weapon embodied all the essential features which distinguish the ordnance of to-day from the cannon of the middle ages - it was built up of rings of metal shrunk upon an inner steel barrel; it was loaded at the breech; it was rifled; and it threw, not a round ball, but an elongated projectile with ogival head.
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  • Bokhara has for ages been a centre of learning and religious life.
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  • The mysticism which took hold on Persia in the middle ages spread:also to Bokhara, and later, when the Mongol invasions of the 13th century laid waste Samarkand and other Moslem cities, Bokhara, remaining independent, continued to be a chief seat of Islamitic learning.
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  • In Austria, Hungary and Switzerland there are some thirty great abbeys, most of which have had a continued existence since the middle ages.
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  • In the middle ages it had six churches and four monastic establishments, the oldest a Benedictine nunnery (1170).
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  • Aschaffenburg, called in the middle ages Aschafaburg and also Askenburg, was originally a Roman settlement.
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  • In 1906 he began to publish, under the title of Histoire ancienne de l'eglise, a course of lectures which he had already delivered upon the early ages of the Church, and of which a few manuscript copies were circulated.
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  • Most of these sects were stamped out before the period of the middle ages came to a close.
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  • In 1821 an attempt to get a return of ages was made, but it was not repeated in 1831, when the attention of the enumerators was concentrated upon greater detail in the occupation record.
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  • His chapel (which still existed in Leland's time) was a place of pilgrimage in the middle ages.
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  • Hence the area of an ellipse whose axes are 2a and 2b is Trab; and the volume of an ellipsoid whose axes are 2a, 2b and 2c is t rabc. The area of a strip of an ellipse between two lines parallel to an axis, or the volume of the portion (frustum) of an ellipsoid between two planes parallel to a principal section, may be found in the same way.
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  • In the case of the briquette the position of the foot of the ordinate u is expressed by co-ordinates x, y, referred to a pair of axes parallel to a pair of sides of the base of the briquette.
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  • To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.
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  • In the course of ages every detail has been brought under a formal set of rules, which only need mechanical application.
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  • These coils are placed with their axes at right angles to one another, and at the point where the axes intersect a small pivoted needle of soft iron is placed, carrying a longer index needle moving over a scale.
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  • The compulsory education law as amended in 1907 and 1909 requires the full attendance at a public school, or at a school which is an approximate equivalent, of all children who are between seven and fourteen years of age, are in the proper physical and mental condition, and reside in a city or school district having a population of 5000 or more and employing a superintendent of schools; in such a city or district children between fourteen and sixteen years must attend school unless they obtain an employment certificate and are regularly engaged in some useful employment or service; and outside of such a city or district all children between the ages of eight and fourteen years and those between fourteen and sixteen years who are not regularly employed must attend school on all school days from October to June.
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  • He had already made himself known by critical studies on the history of the middle ages, of which the most important was his Geschichte des ersten Kreuzzuges (Dusseldorf, 1841; new ed., Leipzig, 1881), a work which, besides its merit as a valuable piece of historical investigation, according to the critical methods which he had learnt from Ranke, was also of some significance as a protest against the vaguely enthusiastic attitude towards the middle ages encouraged by the Romantic school.
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  • a point which divides a line, or a line which divides an angle, into two equal parts; in crystallography it denotes the bisector of the angle between the optic axes.
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  • Each school district is required by law to keep its school open at least three months a year and all children between the ages of eight and fourteen are required to attend for the full term; if unemployed they are required to continue in school until they have attained the age of sixteen.
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  • Among the other sources of revenue are a poll-tax of two dollars on each man between the ages of twenty-one and sixty, licences, an inheritance tax, rent of state lands and the income from invested funds received from the sale of state lands.
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  • But considerable as is the prosperity of modern Courtrai it is but a shadow of what it was in the middle ages during the halcyon period of the Flemish communes.
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  • Among the theories prevalent in the middle ages was one that mankind formed a unity, with the pope and the emperor at the head of it: the universal Church and the universal emperor ruled the world (Rehm, Geschichte der Rechtswissenschaft, p. 198.) Even to Leibnitz, writing in the 17th century, it seemed that "totam Christianitatem unam velut Rempublicam componere, in qua Caesari auctoritas aliqua competit" (Opera, 4.330).
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  • Gierke, in his book Johannes Althusius and die Entwickelung der naturrechtlichen Staatstheorie, shows (p. 76) that the conception of a treaty or agreement as the basis of the state was in the middle ages a dogma which passed almost unchallenged, and that this theory was maintained up to a late period.
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  • For the position shown the distribution of bending moment due to W 1 is given by ordinates of the triangle 000 A'CB'; that due to W2 by ordin al, W, WW1 W„ ates of A'DB'; and that due to W3 by ordinates of A EB'.
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  • In this sense the word was applied in the later middle ages to the Germans studying at Italian universities and - to take a particular example - to the French cardinals at the election of Clement V.
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  • (4) Until the Middle Ages the form of absolution after private confession was of the nature of a prayer, such as "May the Lord absolve thee"; and this is still the practice of the Greek church.
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  • In September this was taken by storm; Kolokotrones rode in triumph to the citadel over streets carpeted with the dead; and the crowning triumph of the Cross was celebrated by a cold-blooded massacre of 2000 prisoners of all ages and both sexes.
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  • The most notable fact in the geological history of the archipelago is the discovery in Java of the fossil remains of Pithecanthropus erectus, a form intermediate between the higher apes and man.
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  • - Ptolemy and other ancient geographers describe the Malay Archipelago, or part of it, in vague and inaccurate terms, and the traditions they preserved were supplemented in the middle ages by the narratives of a few famous travellers, such as Ibn Batuta, Marco Polo, Odoric of Pordenone and Niccolo Conti.
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  • Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (�2u',�2vi,�2w') is the gradient of a continuous function.
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  • In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to -u,-v,-w, as they refer to axes moving with the matter.
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  • We may now, as is somewhat the more natural course in the terrestrial application, take axes (x,y,z) which move with the matter; but the current must be invariably defined by the flux across surfaces fixed in space, so that we may say that relation (i) refers to a circuit fixed in space, while (ii) refers to one moving with the matter.
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  • For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.
