Angles sentence example

angles
  • The other streets run at right angles to one another.
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  • In the second class there are, in addition to the lifting motion, two horizontal movements at right angles to one another.
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  • I can't stand all the right angles in here, by the way.
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  • It is penetrated by numerous spurs of this range, which strike the sea abruptly at right angles to the coast, and in many cases plunge down into it sheer.
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  • They comprise several ranges which the roads from the sea to the interior have to cross at right angles, thereby rendering communication and transport very difficult.
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  • Other elements of the problem there are none, except mere numbers and angles, which do not depend upon the fundamental measurements of space, time and mass.
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  • It may be asked, Why can God not create a triangle whose three angles shall not be equal to two right angles?
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  • When he withdrew, she reached out to touch the planes and angles of his face.
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  • The streets cross each other at right angles and afford fine vistas on every side.
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  • From these streets others strike at right angles down to the harbour, while others again lead obliquely up towards the Belt, beyond which are extensive suburbs.
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  • It became, in fact, essential to invent a " micrometer " for measuring the small angles which were thus for the first time rendered sensible.
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  • Instruments have been invented by Alvan Clark and Sir Howard Grubb for measuring with the spider-line micrometer angles which are larger than the field of view of the eyepiece.
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  • The situation of the town proper, on a small triangular islet only connected with the mainland by three moles and bridges at the angles, has always rendered its fortification comparatively easy, and down to 1873 it was a fortress of the first rank.
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  • On each side of this, in the western pediment, is a group of two combatants over a fallen warrior; in the eastern pediment, a warrior whose opponent is falling into the arms of a supporting figure; other figures also - the bowmen especially - face towards the angles, and so give more variety to the composition.
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  • The walls still stand at many of the angles with a height of from 40 to 50 ft., and indicate an original elevation of several storeys, perhaps six or seven.
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  • It consists of four hemispherical cups, mounted one on each end of a pair of horizontal arms, which lie at right angles to each other and form a cross.
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  • Two holes are made near its lower angles.
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  • Two of the brothers led Pierre up to the altar, placed his feet at right angles, and bade him lie down, saying that he must prostrate himself at the Gates of the Temple.
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  • Thick dark lashes and a deep tan intensified the blue of his eyes, and his freshly shaven face had attractive angles.
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  • You have to be inventive, try to get into the criminal mind, think of all the angles....
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  • Its covers were loose, the pages within protruding at odd angles.
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  • Bede gives no information about its origin except that its earliest settlers were Angles.
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  • According to the Historia Brittonum Guffa (Wuffa) was the son of (Guecha) Wehha, who first ruled the East Angles in Britain.
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  • At right angles to this street lanes ascend the hill-side to Hillhead, where the more modern structures and villas have been built.
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  • The grubs, when hatched, start galleries nearly at right angles to this, and when fully grown form oval cells in which they pupate; from these the young beetles emerge by making circular holes directly outward through the bark.
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  • Occupying the southern slopes of a hill on the left bank of the Earn, here crossed by a bridge, it practically consists of a main street, with narrower streets branching off at right angles.
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  • The summer isotherms cross the winter isotherms nearly at right angles, so that Kiev and Ufa, Warsaw and Tobolsk, Riga and the upper Kama have the same average summer temperatures of 64°, 622° and 61° respectively.
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  • They are placed either on the departure side parallel to the platform (" side " stations) or at right angles to the rails and platforms (" end " stations).
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  • In this engine the two piston-rods of one side are not coupled to a common cross-head, but drive on separate cranks at an angle of 180°, the pair of 180° cranks on each side being placed at right angles.
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  • This hook swings on the pivot B, and has an arm which extends backwards, practically at right angles with the working face of the hook, FIG.
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  • The blocks are angular, and rest irregularly one upon another, supported in all positions by the angles and edges of those beneath.
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  • The town consists of one wide street, down which a stream of water runs, extending for about 1 m., and crossed at right angles by a lesser street.
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  • In general it rather resembles a closed crown, consisting of a circlet from which rise two arches intersecting each other at right angles.
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  • This column stands up from the base of the flower, almost at right angles to the lip, and it bears at the top an anther, in the two hollow lobes of which are concealed the two pollen-masses, each with its caudicle terminating below in a roundish gland, concealed at first in the pouch-like rostellum at the front of the column.
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  • In plan it is a triangle, protected by a double moat, and has round towers at the angles.
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  • From it again there shoot away at right angles, one on each side, the ranges of the Dar-alagoz and Bergushet.
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  • The earliest English settlements in the district which is now Derbyshire were those of the West Angles, who in the course of their northern conquests in the 6th century pushed their way up the valleys of the Derwent and the Dove, where they became known as the Pecsaetan.
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  • In some Pulmonata (snails) the foot is extended at right angles to the visceral hump, which rises from it in the form of a coil as in Streptoneura; in others the visceral hump is not elevated, but is extended with the foot, and the shell is small or absent (slugs).
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  • The foliation is often parallel to the bedding, but may cross it obliquely or at right angles; or the bedding may be folded and contorted while the foliation maintains a nearly uniform orientation.
