Circle Sentence Examples

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  • The torches around the circle were lit.

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  • She drew a circle in the air.

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  • She walked in a circle until she found the strongest of the energy patterns in the vicinity and paused above it.

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  • She absently drew a circle in the sand.

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  • She held her hands up in a circle to demonstrate.

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  • But this circle never attained to the unity of a philosophical school.

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  • The car made one more circle in the road and then lunged at the cliff.

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  • The man at the center of the circle shifted.

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  • Gaston Paris endeared himself to a wide circle of scholars outside his own country by his unfailing urbanity and generosity.

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  • The electric lamp a gives illumination of the webs in a dark field, nearly in the manner described for the Cape transit circle micrometer; the intensity of illumination is regulated by a carbon-resistance controlled by the screw b.

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  • The erection of the cells in straight lines may cause some little complication in charging, but it allows the hot spent slices to be discharged upon a travelling band which takes them,to an elevator, an arrangement simpler than any which is practicable when the cells are disposed in a circle.

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  • Tschirnhausen, which are both related to the circle.

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  • Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it effected a mechanical solution of squaring the circle.

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  • The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected.

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  • He was, it is true, again elected to the Chamber of Baden by the circle of Thiengen, but the government, no longer willing to respect his immunity as a deputy, refused its ratification.

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  • The blackbird is found in every country of Europe, even breeding - although rarely - beyond the arctic circle, and in eastern Asia as well as in North Africa and the Atlantic islands.

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  • The inner city, or Vienna proper, was formerly separated from the other districts by a circle of fortifications, consisting of a rampart, fosse and glacis.

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  • While in exile he was elected supreme commander of the Knights of the Golden Circle in Ohio and received the Democratic nomination for governor of Ohio, but was defeated.

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  • Even within the Arctic Circle they are in many localities abundant and excessively bloodthirsty during the short summer.

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  • Creevey was a Whig and a follower of Fox, and his active intellect and social qualities procured him a considerable intimacy with the leaders of this political circle.

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  • Her innate humanity and sound sense, however, led her gradually to return to her place in the family circle, and she began also to seek out and help the poor and the sick.

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  • During the following years she became known to an increasingly wide circle, especially as a peacemaker, and entered into correspondence with many friends.

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  • The measurement of position angles is provided for by a graduated circle attached to the head.

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  • It forms an arc of a circle of which the convexity turns slightly to the north; neither bay nor promontory breaks the regularity of its outline.

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  • As a straggler it has occurred within the Arctic Circle (as on the Varanger Fjord in Norway), as well as in Iceland and even Greenland; while it not unfrequently appears in Madeira and the Azores.

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  • In the figure the radius of the inner circle is 3 mm.

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  • Hence the note produced with any given circle of holes rises in pitch as the disk revolves more rapidly; and if, the revolution of the disk being kept as steady as possible, the tube be passed rapidly across the circles of the first series, a series of notes is heard, which, if the lowest be denoted by C, form the sequence C, C1, El, G1, C2, &c. In like manner, the first circle in which we have two sets of holes dividing the circumference, the one into say 8 parts, and the other into Io,.

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  • An "anchor ring" or "tore" results when a circle revolves about an axis in its plane.

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  • Some have supposed the circle of slabs to be the retaining wall of a tumulus; but its structure is not solid enough for such a purpose, and it can hardly be anything but a sacred enclosure.

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  • The circle on the line joining the internal and external centres of similitude as diameter is named the " circle of similitude."

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  • That there is a tendency in such groups as are placed at the opposite points of a circle of affinity ` to meet each other.'

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  • That every natural series of beings, in its progress from a given point, either actually returns, or evinces a tendency to return, again to that point, thereby forming a circle.

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  • Atlanta was laid out in the form of a circle, the radius being 14 m.

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  • Thus the distance between New York and Oporto, following the former (great circle sailing), amounts to 3000 m., while following the rhumb, as in Mercator sailing, it would amount to 3120 m.

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  • The shell thus formed is then cut along the line of the intended equator into two hemispheres, they are then again glued together and made to revolve round an axis the ends of which passed through the poles and entered a metal meridian circle.

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  • Still further in the same direction is a third system at Kerlescan (Place of Burning), composed of 262 stones, which are distributed into thirteen lines, terminated by an irregular circle, and altogether extend over a distance of 1000 ft.

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  • All this, and the almost mutinous discontent of his generals and his enemies of the court circle, shook his resolution of acting as anvil for the Russians, of whose delay also he was aware, and about the 8th of Octoberhedetermined to march out north-eastward across the French lines of communication and save his sovereign's army by taking refuge if necessary in Saxony.

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  • Leonardo certainly was in relation with some persons belonging to that circle when he published in 1220 another more extensive work, De practica geometriae, which he dedicated to the imperial astronomer Dominicus Hispanus.

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  • The surface of the inland ice forms in a transverse section from the west to the east coast an extremely regular curve, almost approaching an arc of a wide circle, which along Nansen's route has its highest ridge somewhat nearer the east than the west coast.

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  • In Cathays Park there is also a "gorsedd" or bardic circle of huge monoliths erected in connexion with the eisteddfod of 1899.

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  • The whole plan is drawn from three centres, the outer portion of the curves being arcs of a larger circle than the one used for the central portion; the complete circle of the orchestra is marked by a sill of white limestone, and greatly enhances the effect of the whole.

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  • They consist of a long rectangular building, with a proscenium or column front which almost forms a tangent to the circle of the orchestra; at the middle and at either end of this proscenium are doors leading into the orchestra, those at the end set in projecting wings; the top of the proscenium is approached by a ramp, of which the lower part is still preserved, running parallel to the parodi, but sloping up as they slope down.

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  • He soon changed his mind, however, and, admitting them to the circle of his intimates, loaded them with favours.

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  • That he was the most attractive figure of a man of letters in his generation is admitted; and the acknowledged fascination of his character was deepened, and was extended over an extremely wide circle of readers, by the publication in 1899 of his Letters, which have subdued even those who were rebellious to the entertainment of his books.

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  • The stories of a scorpion stinging itself to death when placed in a circle of burning coals are due to erroneous observation.

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  • According to his view, all mountain ranges parallel to the same great circle of the earth are of strictly contemporaneous origin, and between the great circles a relation of symmetry exists in the form of a pentagonal reseau.

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  • From Heaven and Earth sprang the remaining members of a circle analogous to the Olympic gods.

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  • Mithras was the most important member of the circle.

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  • The determination of the side of a regular heptagon which can be inscribed or circumscribed to a given circle was reduced to a more complicated equation which was first successfully resolved by Abul Gud.

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  • These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

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  • The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

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  • The question is thus reduced to that of finding the effect of the first zone, or central circle, of which the area is 7rXr.