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  • 59) worshipped chiefly a war god, and that certain Thracian settlements, formed in Greece in prehistoric times, left behind them traces of the worship of a god whom the Greeks called Ares.
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  • In Homer Ares is the lover of Aphrodite, the wife of Hephaestus, who catches them together in a net and holds them up to the ridicule of the gods.
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  • In the legend of Cadmus and his family Ares plays a prominent part.
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  • It was here, according to the legend, that he was tried and acquitted by a council of the gods for the murder of Halirrhothius, who had violated Alcippe, the daughter of Ares by Agraulos.
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  • But before this grouping had recommended itself to the Romans, with their legend of Mars and Rhea Silvia, the Greek Ares had again become under Macedonian influence a bearded, armed and powerful god.
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  • - Ancient and medieval times were not separated by so deep a gulf in the East as in the West; for in the East the Empire continued to exist, although within narrow limits, until towards the end of the middle ages.
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  • He is the first of a series of theological mystics which continued through every century of the middle ages.
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  • The middle ages were far more disastrous for the Monophysites than for the Nestorians; in their case there was no alternation of rise and decline, and we have only a long period of gradual exhaustion to chronicle.
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  • (a) The Early Middle Ages.
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  • 849), was the author of the Glossa Ordinaria, a work which formed the foundation of biblical exposition throughout the middle ages.
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  • But, on the other hand, the material influence of the priests was greater than it had ever been before; the Temple was the only visible centre of national life in the ages of servitude to foreign power, and the priests were the only great national functionaries, who drew to themselves all the sacred dues as a matter of right and even appropriated the tithes paid of old to the king.
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  • Doullens, the ancient Dulincum, was seat of a viscountship and an important stronghold in the middle ages.
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  • It was not till - towards the close of the middle ages that a sense of conflict between reason and revelation became "truth' widely prevalent and took shape in the essentially sceptical theory of the twofold nature of truth.
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  • Silk culture and carpet manufacture have flourished for ages at Khotan, and the products always find a ready sale at Kashgar.
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  • Proceeding to the earlier history of Poland, Lelewel's Poland in the Middle Ages (4 vols., Posen, 1846-1851) is still a standard work, though the greatest authority on Polish antiquities is now Tadeusz Wojciechowski, who unites astounding learning with a perfect style.
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  • (In some versions it is respectively a vine and a rose which grow from either tomb and interlace midway.) We need have little wonder that this beautiful love-story was extremely popular throughout the middle ages.
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  • Such remission was popularly called a pardon in the middle ages - a term which still survives, e.g.
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  • Etaples has a small fishing and commercial port which enjoyed a certain importance during the middle ages.
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  • 636), whose comprehensive encyclopaedia was a favourite text-book in the middle ages.
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  • About the middle of the same century grammar had a far abler exponent at Rome in the person of Aelius Donatus, the preceptor of St Jerome, as well as the author of a text-book that remained in use throughout the middle ages.
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  • He is a link between the ancient world and the middle ages, having been the last of the learned Romans who understood the language and studied the literature of Greece, and the first to interpret to the middle ages the logical treatises of Aristotle.
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  • This was partly due to the recovery of some of the lost works of ancient literature, and the transition from the middle ages to the revival of learning was attended by a general widening of the range of classical studies and by a renewed interest in Plato.
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  • He is, in a limited sense, a precursor of the Renaissance, but he is far more truly to be regarded as the crowning representative of the spirit of the middle ages.
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  • priour), a title applied generally to certain monastic superiors, but also in the middle ages to other persons in authority.
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  • The term prior was applied also in the middle ages in a very general manner.
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  • Exclusive of the city of Baltimore, the state is divided into seven judicial circuits, in each of which are elected for a term of fifteen years one chief judge and two associate judges, who at the time of their election must be members of the Maryland bar, between the ages of thirty and seventy, and must have been residents of the state for at least five years.
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  • A compulsory education law of 1902 - to operate, however, only in the city of Baltimore and in Allegany county - requires the attendance for the whole school year of children between the ages of eight and twelve and also of those between the ages of twelve and sixteen who are not employed at home or elsewhere.
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  • Rocks of Archean and Palaeozoic ages contribute only a small share, but there is a Scale, 1:7,700,000 English Miles o 60 80 too 200 �-' 4,, ,% 4s o,r^ ° o ?
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  • The rocks of Secondary and Tertiary ages have been profoundly affected by the Alpine movements, and are thrown into a series of complex folds, so that in numerous instances their stratigraphy is imperfectly understood.
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  • The picture of Apostolical Christianity found in the New Testament offered indeed a glaring g g contrast to the papal system of the later middle ages.
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  • dealing with Adam, Moses or Isaiah) will always be a matter of dispute, the teaching to which it is applied stands on an independent footing as also does the application of that teaching to other ages.
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  • buzino d'oro, " golden bark," latinized in the middle ages as bucentaurus on the analogy of a supposed Gr.
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  • When the currents flow through the two coils, forces are brought into action compelling the coils to set their axes in the same direction, and these forces can be opposed by another torque due to the control of a spiral spring regulated by moving a torsion head on the instrument.
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  • The thoroughbred Kentucky horse has long had a world-wide reputation for speed; and the Blue Grass Region, especially Fayette, Bourbon and Woodford counties, is probably the finest horse-breeding region in America and has large breeding farms. In Fayette county, in 1900, the average value of colts between the ages of one and two years was $377.78.
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  • In each city of the first, second and third class there must be, and of the fourth class there may be, maintained under control of a city Board of Education a system of public schools, in which all children between the ages of 6 and 20 residing in the city may be taught at public expense.
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  • Except in a few cases, we shall not here consider any units of the middle ages.
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  • The last two branches of inquiry are regarded as forming but a single body of doctrine in the well-known passage of the Theory of Moral Sentiments in which the author promises to give in another discourse "an account of the general principles of law and government, and of the different revolutions they have undergone in the different ages and periods of society, not only in what concerns justice, but in what concerns police, revenue and arms, and whatever else is the subject of law."
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  • During the middle ages it was a considerable centre of commerce and shipping, and under the Hohenstaufen emperors was raised to the rank of a free imperial city.