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  • The vomer is broad, abruptly truncated in front, and deeply cleft behind, so as to embrace the rostrum of the sphenoid; the palatals have produced postero-external angles; the maxillo-palatals are slender at their origin, and extend obliquely inwards and forwards over the palatals, ending beneath the vomer in expanded extremities, not united either with one another or with the vomer, nor does the latter unite with the nasal septum, though that is frequently ossified.
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  • At each of the three free angles is a large group immediately over the lower column.
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  • These webs, which are typically subcircular in form, consist of a system of threads radiating from a common centre and crossed at intervals, and approximately at right angles, by a series of concentric lines, the whole being suspended in a triangular, quadrangular or polygonal framework formed of so-called foundation lines, attached to the branches or leaves of trees or other firm objects in the neighbourhood.
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  • The probable reason for the wall-lines being concentric is that lines passing over the radii as nearly as possible at right angles are the shortest that can be laid on; they therefore use up a smaller quantity of silk and take a shorter time to spin than threads crossing the radii in any other direction; and at the same time they afford them the greatest possible support compatible with delicacy and strength of construction.
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  • Channels formed at right angles to the cultivation ridges provide for the access of water to the crop. The seeds, previously soaked, are sown, usually in March, on the sides of the ridges, and the land watered.
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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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  • The streets are wide and cross at right angles; the houses are generally low and built of clay.
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  • In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.
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  • The town was laid out at great expense in straight, broad streets, intersecting each other at right angles, by the architect Hippodamus of Miletus in the time of Pericles.
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  • The temples are mostly small and are placed in the angles of the streets, under the shadow of the lofty houses.
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  • The piers carrying the arches have shafts at their angles, the earliest examples known, and the decoration of the walls consists of friezes, borders, and impost-bands, all enriched with conventional patterns interwoven with cufic characters and modelled in stucco.
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  • Baeyer supposes that in the formation of carbon, rings " the valencies become deflected from their positions, and that the tension thus introduced may be deduced from a comparison of this angle with the angles at which the strained valencies would meet.
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  • The ringed structure of benzene, C 6 H 61 was first suggested in 1865 by August Kekule, who represented the molecule by six CH groups placed at the six angles of a regular hexagon, the sides of which denoted the valencies saturated by adjacent carbon atoms, the fourth valencies of each carbon atom being represented as saturated along alternate sides.
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  • Marsh also devised a form closely resembling that of Thomsen, inasmuch as the carbon atoms occupied the angles of a regular octahedron, and the diagonal linkages differed in nature from the peripheral, but differeng from Thomsen's since rupture of the diagonal and not peripheral bonds accompanied the reduction to hexamethylene.
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  • Two parallel triangular faces are removed from a cardboard model of a regular octahedron, and on the remaining six faces tetrahedra are then placed; the hydrogen atoms are at the free angles.
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  • A crystal may be regarded as built up of primitive parallelepipeda, the edges of which are in the ratio of the crystallographic axes, and the angles the axial angles of the crystals.
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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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  • Many instances have been recorded where substitution has effected a deformation in one particular direction, the crystals of homologous compounds often exhibiting the same angles between faces situated in certain zones.
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  • Benzoic acid is pseudo-tetragonal, the principal axis being remarkably long; there is no cleavage at right angles to this axis.
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  • Across it were drawn seven parallels, running through Meroe, Syene, Alexandria, Rhodes, Lysimachia on the Hellespont, the mouth of the Borysthenes and Thule, and these were crossed at right angles by seven meridians, drawn at irregular intervals, and passing through the Pillars of Hercules, Carthage, Alexandria, Thapsacus on the Euphrates, the Caspian gates, the mouth of the Indus and that of the Ganges.
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  • Parallels and meridians were represented by straight lines intersecting each other at right angles, the relative proportions between degrees of longitude and latitude being retained only along the parallel of Rhodes.
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  • Marco Polo mentions such charts; Vasco da Gama (1498) found them in the hands of his Indian pilot, and their nature is fully explained in the Mohit or encyclopaedia of the sea compiled from ancient sources by the Turkish admiral Sidi Ali Ben Hosein in 1554.1 These charts are covered with a close network of lines intersecting each other at right angles.
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  • The strips (inae, philyrae), which were cut with a sharp knife or some such instrument, were laid on a board side by side to the required width, thus forming a layer (scheda), across which another layer of shorter strips was laid at right angles.
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  • When these first four galleries were full others were mined on the same level at right angles to them, thus gradually converting the whole area into a net-work of corridors.
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  • From both ridges spurs of greater or less length are sent off at various angles, whence a magnificent view is obtained from Breslau to Prague; the lowlands of Silesia, watered by the Oder, and those of Bohemia, intersected by the Elbe and the Moldau, appearing to lie mapped in relief.
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  • Both the eastern and the western part of the city were formerly enclosed by brick walls, with large round towers at the principal angles and smaller towers intervening at shorter distances, the whole surrounded by a deep fosse.
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  • Correlated with the presence of the genital pleurae there is a pair of vascular folds of the basement membrane proceeding from the dorsal wall of the gut in the postbranchial portion of the branchio-genital region, and from the dorsal angles made by the pleural folds with the body-wall in the pharyngeal region; they pass, in their most fully developed condition, to the free border of the genital pleurae.