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  • The phase of the resultant is midway between those of the extreme elements, that is to say, a quarter of a period behind that due to the element at the centre of the circle.

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  • Again, if we compare the complete circle with a narrow annular aperture of the same radius, we see that in the latter case the first dark ring occurs at a much smaller obliquity, viz.

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  • We will now investigate the total illumination distributed over the area of the circle of radius r.

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  • In any case the proportion of the whole illumination to be found outside the circle of radius r is given by J02(z)+J12(z).

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  • For the osculating circle at any point includes the whole of the y curve which lies beyond; and the successive convolutions envelop one another without intersection.

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  • A year later they strangled fifty youths of the dead man's servants (all Scyths born) and fifty of the best horses, stuffed them and mounted them in a circle about the tomb.

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  • In the German Mercury he published, in the years 1786-87, his Briefe fiber die Kantische Philosophie, which were most important in making Kant known to a wider circle of readers.

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  • The circle of spearmen around the king grew less and less, and in the end James and a few of his nobles were alone left standing.

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  • Within this nearly complete circle of crystalline rocks several geological formations have been determined, of which the age cannot be more definitely fixed than that they are vastly older than the Karroo formation and newer than the Swaziland schists.

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  • This phenomenon is known as the "white rainbow" or "Ulloa's Ring or Circle," after Antonio de Ulloa.

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  • A third hypothesis is that advanced by Karl Rieder (Der Gottesfreund von Oberland, Innsbruck, 1905), who thinks that not even Merswin himself wrote any of the literature, but that his secretary and associate Nicholas of Lowen, head of the House of St John at Griinenworth, the retreat founded by Merswin for the circle, worked over all the writings which emanated from different members of the group but bore no author's names, and to glorify the founder of the house attached Merswin's name to some of them and out of his imagination created "the Friend of God from the Oberland," whom he named as the writer of the others.

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  • Among the works which he translated into Syriac and of which his versions survive are treatises of Aristotle, Porphyry and Galen, 3 the Ars grammatica of Dionysius Thrax, the works of Dionysius the Areopagite, and possibly two or three treatises of Plutarch.4 His own original works are less important, but include a " treatise on logic, addressed to Theodore (of Merv), which is unfortunately imperfect, a tract on negation and affirmation; a treatise, likewise addressed to Theodore, On the Causes of the Universe, according to the Views of Aristotle, showing how it is a Circle; a tract On Genus, Species and Individuality; and a third tract addressed to Theodore, On the Action and Influence of the Moon, explanatory and illustrative of Galen's IIEpi rcptaiµwv r t µepwv, bk.

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  • The toga was a piece of woollen cloth in the form of a segment of a circle, 2 the chord of the arc being about three times the height of the wearer, and the height a little less than one-half of this length.

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  • He belonged to the circle of Peisistratus at Athens, and was the founder of an Orphic community.

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  • In the circle of Scipio he doubtless met the historian Polybius, who was brought to Italy in 167.

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  • Like his brother Isaac, Jacob Abendana had a circle of Christian friends, and his reputation led to the appreciation of Jewish scholarship by modern Christian theologians.

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  • Haller occupied in the new university of Gottingen (founded 1737) a position corresponding to that of Boerhaave at Leiden, and in like manner influenced a very large circle of pupils, The appreciation of his work in physiology belongs to the history of that science; we are only concerned here with its influence on medicine.

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  • Though a prominent member of the inner Liberal circle and a stanch party man, it was not supposed by the public at this time that any ambition for the highest place could be associated with Sir Henry CampbellBannerman; but the divisions among the Liberals, and the rivalry between Lord Rosebery and Sir William Harcourt, made the political situation an anomalous one.

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  • He was now introduced to a less questionable and even more distinguished coterie than Vendome's, to the famous "court of Sceaux," the circle of the beautiful and ambitious duchesse du Maine.

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  • In the parish of Lochrutton, a few miles south-west of Maxwelltown, there is a good example of a stone circle, the "Seven Grey Sisters," and an old peel-tower in the Mains of Hills.

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  • This company combines with the Metropolitan District to form the Inner Circle line, which has stations close to all the great railway termini north of the Thames.

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  • For the special supervision and encouragement of indigenous primary education in monastic and in lay schools, each circle of inspection is divided into sub-circles corresponding with one or more of the civil districts, and each sub-circle is placed under a deputyinspector or a sub-inspector of schools.

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  • There is a gold mine at Kyaukpazat in the Mawnaing circle of the Kathra district, where the quartz is crushed by machinery and treated by chemical processes.

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  • He was a staunch supporter of Charlemagne's principles of government and educational reforms; he established schools, and by his own literary achievements showed himself a worthy member of the learned circle which graced the Carolingian court.

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  • Thus the core of a circle or an ellipse is a concentric circle or ellipse of one quarter the size.

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  • There is no need to doubt the reality of Catherine's exaltation, but it should be remembered that she and her circle were Dominicans, and that the stigmata of St Francis of Assisi were considered the crowning glory of the saint, and hitherto the exclusive boast of the Franciscans.

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  • To this year, 1376, belongs the admission to Catherine's circle of disciples of Stefano di Corrado Maconi, a Sienese noble distinguished by a character full of charm and purity, and her healing of the bitter feud between his family and the Tolomei.

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  • He was forced to resign office, but still continued to advise Louis, and was one of the inner circle of the king's friends, called by the revolutionists "the Austrian Committee."

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  • The lophophore is a simple circle in all Polyzoa except in the Phylactolaemata, where it typically has the form of a horse shoe outlined by the bases of the tentacles.

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  • Madame Comte conceived a dislike to the circle she found there, and this was the too early beginning of disputes which lasted for the remainder of their union.

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  • It was true that the bent of his genius was slightly altered, in a direction which seemed less purely and austerely that of the highest art; but his concessions to public taste vastly added to the width of the circle he now addressed.

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  • In 1857 two Arthurian poems had been tentatively and privately printed, as Enid and Nimue, or the True and the False, to see how the idyllic form would be liked by the inner circle of Tennyson's friends.

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  • Verona, which is the chief military centre of the Italian province of Venetia, is now being surrounded with a circle of forts far outside the obsolete city walls.

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  • The bishops of Eichstatt were princes of the Empire, subject to the spiritual jurisdiction of the archbishops of Mainz, and ruled over considerable territories in the Circle of Franconia.

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  • If the box be round, they will seek to lead the eye away from the naked regularity of the circle by a pattern distracting attention, as, for example, by a zigzag breaking the circular outline, and supported by other ornaments.

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  • Down to the end of this era painting was entirely in the hands of a patrician castecourtiers, priests, feudal nobles and their military retainers, all men of high education and gentle birth, living in a polished circle.