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  • So man was made first of clay, but he was strengthless and senseless and melted in the water; then they made a race of wooden mannikins, but these were useless creatures without heart or mind, and they were destroyed by a great flood and pitch poured down on them from heaven, those who were left of them being turned into the apes still to be seen in the woods.
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  • All children between the ages of eight and fourteen and those between the ages of fourteen and sixteen who cannot read and write English are required to attend either a public or an approved private school for the full term unless excused by the school board on account of physical or mental infirmity.
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  • The income of the state, counties and towns is derived mainly from taxes levied on real estate, on male polls between the ages of twenty-one and seventy, on stock in public funds, on stock in corporations that pay a dividend and are not subject to some special form of tax, on surplus capital in banks, on stock in trade, on live-stock, on railways, on telegraph and telephone lines, on savings banks and on the stock of fire insurance companies.
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  • The castle from which Chateauroux takes its name was founded about the middle of the 10th century by Raoul, prince of Deols, and during the middle ages was the seat of a seigniory, which was raised to the rank of countship in 1497, and in 1616, when it was held by Henry II., prince of Conde, to that of duchy.
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  • His publications include: Compleat View of Episcopacy, as Exhibited in the Fathers of the Christian Church, until the close of the Second Century (1771); Salvation of All Men, Illustrated and Vindicated as a Scripture Doctrine (1782); The Mystery Hid from Ages and Generations made manifest by the Gospel-Revelation (1783); and Five Dissertations on the Fall and its Consequences (1785).
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  • With the exception of his description of the French Revolution, which was chiefly a political manifesto, all his early works refer to the middle ages - De La feodalite, des institutions de Saint Louis et de l'influence de la legislation de ce prince (1822); La Germanic au vin e et au ix' siecle, sa conversion au christianisme, et son introduction dans la societe civilisee de l'Europe occidentale (1834); Essai sur la formation territoriale et politique de la France depuis la fin du xi e siècle jusqu'et la fin du xv e (1836); all of these are rough sketches showing only the outlines of the subject.
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  • And the self-governing communities of the middle ages were a restoration, rather than a development, of the flourishing and independent municipalities of the age of Augustus and his immediate successors.
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  • The town is a coal-mining centre and has cold mineral springs, known in the middle ages.
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  • high, half a mile or a mile long, with axes parallel to the direction of the ice motion as indicated by striae on the underlying rock floor; these hills are known by the Irish name, drumlins, used for similar hills in north-western Ireland.
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  • The mountains rapidly grow wider and higher northward, by taking on new complications of structure and by including large basins between the axes of uplift, tintil in northern Colorado and Utah a complex of ranges has a breadth of 300 m., and in Colorado alone there are 40 summits over 14,000 ft.
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  • the greatest proportion (14%) of the total were of this size; but in F mill 1900 the model family was that of 3 persons by a more a es.
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  • In the middle ages it became a bishopric, but was destroyed in 1276.
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  • The use of the fleur-de-lis in heraldry dates from the 12th century, soon after which period it became a very common charge in France, England and Germany, where every gentleman of coat-armour desired to adorn his shield Middle Ages.
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  • The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the Cartesian equation referred to oblique axes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity.
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  • While it is throughout essentially a mountainous country, very complicated in its orographic features and interlocking river systems, two principal mountain axes form its ruling features - the Rocky Mountains proper, above referred to, and the Coast Ranges.
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  • In this all able-bodied citizens between the ages of 18 and 6!o are nominally enrolled, but the active militia consists of about 45, 00 0 men of all ranks, in a varying state of efficiency.
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  • In the middle ages Malmesbury possessed a considerable cloth manufacture, and at the Dissolution the abbey was bought by a rich clothier and fitted with looms for weaving.
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  • Thus, to take an example, he will not print a critical text of Plautus with two letters (Y and Z) which were no part of the Latin alphabet in the age of that comedian; still less will he introduce into Latin texts distinctions, such as i,j and u, v, which were not used till long after the middle ages.
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  • In disposing of some of the stock of this company, Ames in1867-1871sold a number of shares to members of Congress at a price much below what these shares eventually proved to be worth.
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  • After an investigation by a committee of the House, which recommended the expulsion of Ames, a resolution was passed on the 28th of February 1873, "that the House absolutely condemns the conduct of Oakes Ames ...
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  • Many have since attributed this resolution to partisanship, and the influence of popular clamour, and in 1883 the legislature of Massachusetts passed a resolution vindicating Ames.
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  • It was a military position of some importance in the middle ages.
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  • In the early ages of Rome, and even down to the middle of the 5th century after the foundation of the city, no other divisions of the day were known than sunrise, sunset, and midday, which was marked by the arrival of the sun between the Rostra and a place called Graecostasis, where ambassadors from Greece and other countries used to stand.
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  • Certificates of children's ages are necessary before a child is employed; false certification is forbidden under penalty of a fine of from $5 to $100 or hard labour not exceeding three months.
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  • Georgia had responded freely to the call for volunteers, but when the Confederate Congress had passed, in April 1862, the Conscript Law which required all white men (except those legally exempted from service) between the ages of 18 and 35 to enter the Confederate service, Governor Brown, in a correspondence with President Davis which was continued for several months, offered serious objections, his leading contentions being that the measure was unnecessary as to Georgia, unconstitutional, subversive of the state's sovereignty, and therefore " at war with the principles for the support of which Georgia entered into this revolution."
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  • He had a striking resemblance to the Italian princes of the later middle ages and the early renaissance, of the stamp of Filipo Maria Visconti.
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  • By the time of the VIth Dynasty it was usual to lay the corpse on its left side in the attitude of sleep, and a wooden coffin was often provided upon which were inscribed magic formulae that had already been employed for ages in ritual.
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  • Until recently he was looked upon as semi-mythical, but the discovery of the tombs of many kings of the 1st Dynasty including probably that of Menes himself, as well as an abundance of remains of still earlier ages in Egypt has given him a personality.
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  • The industries of Pistoia include iron and steel works, especially manufactures of glass, silk, macaroni, woollens, olive oil, ropes, paper, vehicles and fire-arms. The word "pistol" is derived (apparently through pistolese, a dagger - dagger and pistol being both small arms) from Pistoia, where that weapon was largely manufactured in the middle ages.