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  • The flowers are regular, with four free sepals arranged in two pairs at right angles, four petals arranged crosswise in one series, and two sets of stamens, an outer with two members and an inner with four, in two pairs placed in the middle line of the flower and at right angles to the outer series.
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  • On the other hand, there are on the western outskirts of the plateau a few mountain chains which take a direction at right angles to the above (that is, from north-west to south-east), and parallel to the great line of upheavals in south-west Asia.
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  • The angles between these pyramids and the basal plane are 852° and 73° respectively.
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  • The different species of mica have very nearly the same forms and interfacial angles, and they not infrequently occur intergrown together in parallel position.
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  • A similar six-rayed system of cracks, bisecting the angles between the rays of the previous set, is produced when a blunt punch is gradually pressed against a sheet of mica; this is known as the "pressure figure."
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  • The pedicle passes out at right angles to the plane of junction of the valves of the shell; the opening is confined to the ventral valve, and may take the form of a slit, or may be closed by the development of a special plate called the listrium, or by a pseudo-deltidium.
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  • As new axes of co-ordinates we may take any other pair of lines through the origin, and for the X, Y corresponding to x, y any new constant multiples of the sines of the angles which the line makes with the new axes.
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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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  • There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .
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  • The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.
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  • By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the parallax derived from each.
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  • It will not in general move along a line of force, as would an isolated pole, but will follow the direction in which the magnetic force increases most rapidly, and in so doing it may cross the lines of force obliquely or even at right angles.
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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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  • The magnetic field due to a long straight wire in which a current of electricity is flowing is at every point at right angles to the plane passing through it and through the wire; its strength at any point distant r centimetres from the wire is H = 21/r, (2) i being the current in C.G.S.
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  • The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.
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  • If r and r' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.
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  • If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.
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  • If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.
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  • A magnet consisting of a series of plane shells of equal strength arranged at right angles to the direction of magnetization will be uniformly magnetized.
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  • If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.
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  • There are, however, always three principal axes at right angles to one another along which the magnetization and the force have the same direction.
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  • If two magnets having moments M, M' are arranged at right angles to each other upon a horizontal support which is free to rotate, their resultant R will set itself in the magnetic meridian.
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  • A compass having a very short needle is placed on the line which bisects the axis of the magnet at right angles, and is moved until a neutral point is found where the force due to the earth's field H is balanced by that due to the magnet.
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  • The magnetized body which is to be tested should be placed in such a position that the force H P due to its poles may, at the spot occupied by the suspended needle, act in a direction at right angles to that due to the earth - that is, east and west.
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  • In order to fulfil the requirement that the field which a magnetized rod produces at the magnetometer shall be at right angles to that of the earth, the rod may be conveniently placed in any one of three different positions with regard to the suspended needle.
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  • On the other hand, a vertically placed rod is subject to the inconvenience that it is influenced by the earth's magnetic field, which is not the case when the rod is horizontal and at right angles to the magnetic meridian.
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  • If the field is uniform, H=O/wd, where 0 is the rotation, d the thickness of the substance arranged as a plate at right angles to the direction of the field, and w Verdet's constant for the substance.
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  • C. Oersted 6 that a magnet placed near a wire carrying an electric current tended to set itself at right angles to the wire, a phenomenon which indicated that the current was surrounded by a magnetic field.
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  • The castle is a quadrangular structure of great strength, with rounded towers at three of the angles, and has a circumference of about 400 ft.
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  • The centre of the town is formed by the Piazza Vittorio Emanuele (formerly Piazza Maggiore), and the Piazza del Nettuno, which lie at right angles to one another.
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  • From the Devonian onwards the beds lie flat or dip at low angles.
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  • At the west end of George Street, in the centre of Charlotte Square, stands the Albert Memorial, an equestrian statue of the prince consort, with groups at each of the four angles of the base.
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  • It has a fine and well-preserved castle, built in 1490 by Gentile Virginio Orsini; it is square, with round towers at the angles.
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  • Spurs from the Drakensberg, at right angles to the main range, cross the plateaus.
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  • We take a fixed line OX, usually drawn horizontally; for each value of X we measure a length or abscissa ON equal to x.L, and draw an ordinate NP at right angles to OX and equal to the corresponding value of y .
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  • The larger the aperture the smaller are the angles through which it is necessary to deviate from the principal direction in order to bring in specified discrepancies of phase - the more concentrated is the image.
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  • It then appeared that under certain angles of incidence parts of the resulting spectra were completely polarized.
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  • If 8 and 4' denote the angles with the normal made by the incident and diffracted rays, the formula (5) still holds, and, if the deviation be reckoned from the direction of the regularly reflected rays, it is expressed as before by (0+0), and is a minimum when 8 = 0, that is, when the diffracted rays return upon the course of the incident rays.
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  • The grating at A and the eye-piece at 0 are rigidly attached to a bar AO, whose ends rest on carriages, moving on rails OQ, AQ at right angles to each other.
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  • In this case the motion in different directions varies as cos°, vanishing at right angles to the direction of propagation of the primary wave.
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  • In consequence of the breaking away of the lower part of "Cleopatra's Needles" when removed to Alexandria and re-erected, the Roman engineers supported the angles on bronze crabs, one of which with three reproductions now supports the angles of the obelisk on the Thames Embankment.