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  • But it is impossible to admit within the circle of high-art productions these wooden figures of everyday men and women, unrelieved by any subjective element, and owing their merit entirely to the fidelity with which their contours are shaped, their muscles modelled, and their anatomical proportions preserved.

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  • After the outbreak of the Civil War many of the Democrats of the Middle West, who were opposed to the war policy of the Republicans, organized the Knights of the Golden Circle, pledging themselves to exert their influence to bring about peace.

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  • The great importance of the Knights of the Golden Circle and its successors was due to its opposition to the war policy of the Republican administration.

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  • The demolition of the ramparts of Old Calais was followed by the construction of a new circle of defences, embracing both the old and new quarters, and strengthened by a deep moat.

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  • And since, in the series for the circle, the second term was 2 3 3, I put m=?„....

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  • He returned to Paris before the end of the year, was well received by his family, and mixed in the cultivated circle which frequented the salon of his mother, among them Lebrun-Pindare, Lavoisier, Lesueur, Dorat, Parmy, and a little later the painter David.

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  • The domestic dog would be brought into the sacred circle through the increased veneration for animals, and the more pronounced view in later times of Anubis as servant, messenger and custodian of the gods.

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  • By looking at them together we understand how much the comedy of Terence was able to do to refine and humanize the manners of Rome, but at the same time what a solvent it was of the discipline and ideas of the old republic. What makes Terence an important witness of the culture of his time is that he wrote from the centre of the Scipionic circle, in which what was most humane and liberal in Roman statesmanship was combined with the appreciation of what was most vital in the Greek thought and literature of the time.

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  • But in the last years during which this circle kept together a new spirit appeared in Roman politics and a new power in Roman literature, the revolutionary spirit evoked by the Gracchi in opposition to the long-continued ascendancy of the senate, and the new power of Roman satire, which was exercised impartially and unsparingly against both the excesses of the revolutionary spirit and the arrogance and incompetence of the extreme party among the nobles.

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  • Roman satire, though in form a legitimate development of the indigenous dramatic satura through the written satura of Ennius and Pacuvius, is really a birth of this time, and its author was the youngest of those admitted into the intimacy of the Scipionic circle, C. Lucilius of Suessa Aurunca (c. 180-103).

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  • One or two of the circle of Catullus survived into that age; but an entirely new spirit came over the literature of the new period, and it is by new men, educated indeed under the same literary influences, but living in an altered world and belonging originally to a different order in the state, that the new spirit was expressed.

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  • Amboyna Island lies off the south-west of Ceram, on the north side of the Banda Sea, being one of a series of volcanic isles in the inner circle round the sea.

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  • Like his father, he was nowhere happier than in the family circle, and he was particularly attached to his -sister, the grand-duchess Xenia, who was seven years younger than himself.

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  • The etiquette of the imperial circle, scenes from the law-courts and the recitationroom, the reunions of dilettanti and philosophers, the busy life of the capital or of the municipal town, the recreations of the seaside and of the country - all these he brings vividly before our eyes.

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  • Lord Ashley now retired into Holland, where he became acquainted with Le Clerc, Bayle, Benjamin Furly, the English Quaker merchant, at whose house Locke had resided during his stay at Rotterdam, and probably Limborch and the rest of the literary circle of which Locke had been a cherished and honoured member nine or ten years before.

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  • The Copenhagen post gave him, as well as some other diplomats, an exceptional opportunity of watching the principal moving powers of European politics from a point of vantage, as the matrimonial alliances of the Danish royal family occasionally brought together in a friendly family circle the widow of Alexander III, Nicholas II and the Prince of Wales who was to become King Edward VII.

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  • But as the orbits are not centred on the sun, which is in a focus of each, the displacement of the seeming circle would be readily seen in the case of Mercury and of Mars.

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  • His influence on literature, which he encouraged after the manner of Maecenas, was considerable, and the group of literary persons whom he gathered round him - including Tibullus, Lygdamus and the poet Sulpicia - has been called "the Messalla circle."

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  • In order that no other settlements should encroach upon his centre of government, New Castle, the northern boundary was determined by drawing an arc of a circle, 12 m.

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  • There is also a position circle, attached at m to the eye-end, provided with a slide to move the eye-piece radially from the axis of the telescope, and with a micrometer to measure the distance of an object from that axis.

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  • Complete rotation of the head is obviously impossible because of the interference of the declination axis with the rods, and therefore, in some angles, objects cannot be measured in two positions of the circle.

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  • It permits complete rotation of the tube and measurement of all angles in reversed positions of the circle; the handles that move the slides can be brought down to the eye-end, inside the tube, and consequently made to rotate with it; and the position circle may be placed at the end of the cradle next the eyeend where it is convenient of access.

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  • The hour circle is also read by microscopes, and the instrument can be used in both positions (tube preceding and following) for elimination of the effect of flexure on the position angles.

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  • When a shaft is driven by means of gearing the driving torque is measured by the product of the resultant pressure P acting between the wheel teeth and the radius of the pitch circle of the wheel fixed to the shaft.

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  • The use of a coronet by the barons dates from the coronation of Charles II., and by letters patent of the 7th of August 1661 their coronet is described as a circle of gold with six pearls on it.

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  • Ptolemy Soter (reigned 323-285 B.C.), to whom, in the general distribution of Alexander's conquests, this kingdom had fallen, began to draw around him from various parts of Greece a circle of men eminent in literature and philosophy.

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  • Their works are never national, never addressed to a people, but to a circle of learned men.

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  • To perform their task adequately required from the critics a wide circle of knowledge; and from this requirement sprang the sciences of grammar, prosody, lexicography, mythology and archaeology.

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  • In 1848 he removed to London to fill a post in the board of health, under Edwin Chadwick, and became a prominent member of the brilliant circle which included George Grote and John Stuart Mill.

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  • In the circle of his family and intimate friends, away from the great world in which he made so poor a figure, he was greatly esteemed.

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  • A few months later Thomas Cranmer, who had been one of those to discuss sympathetically Luther's works in the little circle at Cambridge, and who believed the royal supremacy would tend to the remedying of grave abuses and that the pope had acted ultra vires in issuing a dispensation for the king's marriage with Catherine, was induced by Henry to succeed Warham as archbishop of Canterbury.

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  • On the other hand he insisted on the synthetic character of this activity without which it was impossible to get beyond the circle of our own thoughts.

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  • If there be any truth in this suggestion it seems likely that the last word of idealism, like the first, will prove to be that the type of the highest reality is to be sought for not in any fixed Parmenidean circle of achieved being but in an ideal of good which while never fully expressed under the form of time can never become actual and so fulfil itself under any other.

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  • The defences consist of an inner line of works which preserve the place against surprise, and of an outlying chain of detached forts of fairly modern construction, forming roughly two-thirds of a circle of three miles radius.