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  • A collection of casts, likewise in the museum, is designed to display the progress of plastic art from the time of the Egyptians and Assyrians to modern ages.
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  • In the middle ages the Teutonic Order established a frontier belt on the side of Lithuania.
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  • Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.
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  • Every child between the ages of six and fifteen must attend either a public school or a duly authorized private school.
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  • This is, of course, more true of the middle ages than of the times that preceded and followed them; the Church under the Roman empire hardly as yet realized the possibilities of " sermons in stones," and took over, with little change, the model of the secular and religious buildings of pagan Rome; the Renaissance, essentially a neo-pagan movement, introduced disturbing factors from outside, and, though developing a style very characteristic of the age that produced it, started that archaeological movement which has tended in modern times to substitute mere imitations of old models for any attempt to express in church architecture the religious spirit of the age.
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  • The number of relics increased to a fabulous extent during the middle ages.
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  • On an isolated hill close by stand the extensive ruins of the castle of Starkenburg, built by the abbot, Ulrich von Lorsch, about 1064 and destroyed during the Seven Years' War, and another hill, the Landberg, was a place of assembly in the middle ages.
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  • Fichte's " Wissenschaftslehre," he said, is a completely untenable system, and a metaphysics of fruitless apices, in which he disclaimed any participation; his own Kritik he refused to regard as a propaedeutic to be construed by the Fichtian or any other standpoint, declaring that it is to be understood according to the letter; and he went so far as to assert that his own critical philosophy is so satisfactory to the reason, theoretical and practical, as to be incapable of improvement, and for all future ages indispensable for the highest ends of humanity.
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  • Hence, when the microscopes are adjusted so as to coincide with the points of the dipping needle a, the axes of the two needles must be at right angles.
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  • In this it resembled the middle ages rather than the Roman empire or the present day, and it resembled them all the more in that its love of beauty, like theirs, was mixed with a feeling for the fantastic and the grotesque.
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  • The Danish settlements at the end of the 9th century and the defensive system initiated by King Alfred gave birth to a new series of fortified towns, from which the boroughs of the middle ages are mainly descended.
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  • But in the middle ages the altars were placed against the east wall of the churches, or else against a reredos erected at the east side of the altar, so as to prevent all access to the table from that side; the celebrant was thus brought round to the west side and caused to stand between the people and the altar.
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  • In English documents also we find eponymous national ancestors grouped together in genealogical trees, and there is reason to believe that the common origin of the various Teutonic peoples was remembered to a certain extent until comparatively late in the middle ages.
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  • Further, since the grantees as a rule naturally sent their sons into the service of their own lords, such grants tended to become hereditary, and in them we have the origin of the baronage of the middle ages.
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  • chap. 9, part 2); but the earliest definite mention as yet known of the use of the mariner's compass in the middle ages occurs in a treatise entitled De utensilibus, written by Alexander Neckam in the r 2th century.
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  • For ten years a Germany weakened and divided by the rivalry of Philip of Swabia and Otto of Brunswick left his hands free to act in Italy, and his pontificate marks a period of comparative quiet in the ardent Empire* conflict between pope and emperor which continued throughout the middle ages.
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  • was, in his eyes, merely a new attempt to build up afresh the theocracy of the middle ages upon the ruins of the old monarchies, utilizing to this end the inexperience of the young and easily beguiled democracies of the dawning 20th century.
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  • The name Castile is commonly said to be derived from the numerous frontier forts (castillos) erected in the middle ages as a defence against the Moors.
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  • Hopper: a True Life (1853), The Progress of Religious Ideas through Successive Ages (3 vols., 1855), Autumnal Leaves (1857), Looking Toward Sunset (1864), The Freedman's Book (1865), A Romance of the Republic (1867), and Aspirations of the World (1878).
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  • Antwerp, famous in the middle ages and at the present time for its commercial enterprise, enjoyed in the 17th century a celebrity not less distinct or glorious in art for its school of painting, which included Rubens, Van Dyck, Jordaens, the two Teniers and many others.
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  • St Canute's shrine was a great resort of pilgrims throughout the middle ages.
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  • It is probable that in remote ages Babylonia exercised a considerable influence upon Syria and its coast towns; but Mr L.
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  • Besides busts and figurines, which belong as a rule to the Greek period, the smaller objects usually found are earthen pitchers and lamps, glass-wares, tesserae and gems. Of buildings which can be called architectural few specimens now exist on Phoenician soil, for the reason that for ages the inhabitants have used the ruins as convenient quarries.
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  • The axes will take up any position, and consequently give rise to a continuous series of parhelia which touch externally the inner halo, both above and below, and under certain conditions (such as the requisite altitude of the sun) form two closed elliptical curves; generally, however, only the upper and lower portions are seen.
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  • The term survived throughout the middle ages wherever the Roman law gained a foothold.
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  • In a tertiary sense the word appears to have been occasionally employed as equivalent to the Latin miles - usually translated by thegn - which in the earlier middle ages was used as the designation of the domestic as well as of the martial officers or retainers of sovereigns and princes or great personages.
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  • In the middle ages it was a common practice for sovereigns and princes to dub each other knights much as they were afterwards, and are now, in the habit of exchanging the stars and ribbons of their orders.
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  • The knightly ages will always enjoy the glory of having formulated a code of honour which aimed at rendering the upper classes worthy of their exceptional privileges; yet we must judge chivalry not only by its formal code but also by its practical fruits.
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  • Then turning to a wider theme Prutz contributed to Oncken's university history the two volumes on the political history of Europe during the middle ages (Staatengeschichte des Abendlandes im Mittelalter, Berlin, 1885-1887).
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  • But, however that may be, his tomb appears to have been venerated at Alexandria, and there was a firm belief at Venice in the middle ages that his remains had been translated thither in the 9th century (the fact of the translation is denied even by Tillemont; the weakness of the evidence in support of the tradition is apparent even in Molini's vigorous defence of it, lib.
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  • Grand-Carteret, La Montagne a travers les ages (2 vols., 1902-1904); G.
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  • In the middle ages Baeza was a flourishing Moorish city, said to contain 50,000 inhabitants; but it was sacked in 1239 by Ferdinand III.