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  • On the 6th of September Buller, crossing the track of the main army at right angles, occupied Lydenburg in the bush-veld, and five days later the aged presi dent of the republic took refuge in Lourenco Marques.
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  • It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.
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  • It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays.
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  • Similarly, drops transmitting rays after two internal reflections will be situated on covertical and coaxial cones, of which the semi-vertical angles are 51° for the red rays and 54° for the violet.
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  • When the Orinoco is reached its lower basin is contracted between the Guiana highlands and the northern sierras, and its tributaries begin to come in more nearly at right angles, showing that the margins of the actual valley are nearer and higher.
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  • These cells of various shapes are seen in large numbers, mainly lying in a direction parallel to the new vessels and capillaries, which all run at right angles to the wound surface.
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  • Above is a graceful balustrade behind which is a lofty roof, and at the angles are towers perforated for the passage of the light.
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  • Then, since these three forces maintain equilibrium, and R makes equal angles with P and Q, therefore P and Q must be equal.
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  • There may be the folk-right of West and East Saxons, of East Angles, of Kentish men, Mercians, Northumbrians, Danes, Welshmen, and these main folk-right divisions remain even when tribal kingdoms disappear and the people is concentrated in one or two realms. The chief centres for the formulation and application of folkright were in the 10th and iith centuries the shire-moots, while the witan of the realm generally placed themselves on the higher ground of State expediency, although occasionally using folkright ideas.
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  • Its formal, straight streets, crossing one another regularly at right angles, and its uniform, two-storeyed houses were built in imitation of the Dutch style, under the direction of Jeronimo, marquis de Grimaldi (1716-1788), ambassador of Charles III.
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  • A third type is made on the "balance" principle, two plough beams with mould-boards being placed at right angles to one another, so that while the right-hand plough is at work the left-hand is elevated above the ground.
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  • The towns of the coast region are usually built on the same general plan, the streets crossing each other at right angles and enclosing squares, or quadras.
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  • A broad central avenue led straight to the palace, and on either side of it ran four parallel streets, crossed at right angles by smaller thoroughfares.
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  • They are enlarged replicas of the primeval wooden hut described above, having rafters with their upper ends crossed; thatched or shingled roof; boarded floors, and logs laid on the roof-ridge at right angles for the purpose of binding the ridge and the rafters firmly together.
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  • They were built on a rectangular plan, with a large central square and straight thoroughfares running at right angles or parallel to one another, this uniformity of construction being well exemplified in the existing bastide of Monpazier (Dordogne) founded by the English in 1284.
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  • In both Greek and Latin, however, although the upright and cross stroke are frequently not exactly at right angles and the upright often projects beyond the cross stroke, the forms approach more nearly to the modern than to the Semitic shape.
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  • If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.
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  • The citadel is square with round towers at the angles; it dates from 1304, and is now used as a prison.
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  • After passing the altar, it turns to the left again at right angles, and so enters the space in front of the temple.
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  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.
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  • This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.
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  • The stream issues through a nozzle, termed a " monitor " or " giant," which is fitted with a ball and socket joint, so that the direction of the jet may be varied through considerable angles by simply moving a handle.
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  • The plain and the, road are crossed at right angles by the course of the Brocksburn, or Spott Burn, which at first separated the hostile armies.
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  • The Bingemma range, rising 726 ft., is nearly at right angles to the axis of the main island.
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  • It crystallizes in rhombohedra belonging to the hexagonal system, having interfacial angles of 87° 40'.
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  • From the bottom there leads P another fine tube, bent upwards, and then at right angles so as to be at the same level as the capillary branch.
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  • Many variations of this apparatus are in use; in one of the commonest there are two cylindrical chambers, joined at the bottom, and each provided at the top with fine tubes bent at right angles; sometimes the inlet and outlet tubes are provided with caps.
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  • They lay their parthenogenetically produced eggs in the angles of the veins of the leaves, in the buds, or, if the season is already far advanced, in the bark.
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  • The measurement of position angles is provided for by a graduated circle attached to the head.
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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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  • The optical centres of the segments would also remain at the same distance from the eye-piece at all angles of separation.
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  • Thus, in measuring the largest as well as the smallest angles, the images of both stars would be equally symmetrical and equally well in focus.
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  • Modern heliometers made with cylindrical slides measure angles over 2°, the images remaining as sharp and perfect as when the smallest angles are measured.
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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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  • Heliometer observations of distance in their most refined sense cannot be considered absolute measures of angles.
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  • Of course, for many purposes, mean conditions may be adopted and mean scale-values be found which are applicable with considerable pre cision to small angles or to comparatively crude observations of large distances; but the highest refinement is lost unless means are provided for determining the scale-value for each observer at each epoch of observation.
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  • When the inclination of the movable half with respect to the axis of the telescope is changed by rotation about an axis at right angles to the plane of division, two images are produced.
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  • They are liable to the objection that their employment is limited to the measurement of very small angles, viz.
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  • Large angles of slope may, however, occur on the flanks of oceanic islands and the continental borders.
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  • On the submarine slopes leading up to isolated volcanic islands angles of 15° to eo are not uncommon, at St Helena the slopes run up to 382° and even 40°, at Tristan d'Acunha to 331°.