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  • Their arms comprise two short swords, a longer spear, a round shield, and they sometimes wear a coat of mail; a curious feature is their tactics of fighting in a circle of protecting shields.

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  • There is some ground for believing that it was the third-abbot of Monte Cassino who began to spread a knowledge of the Rule beyond the circle of St Benedict's own foundations.

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  • Probably the original tradition goes back to a time when Yahweh was recognized as a deity of a circle of connected tribes of which the Israelite tribes formed a part.

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  • He places himself in a sense within the dogmatic circle by his declaration that guidance is to be expected from developments - in a " free Protestant evangelical spirit " - out of the old confessions of the Protestant churches.

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  • The word is used also to designate the supporting frame or arms carrying the microscopes or verniers of a graduated circle.

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  • From the Porte electric trams run to the harbour and also in a circle round the native city.

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  • If a .JP solid circle be fixed in any one position and a tube be pivoted on its centre so as to move; and if the line C D be drawn upon the circle pointing towards any object Q in the heavens which lies in the plane of the circle, by turn ing the tube A B towards any other object P in the plane of the circle, the angle B 0 D will be the angle subtended by the two objects P and Q at the eye.

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  • A collection of circles such as is the armillary sphere, if each circle were fitted with a view-tube, might be considered a complete astrolabe.

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  • In fact the modern equatorial, and the altitude and azimuth circle are astrolabes in the strictest and oldest meaning of the term; and Tycho in one of his astrolabes came so near the modern equatorial that it may be taken as the first of the kind.

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  • The term " mensuration " is therefore ordinarily restricted to the measurement of areas and volumes, and of certain simple curved lengths, such as the circumference of a circle.

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  • This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

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  • The ordinary definition of a circle is equivalent to definition as the figure generated by the rotation of a radius of constant length in a plane, and is thus essentially analytical.

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  • The ideas of the centre and of the constancy of the radius do not, however, enter into the elementary conception of the circle as a round figure.

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  • The ratio 47r would thus first appear as the ratio of the average breadth of a circle to the greatest breadth; the interpretation of 7 as the ratio of the circumference to the diameter being a secondary one.

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  • A collection of formulae relating to the circle, for instance, would comprise not only geometrical and trigonometrical formulae, but also approximate formulae, such as Huygens's rule (§ 91), which are the result of advanced analysis.

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  • For fuller discussion reference should be made to Geometry and Trigonometry, as well as to the articles dealing with particular figures, such as Triangle, Circle, &C.

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  • The length of the arc of a circle, for instance, is known if the length of the chord and its distance from the middle point of the arc are known; but it may be more convenient in such a case to use a formula such as Huygens's rule than to obtain a more accurate result by means of trigonometrical tables.

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  • Denoting the constant ratio by fir, the area of a circle is ira 2, where a is the radius, and ir=3.14159 approximately.

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  • The figure Abdc is a sector of an annulus, which is the portion of a circle left after cutting out a concentric circle.

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  • By considering the circle as the limit of a polygon, it follows that the formulae (iii) and (v) of § 26 hold for a right circular cylinder and a right circular cone; i.e.

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  • The circle, for instance, is regarded geometrically as a line described in a particular way, while from the point of view of mensuration it is a figure of a particular shape.

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  • Certain approximate formulae for the length of an arc of a circle are obtained by methods similar to those of §§ 71 and 79.

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  • In 1589 Greenwood and Barrow composed " A true Description out of the Word of God of the visible Church," which represents the ideal entertained in their circle.

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  • In 1848 he retired to Macon; but there, as in Paris, he was the centre of a brilliant circle, for he was a wonderful causeur, and an equally good listener, and had many interesting experiences to recall.

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  • It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."

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  • The idea of Oceanus as a river flowing unceasingly round the earth, which was regarded as a flat circle, was of long continuance.

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  • Then the reflected ray QR and the ray reflected at R, and so on, will all touch the circle drawn with ON as radius.

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  • A ray making an angle less than 0 with the tangent will, with its reflections, touch a larger circle.

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  • Hence all rays between =0 will be confined in the space between the outer dome and a circle of radius OP cos 0, and the weakening of intensity will be chiefly due to vertical spreading.

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  • The cylinder is mounted on an axis and turned round, while the style attached to the vibrating body is in light contact with it, and traces therefore a wavy circle, which, on taking off the paper and flattening it, becomes a wavy straight line.

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  • If the two forks have the same frequency, it is easily seen that the figure will be an ellipse (including as limiting cases, depending on relative amplitude and phase, a circle and a straight line).

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  • If the rod is circular in section and perfectly uniform the end will describe a circle, ellipse or straight line; but, as the elasticity is usually not exactly the same in all directions, the figure usually changes and revolves.

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  • He allowed a limited number of teeth on the arc of a circle to strike against a card.

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  • The circle was complete, but there were no Russians in the centre, and a map of the positions of the Japanese on the evening of the 10th shows the seventeen divisions thoroughly mixed up and pointing in every direction but that of the enemy.

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  • All sections of the 1 The surfaces formed by revolving a circle about any chord also received attention at the hands' of the Greeks.

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  • The surface and solid traced by the revolution of the lesser segment of a circle is termed a "spindle."

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  • If the plane does not contain the centre, the curve of intersection is a "small circle," and the solid cut off is a "segment."

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  • The shortest distance between two points on a sphere is the arc of the great circle containing the points.

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  • The extremities of the diameter perpendicular to a small circle are called the "poles" of that circle, and the distance from the pole to the circle, measured by the arc of the great circle through the pole, is the "polar distance" of the small circle.

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  • The solid enclosed by a small circle and the radii vectores from the centre of the sphere is a "spherical sector"; and the solid contained between two spherical sectors standing on copolar small circles is a "spherical cone."

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  • Calling the radius r, and denoting by the ratio of the circumference to the diameter of a circle, the volume is 31rr 3, and the surface 41rr2.

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  • Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.

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  • It is impossible to adopt the view that the Homeric poets turned the rude shepherd-god of Arcadia into a messenger, in order to provide him with a place in the Olympian circle.

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  • Fauriel was introduced by Madame de Stael to the literary circle of Auteuil, which gathered round Destutt de Tracy.

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  • Finally he quarrelled with Hume because the latter would not acknowledge all his own friends and Rousseau's supposed enemies of the philosophe circle to be rascals.

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  • But he disliked the friction with his family circle which this policy produced.

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  • Formerly it was the general belief that the herring inhabits the open ocean close to the Arctic Circle, and that it migrates at certain seasons towards the northern coasts of Europe and America.

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  • Outside the circle, especially to the south of it, numerous remains of houses of the Mycenaean age have been found, and others, terraced up at various levels, occupy almost the whole of the Acropolis.