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  • These are, indeed, expressly prohibited in the later charter of Bishop Johann Kvag (1294); and the distinctive character of the constitution of Copenhagen during the middle ages consisted in the absence of the free gild system, and the right of any burgher to pursue a craft under license from the Vogt (advocates) of the overlord and the city authorities.
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  • THEODOLITE,' a surveying instrument consisting of two graduated circles placed at right angles to each other, for the measurement of horizontal and vertical angles, a telescope, which turns on axes mounted centrically to the circles, and an alidade for each circle, which carries two or more verniers.
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  • As the middle ages advanced the procession became more and more popular and increasingly a dramatic representation of the triumphal progress of Christ, the bishop riding on an ass or horse, as in the East.
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  • The disposition adopted was one which is found recurring in many sea-fights of the middle ages where a fleet had to fight on the defensive.
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  • The essential difference between monks and regular canons may be explained as follows: monks, whether hermits or cenobites, are men who live a certain kind of life for its own sake, for the purpose of leading a Christian life according to the Gospel's counsel and thus serving God and saving their own souls; external works, either temporal or spiritual, are accidental; clericature or ordination is an addition, an accession, and no part of their object, and, as a matter of fact, till well on in the middle ages it was not usual for monks to be priests; in a word, the life they lead is their object, and they do not adopt it in order the better to compass some other end.
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  • Further mountain torrents (of greater volume than those higher up) fall into the Rhone as it rolls along in a south-westerly direction towards Martigny: the Visp (left), coming from the Zermatt valley, falls in at Visp, at Gampel the Lonza (right), from the Ldtschen valley, at Leuk the Dala (right), from the Gemmi Pass, at Sierre the Navizen (left), from the Einfisch or Anniviers valley, at Sion, the capital of the Valais, the Borgne (left) from the Val d'Herens; soon the Rhone is joined by the Morge (right), flowing from the Sanetsch Pass, and the boundary in the middle ages between Episcopal Valais to the east and Savoyard Valais to the west, and at Martigny by the Dranse (left), its chief Alpine tributary, from the Great St Bernard and the Val de Bagnes.
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  • and the Petit Rhone S.W.; they enclose between them the huge delta of the Camargue, which is cultivated on the banks of the river only, but elsewhere is simply a great alluvial plain, deposited in the course of ages by the river, and now composed of scanty pasturages and of great salt marshes.
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  • This is a curious anticipation of the highly organized and centralized forms of government in religious orders, not met with again till Cluny, Citeaux, and the Mendicant orders in the later middle ages.
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  • Auxonne, the name of which is derived from its position on the Saone (ad Sonam), was in the middle ages chief place of a countship, which in the first half of the 13th century passed to the dukes of Burgundy.
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  • He had early read an account of the Hebrides, and had been much interested by learning that there was so near him a land peopled by a race which was still as rude and simple as in the Middle Ages.
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  • This narrative, as written out by Adamnan, was presented to Aldfrith the Wise, last of the great Northumbrian kings, at York about 701, and came to the knowledge of Bede, who inserted a brief summary of the same in his Ecclesiastical History of the English Nation, and also drew up a separate and longer digest which obtained great popularity throughout the middle ages as a standard guide-book (the so-called Libellus de locis sanctis) to the Holy Places of Syria.
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  • CATHARS (CATHARI or Catharists), a widespread heretical sect of the middle ages.
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  • The commercial and naval successes of the Genoese during the middle ages were the more remarkable because, unlike their rivals, the Venetians, they were the unceasing prey to intestine discord - the Genoese commons and nobles fighting against each other, rival factions amongst the nobles themselves striving to grasp the supreme power in the state, nobles and commons alike invoking the arbitration and rule of some foreign captain as the sole means of obtaining a temporary truce.
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  • Throughout the middle ages Halstead was unimportant, and never rose to the rank of a borough.
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  • His production consists of two elaborate complementary lists: the one describing sign-pictures and giving their meanings, the other cataloguing ideas in order to show how they could be expressed in hieroglyphic. Each seems to us to be made up of curious but perverted reminiscences eked out by invention; but they might someday prove to represent more truly the usages of mystics and magicians in designing amulets, &c., at a time approaching the middle ages.
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  • Apart from the lost Handboc or Encheiridion, which seems to have been merely a commonplace-book kept by the king, the earliest work to be translated was the Dialogues of Gregory, a book enormously popular in the middle ages.
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  • Superficially the language of apocalypses differs from that of rabbinic decisions, and where the seer takes a comprehensive view of the ages the rabbi legislates for particular cases.
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  • On extending his inquiry to other aelotropic crystals he observed a similar variation, and was thus led, in 1825, to the discovery that aelotropic crystals, when heated, expand unequally in the direction of dissimilar axes.
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  • In the XVIIIth-XXth dynasties a large number of fine tombs were made, and later ages continued to bury here till Roman times.
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  • He was a director in many organizations, including the Amoskeag Manufacturing Co., Old Colony Trust Co., Puget Sound Light & Power Co., Walter Baker Co., and Ames Plow Co.
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  • They have been thrown into many folds, the long axes of which run in a general north-easterly direction.
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  • It is divided into three parts, each containing five decades, a decade comprising i Pater, 10 Ayes and a Gloria, in addition to a subject for meditation selected from the "mysteries" of the life of Christ and of the Blessed Virgin.
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  • The textile industries for which Amiens has been celebrated since the middle ages include manufactures of velvet, cotton-, wool-, silk-, hempand flax-spinning, and the weaving of hosiery and a variety of mixed fabrics.
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  • subsequently conferred on Charlemagne at his coronation, and borne, as we gather from medieval documents, indiscriminately, not only by subsequent emperors, but also by a long line of Burgundian rulers and minor princes of the middle ages generally.'
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  • In the early middle ages the term was applied to representatives of a count administering justice for him in the country or small towns and dealing with unimportant cases, levying taxes, &c. Monasteries and religious houses often employed a vicar to answer to their feudal lords for those of their lands which did not pass into mortmain.
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  • In the middle ages there was not a very clear distinction drawn between the vicar and the official of the bishop. When the voluntary and contentious jurisdiction came to be distinguished, the former fell generally to the vicars, the latter to the officials.