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  • Galleries driven at right angles to these are known as a " dip " or " rise headings," according to their position above or below the pit bottom.
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  • In the Gartsherrie machine of Messrs Baird, the earliest of the flexible chain cutter type, the chain of cutters works round a fixed frame or jib projecting at right angles from the engine carriage, an arrangement which makes it necessary to cut from the end of the block of coal to the full depth, instead of holing into it from the face.
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  • When at work it is slowly turned until the carrier is at right angles to the frame, when the cut has attained the full depth.
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  • In a large colliery where the shafts are situated near the centre of the field, and the workings extend on all sides, both to the dip and rise, the drawing roads for the coal may be of three different kinds - (r) levels driven at right angles to the dip, suitable for horse roads, (2) rise ways, known as jinny roads, jig-brows, or up-brows, which, when of sufficient slope, may be used as self-acting planes, i.e.
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  • In such cases the engines may be placed in line on opposite sides of the pit, or at right angles to each other.
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  • The moments of the components of these actions and reactions in a plane to which the axis of rotation is at right angles are the two aspects of the torque acting, and therefore the torque acting on B through the shaft is measured by the torque required to hold A still.
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  • In 1773 there appeared in the Public Advertiser one of Franklin's cleverest hoaxes, " An Edict of the King of Prussia," proclaiming that the island of Britain was a colony of Prussia, having been settled by Angles and Saxons, having been protected by Prussia, having been defended by Prussia against France in the war just past, and never having been definitely freed from Prussia's rule; and that, therefore, Great Britain should now submit to certain taxes laid by Prussia - the taxes being identical with those laid upon the American colonies by Great Britain.
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  • The crystals are orthorhombic, with angles similar to those of marcasite; they are often prismatic in habit, and the prism M is usually terminated by the deeply striated faces of an obtuse dome r.
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  • These " battalias " had their angles strengthened in the oldfashioned way that had prevailed since Marignan, with small outstanding bodies of musketeers, so that they resembled rectangular forts with bastions.
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  • The fact that the interior angles of all triangles are equal to two right angles is not part of the definition, but is universally true.
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  • At greater elevations than this the muzzle notch is used; to align on the target at lesser angles the dispart sight is so used.
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  • The pattern is that of a true sight, that is to say, the base plate is capable of movement about two axes, one parallel to and the other at right angles to the axis of the gun, and has cross spirit-levels and a graduated elevating drum and independent deflection scale, so that compensation for level of wheels can be given and quadrant elevation.
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  • As he surveyed the field from the windmill north of Fleurus it struck him as significant that Blucher's troops were disposed parallel to the Namur road, as if to cover a forward concentration, and not at right angles to it, as they would be had they been covering a retreat.
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  • It is somewhat like an axe reversed, the edge of the blade curving inward and placed at right angles to the handle.
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  • It is remarkable as being contrary to Roman surveyors' practice, according to which the basis of division is the intersection at right angles of the cardo and decumanus, which would give an even (not an odd) number of smaller squares.
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  • Usually they are twinned on a prism plane, M, producing pentagonal stellate groups of five crystals; twinning on the plain g, in which the crystals intercross at angles of nearly 60°, is less common.
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  • This frequent twinning gives rise to characteristic forms, with many re-entrant angles, to which the names "spear pyrites" and "cockscomb pyrites" are applied.
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  • Even in the second sense, the term is a very wide one, since it comprises the measurement of angles (plane and solid), lengths, areas and volumes.
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  • The use of the square bricks familiarizes the scholar with the ideas of parallel lines, of equality of lengths, and of right angles.
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  • The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.
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  • A plane figure bounded by a continuous curve, or a solid figure bounded by a continuous surface, may generally be most conveniently regarded as generated by a straight line, or a plane area, moving in a fixed direction at right angles to itself, and changing as it moves.
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  • This implies the treatment of a plane or solid figure as being wholly comprised between two parallel lines or planes, regarded by convention as being vertical; the figure being generated by an ordinate or section moving at right angles to itself through a distance which is called the breadth of the figure.
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  • The most important form of trapezium is that in which one of the two remaining sides of the figure is at right angles to the two parallel sides.
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  • It would be possible to regard this form of the figure as the general one; the figure considered in (i) would then represent the special case in which the two end-pieces of the broken line are at right angles to the base.
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  • Take any base X'X, and draw lines at right angles to this base through all the angular points of the figure.
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  • The lengths of arcs of the same circle being proportional to the angles subtended by them at the centre, we get the idea of circular measure.
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  • Similarly a surface of revolution can be divided by planes at right angles to the axis into elements, each of which is approximately a section of the surface of a right circular cone.
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  • If we draw a line at right angles to TCV, meeting TCV produced in M and parallels through A and B in K and L, the area of the triangle ATB is KL.
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  • In the ordinary case three of the four lateral surfaces of the prismoid are at right angles to the two ends.
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  • On any line OX take a length ON equal to xG, and from N draw NP at right angles to OX and equal to uH; G and H being convenient units of length.
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  • Elements of the graph are shown from an axis through 0 and at right angles to OX.
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  • A briquette may therefore be defined as a solid figure bounded by a pair of parallel planes, another pair of parallel planes at right angles to these, a base at right angles to these four planes (and therefore rectangular), and a top which is a surface of any form, but such that every ordinate from the base cuts it in one point and one point only.