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  • Tradition ascribes their invention to Tajao, minister of the emperor Hwang-ti, who reigned c. 2697 B.e., and it can scarcely be placed later than the 7th century B.e.4 The Chinese circle of the " animals " obtained early a wide diffusion.

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  • They were called the " media of the whole circle of the zodiac "; 11 each ten-day period of the Egyptian year was consecrated to the decanal god whose section of the ecliptic rose at its commencement; the body was correspondingly apportioned, and disease was cured by invoking the zodiacal regent of the part affected.

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  • The decans are ranged on the outermost of its five concentric zones; the planets and the Greek zodiac in duplicate occupy the next three; while the inner circle is unaccountably reserved for the Chinese cyclical animals.

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  • His satire Babie Kolo (The Women's Circle) gave offence on account of its personalities.

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  • He introduced several practical improvements, such as the measurement of time to tenths of a second; and he prevailed upon the government to replace Bird's mural quadrant by a repeating circle 6 ft.

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  • While his scientific work procured him an extraordinary reputation among his contemporaries, his private character and virtues, the charm of his social manners, his wit and powers of conversation, endeared him to a large circle of personal friends.

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  • Outside this improved inner line, which includes the whole area of the attack and defence of 1870, lies a complete circle of detached forts and batteries of modern construction.

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  • As a pupil of the famous Pomponius Laetus, and, subsequently, as a member of the circle of Cosmo de' Medici, he received a finished education.

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  • If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in F, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an ellipse, or circle with centre F and radius FA; while the time-curve will be a sinusoid.

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  • The north to south distance from Bering Strait to the Antarctic circle is 9300 m., and the Pacific attains its greatest breadth, 10,000 m., at the equator.

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  • This literature is especially valuable because it illustrates contemporary Halaka and Haggada, and it illuminates the circle of thought with which Jesus and his followers were familiar; it thus fills the gap between the Old Testament and the authoritative Rabbinical Midrashim which, though often in a form several centuries later, not rarely preserve older material.'

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  • These general principles and the novelty of the method ensured the success of the undertaking even after the original circle of exceptionally able men who founded it had been dispersed.

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  • It does not, of course, follow that everyone who had shared in the divine afflatus of prophetic enthusiasm gave forth oracles; but the prophets as a class stood nearer than other men to the mysterious workings of Yahweh, and it was in their circle that revelation seemed to have its natural home.

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  • As a man of practical aims he required a circle through Elisha.

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  • Yahweh's kingdom cannot perish even for a time; nay, Isaiah argues that it must remain visible, and visible not merely in the circle of the like-minded whom he had gathered round him and who formed the first germ of the notion of the church, but in the political form of a kingdom also.

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  • He traced his descent from Robert of Mortain, half brother of the Conqueror and first earl of Cornwall; he married about 1200 the daughter of William de Vernon, earl of Devon; and thus, from the beginning of his career, he stood within the circle of the great ruling families.

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  • Either from its Pelasgic or Etrurian use or from Romans, this foot appears to have come into prehistoric remains, as the circle of Stonehenge (26) is 100 ft.

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  • The totality of being may thus be conceived as a series of concentric circles, fading away towards the verge of non-existence, the force of the original Being in the outermost circle being a vanishing quantity.

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  • Round the city lies a circle of populous suburbs - to the north-east Fitzroy (pop. 31,687) and Collingwood (32,749), to the east Richmond (37,824), to the south-east Prahran (40,441), to the south South Melbourne (40,619), to the south-west Port Melbourne (12,176), and to the north-west North Melbourne (18,120).

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  • The circumstances which led to his admission into the apostolic circle are not stated; while the motives by which he was actuated in enabling the Jewish authorities to arrest Jesus without tumult have been variously analysed by scholars.

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  • The umbrella-like body bears a circle of tentacles at the edge, whereby the body can be divided into a convex exumbrella or exumbral surface and a concave subumbrella or subumbral surface.

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  • The eyes are refractive globules set in a cup of red pigment traversed by a nerve fibre, and lie on the proximal side of the body, directly on the postero-dorsal surface of the brain, or at a little distance from it, on the neck, often within the circle on the corona, and usually well within the transparent body.

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  • It is generated by the extremities of a rod which is constrained to move so that its middle point traces out a circle, the rod always passing through a fixed point on the circumference.

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  • The polar equation is r=a+b cos 0, where 2a= length of the rod, and b= diameter of the circle.

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  • It is the inverse of a central conic for the focus, and the first positive pedal of a circle for any point.

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  • The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.

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  • Properties of the limagon may be deduced from its mechanical construction; thus the length of a focal chord is constant and the normals at the extremities of a focal chord intersect on a fixed circle.

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  • There are three fronts; the principal, towards College Green, is a colonnade of the Ionic order, with façade and two projecting wings; it connects with the western portico by a colonnade of the same order, forming the quadrant of a circle.

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  • By Maximilian's administrative organization of the empire in 1500 the duchy of Westphalia was included as an appanage of Cologne in the scattered circle of the Lower Rhine.

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  • The Westphalian circle which was formed at the same time comprised nearly all the rest of the modern province (including Mark) and the lands north of it between the Weser and the frontier of the Netherlands, also Verden, Schaumburg, Nassau, Wied, Lippe, Berg, Cleves, Julich, Liege, Bouillon and Cambrai.

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  • The places of the objects were at the same time determined with the Dorpat meridian circle (Stellarum fixarum imprimis duplicium et multiplicium positiones mediae, St Petersburg, 1852 seq.).

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  • After the manner of the sophists of the period, Bion travelled through Greece and Macedonia, and was admitted to the literary circle at the court of Antigonus Gonatas.

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  • Du Bellay returned with Ronsard to Paris to join the circle of students of the humanities attached to Jean Daurat at the College de Coqueret.

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  • He lived in a literary circle, and fell in love with the beautiful Vittoria Colonna.

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  • When a jack-rabbit starts up before them, one of the coyotes bounds away in pursuit while the other squats on his haunches and waits his turn, knowing full well that the hare prefers to run in a circle, and will soon come round again, when the second wolf takes up the chase and the other rests in his turn..

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  • When hunting antelope (prongbuck) and deer the coyotes spread out their pack into a wide circle, endeavouring to surround their game and keep it running inside their ring until exhausted.

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  • To start the canter, which should always be done from the walk and not the trot, take up the curb rein a little and turn the horse's head slightly to the right, at the same time pressing the left leg behind the girth; the horse will then lead with the off (right) fore leg, which is generally preferred; but a well-broken hack should lead with either leg at command, and if he be cantered in a circle to the left he must lead with the near leg, as otherwise an ugly fall is likely to result from the leg being crossed.