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  • It is as a lyric poet that Goethe's supremacy is least likely to be challenged; he has given his nation, whose highest literary expression has in all ages been essentially lyric, its greatest songs.
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  • Recent research in bringing to light considerable portions of long-forgotten ages is revolutionizing those impressions which were based upon the Old Testament - the sacred writings of a small fraction of this.
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  • The close of Old Testament history (the book of Nehemiah) in the Persian age forms a convenient division between ancient Palestine and the career of the land under non-oriental influence during the Greek and Roman ages.
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  • The most important data bearing upon the first great period are given elsewhere in this work, and it is proposed to offer here a more general survey.5 To the prehistoric ages belong the palaeolithic and neolithic flints, from the distribution of which an attempt might be made to give a synthetic sketch of early Palestinian man.6 A burial cave at Gezer has revealed the existence of a race of slight build and stature, muscular, with elongated crania, and thick and heavy skull-bones.
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  • Indeed the 19th 1 This comparison is made in full realization of the fact that the Bordeaux record is a dry catalogue, and that Fabri's work is swelled by the miscellaneous gossip and " padding " which makes it one of the most delightful books ever written in the middle ages.
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  • Statue-founding is a highly specialized department of metal-work, in which the artists of the middle ages excelled.
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  • It was said that after leaving the cloister he studied the black art in Toledo, which had a great reputation in the middle ages as a school of witchcraft.
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  • After the Chronica the chief work of Severus is his Life of Martin, a contribution to popular Christian literature which did much to establish the great reputation which that wonder-working saint maintained throughout the middle ages.
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  • In 1896 he introduced a system of semi-enforced service whereby one man in every eight between the ages of sixteen and seventy takes his turn at military training.
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  • It is limited to about a thousand members, who are chosen by open competition in England between the ages of twenty-one and twenty-four.
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  • The peculiar form of the tube is eminently suited for rigid preservation of the relative parallelism of the axes of the two telescopes, so that,;i the image of a certain selected star is retained on the intersection of two wires of the micrometer, by means of the driving clock, aided by small corrections given by the observer in right ascension and declination (required on account of irregularity in the clock movement, error in astronomical adjustment of the polar axis, or changes in the star's apparent place produced by refraction), the image of a star will continue on the same spot of the photographic film during the whole time of exposure.
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  • arranged, and are all necessary for the quick and easy working raised and lowered nearly in an arc of a circle of which the point of intersection of the polar and declination axes is the centre.
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  • Beaune was a fortified Roman camp and a stronghold during the middle ages.
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  • The present name is derived from Bellum Quadrum, a descriptive appellation applied in the middle ages either to the château or to the rock on which it stands.
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  • 5), but which enjoyed a great vogue in the middle ages.
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  • - In the middle ages Cicero was chiefly known as a writer on rhetoric and morals.
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  • The excavations at Nippur were the first to reveal to us the extreme antiquity of Babylonian civilization, and, as already stated, they give us the best consecutive record of the development of that civilization, with a continuous occupancy from a period of unknown antiquity, long ante-dating 5000 B.C., onward to the middle ages.
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  • The weapons and axes are mostly iron, a few being bronze.
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  • The fact that a great number of these serfs had been enjoying protection as free ceorls in former ages made itself felt, however, in three directions.
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  • In the middle ages Arlon was the seat of a powerful countship (later marquisate), held after 1235 by the dukes of Luxemburg.
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  • Servois says, with reference to the general representation of a directed line in space: " L'analogie semblerait exiger que le trineme filt de la forme p cos a+q cos a+r cos y; a, 1 3, y etant les angles d'une droite avec trois axes rectangulaires; et qu'on eut (p cos a+ g cos /3+ r cos y)(p' cos a+ q cos /3 + r cos y) =cos 2 a+cos 2) 3+cos 2 y = 1.
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  • Hamilton, still keeping prominently before him as his great object the invention of a method applicable to space of three dimensions, proceeded to study the properties of triplets of the form x+iy+jz, by which he proposed to represent the directed line in space whose projections on the co-ordinate axes are x, y, z.
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  • Also, everything relating to change of systems of axes, as for instance in the kinematics of a rigid system, where we have constantly to consider one set of rotations with regard to axes fixed in space, and another set with regard to axes fixed in the system, is a matter of troublesome complexity by the usual methods.
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  • the line parallel to q' q-- 1 which intersects the axes of Q and Q'; the plane of the member contains a fixed line; the centre is on a fixed ellipse which intersects the transversal; the axis is on a fixed ruled surface to which the plane of the ellipse is a tangent plane, the ellipse being the section of the ruled surface by the plane; the ruled surface is a cylindroid deformed by a simple shear parallel to the transversal.
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  • Portsmouth was important in the middle ages not only as a naval station but 'a trading centre.
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  • In confinement these apes (of which adult specimens have been exhibited in Calcutta) appear very slow and deliberate in their movements; but in their native forests they swing themselves from bough to bough and from tree to tree as fast as a man can walk on the ground beneath.
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  • Modern scientific research has vividly illustrated the stereotyped nature of the human mind; there is a general similarity in the effect of similar phenomena upon people at a similar stage of mental growth; there is an almost inherent or unconscious belief which has been transmitted through the countless ages of man's history.
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  • Such a conception of Christianity can recognize many embodiments in ritual, organization and dogma, but its test in all ages and in all lands is conformity to the purpose of the life of Christ.
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  • It became a town in 1208, and during the middle ages there were many struggles between the abbots and the townsfolk.
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  • On this square stands the Artusor Junker-hof (the merchant princes of the middle ages were in Germany styled Junker, squire), containing a hall richly decorated with wood carving and pictures, once used as a banqueting-room and now serving as the exchange.
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  • His work, however, endured, and in the middle ages the Jacobite hierarchy numbered 150 archbishops and bishops under a patriarch and his maphrian.
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  • All children between the ages of eight and twelve years are required to attend a public school at least twelve weeks in a year (six weeks consecutively) unless excused on account of weakness of mind or body, unless the child can read and write and is attending a private school, or unless the child lives more than two miles from the nearest school and more than one mile from an established public school wagon route.