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  • It may be regarded as generated either by a trapezette moving in a direction at right angles to itself and changing its top but keeping its breadth unaltered, or by an ordinate moving so that its foot has every possible position within a rectangular base.
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  • If the lengths of these sides are H and K, the coordinates of the angles of the base - i.e.
    0
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  • The top is then a parabola whose axis is at right angles to the base; and the area can therefore (§ 34) be expressed in terms of the two bounding ordinates and the midordinate.
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  • Thus we find from (i) that Simpson's second formula, for the case where the top is a parabola (with axis, as before, at right angles to the base) and there are three strips of breadth h, may be replaced by area = 8h(3u i + 2U 1 + 3us).
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  • This value of 0 is the same for all parabolas which pass through D and E and have their axes at right angles to KL.
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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 two coils, the shunt and the series coil, then produce two magnetic fields, with their lines of force at right angles to one another.
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  • If this is done for every point we obtain a continuous curve Apbqcrd, which represents the displacement at every point at the given instant, though by a length at right angles to the actual displacement and on an arbitrary scale.
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  • As with light the ratio involved in the second law is always equal to the ratio of the velocity of the wave in the first medium to the velocity in the second; in other words, the sines of the angles in question are directly proportional to the velocities.
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  • Circular nodal lines unaccompanied by intersecting lines cannot be produced in the manner described; but may be got either by drilling a small hole through the centre, and drawing a horse-hair along its edge to bring out the note, or by attaching a long thin elastic rod to the centre of the plate, at right angles to it, holding the rod by the.
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  • Warren type in which the bracing bars form equilateral triangles, the Whipple Murphy in which the struts are vertical and the ties inclined, and the lattice in which both struts and ties are inclined at equal angles, usually 45° with the horizontal.
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  • It is finely situated on a hill above the Lago Fucino, and is dominated by a square castle, with round towers at the angles, erected in its present form in 1450.
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  • The usual definition of the component current in any direction, as the net amount of electrons which crosses, towards the positive side, an element of surface fixed in space at right angles to that direction, per unit area per unit time, here gives no definite result.
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  • When in Egypt he measured the pyramids, and, finding that the angles formed by the sides of the largest were in the direction of the four cardinal points, he concluded that this position must have been intended, and also that the poles of the earth and meridians had not deviated since the erection of those structures.
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  • The best known of these, which is called Legendre's theorem, is usually given in treatises on spherical trigonometry; by means of it a small spherical triangle may be treated as a plane triangle, certain corrections being applied to the angles.
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  • To become a medusa, the actinula grows scarcely at all in the direction of the principal axis, but greatly along a plane at right angles to it.
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  • On the terraces the streets generally intersect at right angles, but on the hills their directions are irregular.
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  • Bathurst has broad streets, crossing one another at right angles, with a handsome park in the centre of the town, while many of the public buildings, specially the town hall, government buildings, and Anglican and Roman Catholic cathedrals, are noteworthy.
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  • Slates properly so-called do not, except on rare occasions, split along the bedding, but along planes of cleavage, which intersect the bedding usually at high angles.
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  • They will alter the shape of mineral particles by broadening them in a direction at right angles to the principal pressures, while they are thinned in the direction in which the pressure acted.
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  • Pressure will also tend to produce an expansion of the rock mass in a direction (usually nearly vertical) at right angles to the compression, for such rocks as slates are distinctly plastic in great masses.
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  • In this way thin laminae would form, lying at right angles to the direction of greatest stress.
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  • The material is sometimes won by the aid of channelling machines which make a series of cuts at right angles to each other in the face of the rock; a block is then broken off at its base by wedges forced into the cuts, and its removal permits access to other blocks.
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  • High Angle and Curved Fire.-" High angle fire," as defined officially, " is fire at elevations greater than r 5°," and " curved fire is fire from howitzers at all angles of elevation not exceeding 15°."
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  • The movable coil of the wattmeter is normally suspended so that its axis is at right angles to that of the fixed coil, and is constrained by the torsion of a spiral spring.
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  • Parallel to this is Swanston Street, and at right angles to these, parallel to the river.
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  • The mouth may be circular or four-cornered, and in the latter case the manubrium at the angles of the mouth may become drawn out into four lappets, the oral arms, each with a groove on its inner side continuous with the corner FIG.
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  • To produce a medusa the actinula grows greatly along a plane at right angles to the vertical axis of the body, whereby the aboral surface of the actinula becomes the exumbrella, and the peristome becomes the subumbrella.
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  • The posterolateral angles of the gena are commonly produced into spiniform processes, which may project backwards beyond the middle of the body as in Paradoxides, or considerably beyond its posterior termination as in Trinucleus or Ampyx.
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  • When a difference of potential is made between the terminals, a current passes through the movable coil, which then tends to place itself with its plane more at right angles to the lines of force of the field.
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  • In the Cistercian monasteries, to keep the noise and smell of dinner still farther away from the sacred building, the refectory was built north and south, at right angles to the axis of the church.
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  • Euclid devotes his third book entirely to theorems and problems relating to the circle, and certain lines and angles, which he defines in introducing the propositions.