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  • In astronomy, the "celestial equator" is the name given to the great circle in which the plane of the terrestrial equator intersects the celestial sphere; it is consequently equidistant from the celestial poles.

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  • The form of a circle is familiar to all; and we proceed to define certain lines, points, &c., which constantly occur in studying its geometry.

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  • The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.

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  • Since the equation to a circle of zero radius is x 2 +y 2 =o, i.e.

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  • The general equation to the circle in trilinear co-ordinates is readily deduced from the fact that the circle is the only curve which intersects the line infinity in the circular points.

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  • It is also more particularly applied to a mathematical instrument ("pair of compasses") for measuring or for describing a circle, and to the mariner's compass.

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  • It is also provided with an azimuth circle or mirror and a shadow pin or style placed in the centre of the glass cover, by either of which the variable angle between the compass north and true north, called the "total error," or variation and deviation combined, can be observed.

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  • In the second part Peregrinus describes first an improved floating compass with fiducial line, a circle graduated with 90 degrees to each quadrant, and provided with movable sights for taking bearings.

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  • He then describes a new compass with a needle thrust through a pivoted axis, placed in a box with transparent cover, cross index of brass or silver, divided circle, and an external "rule" or alhidade provided with a pair of sights.

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  • The form he recommends for the needle is that of "a true circle, having his Axis going out beyond the circle, at each end narrow and narrower, unto a reasonable sharpe point, and being pure steele as the circle it selfe is, having in the middest a convenient receptacle to place the capitell in."

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  • With joy and pride he welcomed the Byzantine East into the circle of vassal peoples and kingdoms of Rome bound politically to the see of St Peter, and with the same emotions beheld the patriarchate of Constantinople at last recognize Roman supremacy.

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  • Constant, who had met Madame de Stael at Lausanne in 1794, followed her in the next year to Paris, where he rapidly became a personage in the moderate republican circle which met in her salon; and by 1796 he had established with her intimate relations, which, in spite of many storms, endured for ten years.

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  • Much of Constant's time was spent with her at Coppet; but he also made long sojourns at Weimar, where he mixed in the GoetheSchiller circle, and accumulated material for the great work on religion which he had begun, so far back as 1787, at Colom bier.

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  • For the statement of the motions of these bodies uniform motion in a circle was employed as a fundamental type, combinations of motions of this type being constructed to fit the observations.

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  • As a law of acceleration of the planets relatively to the sun, its approximate agreement with Kepler's third law of planetary motion follows readily from a consideration of the character of the acceleration of a point moving uniformly in a circle.

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  • A small body hanging by a string, at rest relatively to the earth, moves relatively to this base uniformly in a circle; that is to say, with constant acceleration directed towards the earth's axis.

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  • In addition to the eyes and the olfactory circle on the head scattered tactile papillae are found on the ectoderm.

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  • The Sea of the Great Bend would seem to be the sea fed by the north-to-south waters of Naharin, just as the Mediterranean, fed by the south-to-north waters of the Nile, is called the Great Circle (šn wr).

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  • It is probable that he was born in Lemnos, studied and taught at Athens, and then settled in Rome (where he would naturally be called atheniensis) as a member of the learned circle with which Julia Domna surrounded herself.

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  • Some lines on the siege of Ostend spread his fame beyond the circle of the learned.

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  • Grotius combined a wide circle of general knowledge with a profound study of one branch of law.

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  • In physical science, a halo is a luminous circle, surrounding the sun or moon, with various auxiliary phenomena, and formed by the reflection and refraction of light by ice-crystals suspended in the atmosphere.

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  • Passing through the luminary and parallel to the horizon, there is a white luminous circle, the parhelic circle (P), on which a number of images of the luminary appear.

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  • The other images on the parhelic circle are the paranthelia (q) and the anthelion (a) (from the Greek av-ri, opposite, and iXcos, the sun).

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  • A vertical circle passing through the sun may also be seen.

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  • Thomas Young explained the parhelic circle (P) as due to reflection from the vertical faces of the long prisms and the bases of the short ones.

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  • If these vertical faces become very numerous, the eye will perceive a colourless horizontal circle.

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  • Reflection from an excess of horizontal prisms gives rise to a vertical circle passing through the sun.

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  • As the sun rises, the rays enter the prisms more and more obliquely, and the angle of minimum deviation increases; but since the emergent ray makes the same angle with the refracting edge as the incident ray, it follows that the parhelia will remain on the parhelic circle, while receding from the inner halo.

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  • The emerging rays are parallel to their original direction and form a colourless image on the parhelic circle opposite the sun.

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  • Three miles south is a fine stone circle, and to the south-east are the wells of Struell, famous as miraculous healers among the peasantry until modern times.

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  • It was not till 1168 that the gigantic four-headed image of Swantevit was destroyed at Arcona, the capital of the island of Riigen, and this Mona of Slavonic superstition was included in the advancing circle of Christian 5 Church, Gifts of Civilization, p. 330.6 Bede, H.E.

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  • The inner circle of communicant members is hardly more than one-third of the total.

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  • These streets are connected by an inner circle of boulevards, constructed just outside the canal, which marks the site of the town moat.

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  • Within this circle the majority of the streets are narrow and crooked, while those between it and the bastions, though broader on the whole, have but little regularity.

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  • An outer circle of boulevards, planted with trees and commanding the view of the suburbs, lies just beyond the present walls of the city, erected by the Spaniards in the 16th century; the entire length of these boulevards is traversed by an electric tramway 7 m.

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  • Until 1898 the octroi circle did not extend beyond the walls; but in that year it was found necessary, owing to the growth of the city and of municipal expenditure, to include the external quarters or Corpi Santi (a name also applied to the extramural portions of Cremona and Pavia), with their large industrial population.

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  • Hence light from any point on the slit will fill a circle about 2 in.

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  • Forcing is the accelerating, by special treatment, of the growth of certain plants, which are required to be had in leaf, in flower or in fruit before their natural season, - as, for instance, the leaves of mint at Eastertide or the leafstalks of sea-kale and rhubarb at Christmas, the flowers of summer in the depth of winter, or some of the choicest fruits perfected so much before their normal period as to complete, with the retarded crops of winter, the circle of the seasons.

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  • The provinces are subdivided into " classes," and the classes again into " circles " (ringen), each circle comprising from 5 to 25 congregations, and each congregation being governed by a " church council " or session.

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  • In Swedish Lapland, near the Arctic circle, are the great Gellivara, Kirunavara and Luossavara magnetite beds, among the largest in Europe.

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  • The qualities do not compare with those species found in North America and the Arctic circle.

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  • The white hares, however, of Russia, Siberia and other regions in the Arctic circle are very largely used in the cheaper trade of Europe, America and the British colonies.