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  • It is clear that a survey of the history of these so-called middle ages - long use makes the term inevitable - must include not only the political phase, but also economics, religion, law, science, literature, &c., since all are involved in the concept.
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  • It is hardly necessary to say that the latter procedure has hitherto been found to be adequate~ As a first step we adopt a system of rectangular axes whos origin is fixed in the earth, but whose directions are fixed b)
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  • At each step there is a gain in itccu racy and comprehensiveness; and the conviction is cherishei that some system of rectangular axes exists with respeci to which the Newtonian scheme holds with all imaginabb accuracy.
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  • If the origin of rectangular axes fixed in the lamina be shifted through a space whose projections on the original directions of the axes are X, u, and if the axes are simultaneously turned through an angle e, the coordinates of a point of the lamina, relative to the original axes, are changed from x, y to X+x cos ey sin e, u+x sin e+y cos e, or X + x ye, u + Xe + y, ultimately.
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  • Now suppose that a body receives first a positive rotation a about OA, and secondly a positive rotation e3 about OB; and let A, B be the intersections of these axes with a sphere described about 0 as centre.
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  • The composition of finite rotations about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane.
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  • Successive half-turns about parallel axes a, b are equivalent to a translation measured by double the distance between these axes in the direction from a to 1,.
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  • Successive halfturns about intersecting axes a, b are equivalent to a rotation about the common perpendicular to a, b at their intersection, Of amount equal to twice the acute angle between them, in the direction from a to b.
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  • Successive half-turns about two skew axes a, b are equivalent to a twist about a screw whose axis is the common perpendicular to a, b, the translation being double the shortest distance, and the angle of rotation being twice the acute angle between a, b, in the direction from a to b.
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  • It is easily inferred as a limiting case, or proved directly, that two infini tesimal rotations a, j3 about c u parallel axes are equivalent to a ..._ -- - -
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  • the positive directions of the axes are assumed to be so arranged that a positive rotation of 90 about Ox would bring Oy into the position of UI, and so on.
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  • In the first place, a cyhindroid can be constructed so as to have its axis coincident with the common perpendicular to the axes of the two given screws and to satisfy thi-ee other conditions, for the position of the centre, the parameter, and the orientation about the axis are still at our disposal.
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  • It follows that when a body has two degrees Of freedom it can twist about any one of a singly infinite system of screws whose axes lie on a certain cylindroid.
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  • If the axes of x and y be taken horizontal and vertical (upwards), we derive x =a log (sec #+tan ~), y= a sec ~.
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  • The method of homogeneous strain can be applied to deduce the corresponding results for an ellipsoid of semi-axes a, b, c. If the co-ordinate axes coincide with the principal axes, we find l0=1/2Ma2, I9=~Mb2, I~ = ~ Me2, whence Ii.~ =3/4M (b1 +ci), &c.
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  • The formula (16) expresses that the squared radius of gyration about any axis (Ox) exceeds the squared radius of gyration about a parallel axis through G by the square of the distance between the two axes.
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  • Since the quadratic moments with respect to w and of are equal, it follows that w is a plane 01 stationary quadratic moment at P, and therefore a principal plane of inertia at P. In other words, the principal axes 01 inertia at P are the normals to the three confocals of the systen (3,~) which pass through P. Moreover if x, y, z be the co-ordinates of P, (33) is an equation to find the corresponding values of 0; and if Of, 02, 03 be the roots we find Oi+O2+81r1a2$-7, (35)
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  • If we write A=Ma, B=M/32, C=M~y, the formula (37), when referred to the principal axes at 0, becomes if p denotes the perpendicular drawn from 0 in the direction (X, u, e) to a tangent plane of the ellipsoid ~+~+~=I (43)
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  • The path is therefore an ellipse of which a, b are conjugate semi-diameters, and is described in the period 24 Ju; moreover, the velocity at any point P is equal to ~ OD, where OD is the semi-diameter conjugate to OP. ~,This type of motion;,s called elliptic harmonic. If the co-ordinate axes are the principal axes of the ellipse, the angle ft in (I o) is identical with the excentric angle.
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  • The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.
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  • Thus taking nny point 0 as base, we have first a linear momentum whose components referred to rectangular axes through 0 are ~(m~), Z(m~), ~(mb); - (I)
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  • The resulting Z+R equations are not as a rule easy of application, owing to the fact that the moments and products of inertia A, B, C, F, G, H are not constants but vary in conse- 0 quence of the changing orientation of the body with respect to the co-ordinate axes.
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  • Take, for example, the case of a sphere rolling on a plane; and let the axes Ox, Oy be drawn through the centre parallel to the plane, so that the equation of the latter is 1=cf.
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  • Let a be the radius of the rolling sphere, c that of the spherical surface which is the locus of its centre, and let x, y, I be the co-ordinates of this centre relative to axes through 0, the centre of the fixed sphere.
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  • The ratio of the axes of the ellipse is sec a, the longer axis being in the plane of 0.
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  • Moving A xes of ReferenceFor the more general treatment of the kinetics of a rigid body it is usually convenient to adopt a system of moving axes.
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  • The moving axes Ox, Oy, 01 form a rigid frame of reference whose motion at time t may be specified by the three component angular velocities p, q, r.
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  • Now consider a system of fixed axes Ox, Oy, Oz chosen so as to coincide at the instant I with the moving system Ox, Oy, Os.
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  • If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,
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  • When the origin of the moving axes is also in motion with a velocity whose components are u, v, w, the dynamical equations are ~rn+qi=X, ~pl+rE=Y, ~f_qE+Pi,=Z, (II)
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  • j To prove these, we may take fixed axes Ox, Oy, Oz coincident with the moving axes at time t, and compare the linear and angular momenta E+E, ~ ~ ?~+~X, u+u, v+~v relative to the new position of the axes, Ox, Oy, Oz at time t+t with the original momenta ~, ~ ~, A, j~i, v relative to Ox, Oy, Oz at time t.
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  • If OA, OB, OC be principal axes of inertia of a solid, and if A, B, C denote the corresponding moments of inertia, the kinetic energy is given by 2TA(~ sin 4,sin 0 cos 44~)2+B Ce cos 4,+sin0 sin$)i +C (~+cos0~)2.