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  • Near the mid line of the body, and at right angles to the last, another reflection, the falciform ligament, runs forward, and the line of attachment of this indicates the junction of the right and left lobes of the liver.
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  • Here Hertha, according to tradition, had her great temple, and hither came from the mainland the Angles to worship at her shrine.
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  • Near the ovary the tubes are closed, but nearer the Fal lopian tube they open into another tube which is nearly at right angles to them, and which runs toward the uterus, though in the human subject is generally lost before reaching that organ.
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  • The best kind of charcoal is that of close-grained pine or alder; it is cut in short prisms, having a flat smooth surface at right angles to the rings of growth.
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  • In astronomy the horizon is that great circle of the sphere the plane of which is at right angles to the direction of the plumb line.
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  • The streets and avenues, almost all of which are straight, cut each other at right angles, forming blocks of houses, here as elsewhere called "islands."
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  • Most of the streets of the old city are parallel and cross at right angles, but they are narrow and enclose blocks of unequal size.
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  • In hares and pacas the inside of the cheeks is hairy; and in some species, pouched rats and hamsters, there are large internal cheek-pouches lined with hair, which open near the angles of the mouth and extend backwards behind the ears.
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  • In all cases where compound prisms are used, the angles must be accurately calculated.
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  • The second great street, Portage Avenue, of the same width as Main Street, runs at right angles to Main Street, and is the mercantile street of the city.
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  • The church of St Nicholas is a large and handsome structure in various styles of architecture, and consists of nave, chancel and aisles, with a square embattled tower having pinnacles at the angles.
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  • This mirror can rotate about a horizontal axis which is at right angles to the line of collimation of the telescope, and is parallel to the surface of the mirror.
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  • The auxiliary magnet has a plane mirror attached, the plane of which is at right angles to the axis of the magnet.
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  • The axis of the magnet is horizontal and at the same level as the mirror magnet, while when the central division of the scale B appears to coincide with the vertical cross-wire of the telescope the axes of the two magnets are at right angles.
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  • What is known as the method of sines is used, for since the axes of the two magnets are always at right angles when the mirror magnet is in its zero position, the ratio M/H is proportional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic - = meridian.
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  • Attached to the cross-arm which carries the microscopes used to observe the ends of the dipping needle is a clamp, which will hold the needle b in such a way that its plane is parallel to the vertical circle and its axis is at right angles to the line joining the two microscopes.
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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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  • Bede declares that Oswald ruled over "all the peoples and provinces of Britain, which includes four languages, those of the Britons, Picts, Scots and Angles."
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  • Although a compass may thus be made practically correct for a given time and place, the magnetism of the ship is liable to changes on changing her geographical position, and especially so when steaming at right angles or nearly so to the magnetic meridian, for then sub-permanent magnetism is developed in the hull.
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  • According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
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  • Following Euclid, a right angle is formed by a straight line standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle.
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  • The generalized view of angles and their measurement is treated in the article Trigonometry.
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  • It is usual to take three axes at right angles to each other to represent pressure, temperature and the composition of the variable phase..
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  • The refectory stretches northwards at right angles to the cloister, which lies to the north of the church, having the chapter-house and sacristy on the east.
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  • Walls, inclined to each other at obtuse angles, enclosed a plot of ground having in the middle a low tumulus of elliptic form, about 35 metres from east to west by 20 from north to south.
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  • The cella - divided, like that of Zeus, into three partitions by a double row of columns - had four " tongue-walls," or small screens, projecting at right angles from its north wall, and as many from the south wall.
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  • There are three refracting angles possible, one of Ito° between two adjacent prism faces, one of 60° between two alternate prism faces, and one of 90° between a prism face and the base.
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  • When in use, it is held at right angles to the periscope above the upper window by a bayonet catch; when not in use, it is lowered and sprung round the body of the periscope just below the upper prism box.
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  • Gears are provided for elevating, levelling, aligning the upper and lower optical systems, adjusting the inclination of the reflector and rotating the mast around a vertical axis so that observations may be made and azimuth angles taken in all directions.
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  • The badge of the military and naval members bears two crossed swords in the angles of the cross.
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  • The badge of the order was a white Maltese cross decorated in gold, with the gold lilies of France at the angles, in the centre a white dove with wings outstretched, the ribbon was sky blue (cordon bleu).
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  • The badge is a red enamelled cross with gold borders and double C's interlaced in the angles; in the centre a white medallion with red monogram over a green mound surmounted by the word Fidelitas in black; the cross is suspended from a ducal crown.
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  • The badge is a green enamel cross with gold clasps in the angles; in the central medallion an enamelled representation of the ruined castle of Zdhringen.
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  • The badge is a blue enamelled cross with white and gold edging suspended from the mouth of a gold lion's head; in the angles of the cross are blue lozenges containing the letters V.I.B.I., Virgini Immaculatae Bavaria Immaculata.
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  • The badge is a blue enamelled cross dependent from a lion surmounted by the ducal crown; the angles of the cross are filled by crowned W's and the centre bears the arms of Brunswick, a crowned pillar and a white horse, between two sickles.
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  • The badge of the military order is a blue cross with gold uncrowned eagles in the angles; on the topmost arm is the initial F., with a crown; on the other arms the inscription Pour le Merite.