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  • The upper plate PP is bored centrally to receive a parallel or conical pillar which supports the lower circle of the theodolite or the arm of the level which carries the telescope.

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  • To the telescope the vertical circle for reading angles in This word has been a puzzle to etymologists.

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  • The Y theodolite differs from the transit in that the supports for the telescope are low, that the telescope rests in a cradle the trunnions of which rest on the supports, and that a segment of a circle attached to the cradle replaces FIG.

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  • The instrument is similar to that described above, except that the vertical circle is not continuous, but is formed of two arcs.

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  • Chamois-shooting is most successfully pursued when a number of hunters form a circle round a favourite feeding ground, which they gradually narrow; the animals, scenting the hunters to windward, fly in the opposite direction, only to encounter those coming from leeward.

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  • The same kind of reputation which Baxter had obtained in the country he secured in the larger and more important circle of the metropolis.

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  • The circle of land formed by the skirts of the mountains, and the valley of Basseterre constitute nearly the whole of the cultivated portion.

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  • The vascular bundles and cellular tissue are sometimes developed in such a way as to form a circle, with a hollow in the centre, and thus give rise to what are called fistular or hollow leaves, as in the onion, and to ascidia or pitchers.

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  • The size of the angle between the median planes of two consecutive leaves in an alternate arrangement is their divergence; and it is expressed in fractions of the circumference of the axis which is supposed to be a circle.

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  • Here the outermost circle represents a section of that portion of the axis bearing the lowest leaf, the innermost represents the highest.

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  • Sometimes they are nearly in a circle at the same level, remaining flat or only slightly convex externally, and placed so as to touch each other by their edges, thus giving rise to valvate vernation.

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  • Within the outer municipal boundary are included (besides Deutz) the suburbs of Bayenthal, Lindenthal, Ehrenfeld, Nippes, Sulz, Bickendorf, Niehl and Poll, protected by another widely extended circle of detached forts on both banks of the Rhine.

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  • Its prosperity now rapidly increased; when railways were introduced it became the meeting-place of several lines, and in 1881 its growth necessitated the pushing outward of the circle of fortifications.

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  • In Florence in 1636 he saw Galileo, for whom he ever retained the warmest admiration, and spent eight months in daily converse with the members of a scientific circle in Paris, held together by Malin Mersenne (q.v.).

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  • It first showed itself in the publication of the De cive, of which the fame, but only the fame, had extended beyond the inner circle of friends and critics who had copies of the original impression.

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  • Accordingly, by the spring of 1660, he had managed to put his criticism and assertions into five dialogues under the title Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii, with a sixth dialogue so called, consisting almost entirely of seventy or more propositions on the circle and cycloid.'

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  • The propositions on the circle, forty-six in number (shattered by Wallis in 1662), were omitted by Hobbes when he republished the Dialogues in 1668, in the collected edition of his Latin works from which Molesworth reprints.

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  • Thus, in Prussia, the representative assembly of the Circle (Kreistag) is composed of delegates of the rural communes, as well as of the large landowners and the towns, while the members of the provincial diet (Provinziallandtag) are chosen by the Kreistage and by such towns as form separate Kreise.

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  • Below the Regierungsbezirk is the Kreis, or Circle, in Prussia, Baden and Hesse, which corresponds to the Distrikt in Bavaria, the Oberamt in Wurttembergi and the Amtshauplmannschaft in Saxony.

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  • The representative assembly of the Circle (Kreistag, Distrikisral in Bavaria, Amtsversammlung in Wtirttemberg, Bczirksversammlung in Saxony) is elected by the communes, and is presided over by an official, either elected or, as in the case of the Prussian Landrat, nominated from a list submitted by the assembly.

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  • Antiquarian remains are somewhat numerous, such as forts and cairns in Cromarty parish, and stone circles in Urquhart and Logie Wester and Knockbain parishes, the latter also containing a hut circle and rock fortress.

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  • Probably these epistles did not originally bear Clement's name at all, but formed a single epistle addressed to ascetics among an actual circle of churches.

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  • After a momentary reconciliation with Louis during his illness at Metz in 1744, Marie shut herself up more closely with her own circle of friends until her death at Versailles on the 24th of June 1768.

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  • It is the seat of a Greek Orthodox (Rumanian) archbishop, and of the superintendent of the Protestants for the Transylvanian circle.

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  • In meeting all the extraordinary demands resulting from the Civil War he displayed great energy and resourcefulness, and was active in thwarting the schemes of the secessionists in the neighbouring state of Kentucky, and of the Knights of the Golden Circle, the Order of American Knights, and the Sons of Liberty (secret societies of Southern sympathizers and other opponents of the war) in Indiana.

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  • Heights have been calculated in various less direct ways, by observing for instance the angular altitude of the summit of an arc and the angular interval between its extremities, and then making some assumption such as that the portion visible to an observer may be treated as a circle whose centre lies over the so-called auroral pole.

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  • Meanwhile the old system of provincial diets and estates was continued or revived (in 1816 in Tirol and Vorarlberg, 1817 in Galicia, 1818 in Carniola, 1828 in the circle of Salzburg), but they were in no sense representative, clergy and nobles alone being eligible, with a few delegates from the towns, and they had practically no functions beyond registering the imperial decrees, relative to recruiting or taxation, and dealing with matters of local police.

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  • The earliest Syriac work which we possess, the book " On Fate," produced in the circle of the heretic Bardaisan or Bardesanes (end of the 2nd century), largely follows Greek models.

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  • At the end of the 3rd century there was a circle of enthusiastic phil-hellenes among the Roman aristocracy, led by Titus Quinctius Flamininus, who in Rome's name proclaimed the autonomy of the Greeks at the Isthmian games of 196.

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  • In the middle of the 2nd century Roman Hellenism centred in the circle of Scipio Aemilianus, which included men like Polybius and the philosopher Panaetius.

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  • Some of these had already passed into general use, while others were confined to a more limited circle.

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  • Corn is threshed by a norag, a machine resembling a chair, which moves on small iron wheels or thin circular plates fixed to axle-trees, and is drawn in a circle by oxen.

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  • When the barrow was a stone structure, the enclosure was usually a circle of standing stones.

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  • In later times the mound itself was frequently dispensed with, and the interments made within the enclosure of a trench, a vallum or a circle of standing stones.

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  • Around its base are the remains of a circle of large standing stones.

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  • The influence of the king's example was felt far beyond the limits of his immediate circle.

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  • Austria received the circle of Burgau, and consented that the king of Prussia should take the Franconian principalities.

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  • Transylvania has the form of an irregular circle, and is a high plateau of a mean altitude of1000-1600ft.