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  • This solution, taken by itself, represents a motion in which each particle of the system (since its displacements parallel to Cartesian co-ordinate axes are linear functions of the qs) executes a simple vibration of period 21r/u.
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  • 92), when the rolling will be towards the opposite hand; and at a given instant let T be the line of coptact of the two cylindrical surfaces, which is at their commor intersection with the plane AB traversing the two axes of figure.
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  • Let a denote the angular velocity with which the plane of axes AB rotates about the fixed axis A.
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  • Application to a Pair of TurnIng Fseces.Let ai, a2 be the angular velocities of a pair of turning pieces; Of, Oi the angles which their line of connection makes with their respective planes of rotation; Ti, r2 the common perpendiculars let fall from the line of connection upon the respective axes of rotation of the pieces.
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  • That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.
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  • That for a pair of turning pieces with parallel axes, and for a turning piece and a shifting piece, the line of contact is straight, and parallel to the axes or axis; and hence that the rolling surfaces are either plane or cylindrical (the term cylindrical including all surfaces generated by the motion of a straight line parallel tO itself).
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  • That for a pair of turning pieces with intersecting axes the line of contact is also straight, and traverses the~ point of intersection of the axes; and hence that the rolling surfaces are conical, with a common apex (the term conical including all surfaces generated by the motion of a straight line which traverses a fixed point).
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  • Cylindrical Wheels and Smooth Racks.In designing cylindrical wheels and smooth racks, and determining their comparati* motion, it is sufficient to consider a section of the pair of pieces made by a plane perpendicular to the axis or axes.
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  • To illustrate this subject, it may be mentioned that an ellipse rotating about one focus rolls completely round in outside gearing with an equal and similar ellipse also rotating about one focus, the distance between the axes of rotation being equal to the major axis of the ellipses, and the velocity ratio varying from to I ~eccentricitY an hyperbola rotating about its further focus rolls in inside gearing, through a limited arc, with an equal and similar hyperbola rotating about its nearer focus, the distance between the axes of rotation being equal to the axis of the hypereccentricity + I
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  • of 39 it appears that the angular velocities of a pair of wheels whose axes meet in a point are to each other inversely as the sines of the angles which the axes of the wheels make with the line of contact.
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  • The motion of two such hyperboloids, turning in contact with each other, has hitherto been classed amongst cases of rolling ~ contact; but that classification is not strictly correct, for, although the corn ponent velocities of a pair of points of G contact in a direction at right angles --- to the line of contact are equal, still, - F as the axes are parallel neither to each - other nor to the line of contact, the velocities of a pair of points of contact FIG have components along the line of contact which are unequal, and their difference constitutes a lateral sliding.
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  • ~ A pair of thin frusta of a pair of hyperboloids are used in practice to communicate motion between a pair of axes neither parallel nor intersect- FIG.
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  • The pitch-circles of a pair of circular toothed wheels are sections of their pitch-surfaces, made for spur-wheels (that is, for wheels whose axes are parallel) by a plane at right angles to the axes, and for bevel wheels by a sphere described about the common apex.
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  • Sliding Contact: Forms of the Teeth of Spur-wheels am Racks.A line of connection of two pieces in sliding contact is line perpendicular to their surfaces at a point where they touch Bearing this in mind, the principle of the comparative motion of pair of teeth belonging to a pair of spur-wheels, or to a spur-whee and a rack, is found by applying the principles stated generally ii 36 and 37 to the case of parallel axes for a pair of spur-wheels, am to the case of an axis perpendicular to the direction of shifting for wheel and a rack.
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  • The ordinary position of a pair of endless screws is with their axes at right angles to each other.
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  • The length L of an endless belt connecting a pair of pulleys whose effective radii are r,, r,, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.
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  • That condition is / fulfilled by a pair of con- B ?-D tinuous cones generated by - \ the revolution of two straight 2 / lines inclined opposite ways to -, their respective axes at equal angles.
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  • The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common perpendiculars let fall from the me of connection upon the respective axes of rotation.
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  • The velocity of the other connected point at such an instant is null, unless it also reaches a dead-point at the same instant, so that the line of connection is in the plane of the two axes of rotation, in which case the velocity ratio is indeterminate.
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  • Coupling of Parallel Axes.Two or more parallel shafts (such as those of a locomotive engine, with two or more pairs of driving wheels) are made to rotate with constantly equal angular velocities by having equal cranks, which are maintained parallel by a coupling-rod of such a length that the line of c000exion is equal to the distance between the axes.
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  • Let the axis Ai carry a wheel of N1 teeth, driving a wheel of ni teeth on the axis Ai, which carries also a wheel of N2 teeth, driving a wheel of 113 teeth on the axis A3, and so on; the numbers of teeth in drivers being denoted by Ns, and in followers by ns, and the axes to which the wheels are fixed being denoted by numbers.
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  • It is often a question of importance to determine the number of teeth in a train of wheels best suited for giving a determinate velocity ratio to two axes.
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  • Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.
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  • On the other hand, the postponement of marriage in the case of women of conceptive ages is a tendency which seems to be growing in other countries as well as in England and undoubtedly has a depressing effect upon the rate of births.
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  • But neither this nor the diminution of the marriagerate amongst women of those ages suffices to account for more than a fraction of the decline.
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  • Marriage and child-bearing, in the first place, are operative amongst a fraction of the population only - those of conceptive age; whereas to the Urn of Death, as Dr Farr expressed it, all ages are called upon to contribute in their differing degrees.
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  • Thus, though the generally higher proportion of females in the community may seldom be enough to depress more than slightly the death-rate as a whole, it has a substantial effect upon it at the ages where women are in more marked numerical predominance, as in later life, and in places where the number of domestic servants is unusually great.
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  • A birthrate continuously in excess of the death-rate tends to lower the latter through the supply it affords of people annually reaching the more healthy ages.
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  • We find it needful to retain both terms, Renaissance and Revival of Learning, and 1 For a somewhat different view of the parcelling out into such periods, see the article Middle Ages.
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  • Here, if anywhere, it seemed as though the ecclesiastical and feudal fetters of the middle ages might be broken, and humanity might enter on a new stage of joyous unimpeded evolution.
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