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  • This family contains numerous species, having a wide geographical distribution, ranging in the New World from the Arctic circle as far south as Patagonia, and in the Old World throughout the whole of Europe and Asia, but absent in Africa south of the Sahara, and, of course, Australasia.

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  • Here Elisha appears as the head of the prophetic gilds, having his fixed residence at Gilga1.4 Another circle, which presupposes the accession of the house of Jehu, places him at Dothan or Carmel, and represents him as a personage of almost superhuman dignity.

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  • He also determined the mass of the moon, and from a discussion of the Greenwich transit circle observations between 1851 and 1865 he found for the constant of nutation the value 9.134".

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  • The newly married couple took a lease of Lansdowne House, which for several years was a salon for the Liberal party and a centre of hospitality for a much wider circle.

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  • Carlyle's connexion with Charles Buller, a zealous utilitarian, introduced him to the circle of " philosophical radicals."

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  • She formed a little circle of friends, attached to her rather than to her husband; and to one of them, Giuseppe Mazzini, she confided her troubles in 1846.

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  • She was wise with the wisdom of the Guises, but sincere friends she had none, and with all her trained fascinations she made few, except in the circle of the Flemings, Beatons, Livingstones and Seatons.

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  • In the first place, a hare, when found, generally describes a circle in her course which naturally brings her upon her foil, which is the greatest trial for hounds.

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  • His circle of friends included men of every denomination, every class and almost of every nation.

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  • Thus, as the cult of a particular divinity spreads farther and farther, so the circle expands from which are drawn those who visit his sanctuary.

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  • And the sympathy of Christendom soon led them beyond this immediate circle.

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  • In 1776 some specimens of Schiller's lyric poetry had appeared in a magazine, and in1777-1778he completed his drama, Die Rduber, which was read surreptitiously to an admiring circle of schoolmates.

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  • The inner town is surrounded by the Innere RingStrasse, a circle of wide boulevards on the site of the old wall.

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  • The influence exercised by this society is very great, and it has attracted within its circle the best writers of Hungary.

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  • It also follows that a line half-way between a point and its polar and parallel to the latter touches the parabola, and therefore the lines joining the middle points of the sides of a self-conjugate triangle form a circumscribing triangle, and also that the ninepoint circle of a self-conjugate triangle passes through the focus.

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  • John Wallis utilized the intersections of this curve with a right line to solve cubic equations, and Edmund Halley solved sextic equations with the aid of a circle.

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  • The Knights of the Golden Circle, and other secret societies, whose aims were the promulgation of state sovereignty and the extension of aid to the Confederate states, began to flourish, and it is said that in 1864 there were 50,000 members of the Sons of Liberty in the state.

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  • The historian's grandfather became within his own circle a highly esteemed interpreter of Scripture, and held fast his profession even in the time of Julian.

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  • By the peace of Paris of 1814 the bulk of Gelderland was incorporated in the United Netherlands, the remainder falling to Prussia, where it forms the circle of Dusseldorf.

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  • Of course this would be true had Thule been situated under the Arctic Circle, which Pytheas evidently considered it to be, and his skill as an astronomer would lead him to accept as a fact what he knew must be true at some point as a voyager proceeded onwards.

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  • During the time that he was crown prince Louis resided chiefly at Innsbruck or Salzburg as governor of the circle of the Inn and Salzach.

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  • Presently, when He told that His mother and brethren were calling for Him, He disclaimed their interference by pointing to a new circle of family relationship, consisting of all those who " do the will of God."

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  • When His disciples afterwards asked for an explanation, He prefaced it by saying that the inner circle only were intended to understand.

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  • And then, addressing a yet wider circle, He demanded of those who should follow Him a self-sacrifice like His own.

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  • More and more the Master devotes Himself to the little circle of His disciples, who are taught that they, as well as He, can only triumph through defeat, succeed by failure, and find their life in giving it away.

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  • In the narrower circle of his friends his birthdays were the signal for congratulatory verses.

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  • Accordingly the history of philosophy is the presupposition of logic, or the three branches of philosophy form a circle.

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  • This construction assumes that the sun describes daily a small circle about the pole of the celestial sphere, and ignores any diurnal variation in the declination.

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  • He never was a member of the Humanist circle; he was too much in earnest about religious questions and of too practical a turn of mind.

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  • At first he expressed himself in the phrases common to scholastic theology, when these were found to be inadequate in words borrowed from the mystical writers of the 14th and 15th centuries, and then in new phrases more appropriate to the circle of fresh thoughts.

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  • Biblical history itself recognizes in the times of Artaxerxes, Nehemiah and Ezra the commencement of a new era, and although only too much remains obscure we have in these centuries a series of vicissitudes which separate the old Palestine of Egyptian, Hittite, Babylonian and Assyrian supremacy from the land which was about to enter the circle of Greek and Roman civilization.

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  • It is equal to the angle at the pole between the hour circle through the body and the meridian, but is usually expressed in time.

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  • The article Transit Circle describes one form of mounting in which the telescope is simply a refined substitute for the sights or pinules of the old astronomers.

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  • If we now attach to the polar axis a graduated circle D D, called the" hour circle,"of which the microscope or vernier R reads o h when the declination axis is horizontal, we can obviously read off the hour angle from the meridian of any star to which the telescope may be directed at the instant of observation.

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  • Since the transit circle is preferable to the equatorial for such observations wherein great accuracy is required, the declination and hour circles of an equatorial are employed, not for the determination of the right ascensions and declinations of celestial objects, but for directing the telescope with ease and certainty to any object situated in an approximately known position, and which may or may not be visible to the naked eye, or to define approximately the position of an unknown object.

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  • Further, by causing the hour circle, and with it the polar axis, to rotate by clockwork or some equivalent mechanical contrivance, at the same angular velocity as the earth on its axis, but in the opposite direction, the telescope will, apart from the effects of refraction, automatically follow a star from rising to setting.

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  • I i shows the whole instrument on a small scale with the telescope directed to the pole, and the hour circle set 6" from the meridian.

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  • The hour circle has two toothed circles cut upon it, one acted upon by a worm screw mounted on the pier and driven by clockwork, the other by a second worm screw attached to the polar axis, which can be turned by a handle in the observer's hand and thus a slow movement can be given to the telescope in right ascension inde FIG.

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  • The declination circle is most inconvenient of access, and slow motion in declination can only be effected when the instrument is clamped by a long and inconvenient handle; so that, practically, clamping in declination was not employed.

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  • The driving circle is also much too small, so that a very slight mechanical freedom of the screw in the teeth involves a large angular freedom of the telescope in right ascension, while its position at the lower end of a too weak polar axis tends to create instability from torsion of that axis.

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  • The driving circle was greatly increased in diameter and placed at the upper end of the polar axis, and both the polar and declination axes were made much stronger in proportion to the mass of the instrument they were designed to carry.

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