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  • The badge is a white cross surmounted by the royal crown, in the centre the initial F surrounded by a crimson fillet on which is the motto Furchtlos and Treu; in the angles of the cross are four golden leopards; the ribbon is crimson with two black stripes.
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  • The badge of the order is a red Jerusalem cross with red Latin crosses in the angles.
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  • The badge is a red enamelled cross with gold eagles in the angles, bearing in a medallion the mounted effigy of St Alexander Nevsky.
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  • The badge of the order is a blue and white cross suspended from a green laurel wreath, in the angles are golden lilies, and the oval centre bears a figure of the Virgin in a golden glory.
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  • The badge is a red rayed cross with gold rays in the angles, in the centre a representation of the pillars of Hercules; the cross is attached to the yellow and white ribbon by a green laurel wreath.
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  • The badge is a white cross, in the angles gold crowns, the points of the cross joined by gold swords entwined with gold and blue belts, in the blue centre an upright sword with the three crowns in gold, the whole surmounted by the royal crown The ribbon is yellow with blue edging.
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  • It is cut in the volcanic plateau, and its ragged broken walls, which are inclined at very steep angles, are of a richness of colouring that almost defies description, a colouring that is produced by the action of the thermal springs, at the base of the canyon, upon the mineral pigments in the lava.
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  • To the former belong the theorems (t), (2), and (3), and to the latter especially the theorem (4), and also, probably, his solution of the two practical problems. We infer, then, [t] that Thales must have known the theorem that the sum of the three angles of a triangle are equal to two right angles.
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  • The east and west walls should run parallel to each other, and at right angles to that on the north side, in all the most favoured localities; but in colder or later ones, though parallel, they should be so far removed from a right angle as to get the sun by eleven o'clock.
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  • The neutralizing conductors for each disk are placed at right angles to each other.
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  • To increase the reservoir capacity of the polder, as well as to conduct the water to the windmills or engines, it is intersected by a network of ditches cut at right angles to each other, the amount of ditching required being usually one-twelfth of the area to be drained.
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  • The Tremellinaceae are characterized by the possession of basidia which are divided by two vertical walls at right angles to one another.
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  • Theodolites are designed to measure horizontal angles with greater accuracy than vertical, because it is on the former that the most important work of a survey depends; measures of vertical angles are liable to be much impaired by atmospheric refraction, more particularly on long lines, so that when heights have to be determined with much accuracy the theodolite must be discarded for a levelling instrument.
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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 level bubble, by which the instrument is brought into a position at right angles to the axis of the earth, is generally placed on the top of the telescope.
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  • The borough lies in the valley of the Lehigh river, along which runs one of its few streets and in another deeply cut valley at right angles to the river; through this second valley east and west runs the main street, on which is an electric railway; parallel to it on the south is High Street, formerly an Irish settlement; half way up the steep hill, and on the north at the top of the opposite hill is the ward of Upper Mauch Chunk, reached by the electric railway.
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  • The most important function they have to perform, that of seizing and holding firmly animals of considerable size and strength, violently struggling for life, is provided for by the great, sharp-pointed and sharp-edged canines, placed wide apart at the angles of the mouth, the incisors between them being greatly reduced in size and kept back nearly to the same level, so as not to interfere with their action.
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  • The plan of the city is rectangular, and the streets intersect at right angles, a peculiarity handed down from Roman times, though the area enclosed by the medieval walls is larger than that of the Roman town,, which occupied the eastern portion of the present one.
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  • There are four main streets crossing each other nearly at right angles, the central "chouk" being covered with a dome.
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  • When leaves are opposite, each successive pair may be placed at right angles to the pair immediately preceding.
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  • The pairs alternate leaves, and the nodes are separated so are placed at right ranged in a penthat each leaf is placed at angles alternately, tastichous or different height on the stem, or in what is called quincuncial manthe leaves are alternate
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  • The general plan of the town is very regular, the streets being generally straight, and crossing one another at right angles or nearly so.
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  • An important character of blende is the perfect dodecahedral cleavage, there being six directions of cleavage parallel to the faces of the rhombic dodecahedron, and angles between which are 600.
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  • The beds should run at or nearly at right angles to the line of the conductor.
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  • The water flows from the ditches as conductors into built conduits formed at right angles to them in parallel lines through the fields; it rises upwards in them as high as the surface of the ground, and again subsides through the soil and the conduits into the ditches as main drains, and thence it passes at a lower level either into a stream or other suitable outfall.
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  • On the left bank of the Aude, between it and the Canal du Midi, lies the new town, clean, well-built and flourishing, with streets intersecting each other at right angles.
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  • These two are much the most important of the periodic terms. The angles loo° 52', 309° 5', &c.,are known as the phase angles of the respective periodic terms, while 3.0 3, 2 '53, &c., are the corresponding amplitudes.
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  • Excluding Jakobshavn, the phase angles in the 6-month term vary wonderfully little, and approach the value 309° in Lovering's general formula.
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  • As shown in the figure, it is evident that the motion of o in the line sop would not be recorded, and to obtain a complete record of horizontal movements it is necessary to have two levers at right angles to each other.
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  • To obtain a complete record of horizontal motion, two of these pendulums are placed at right angles; and by cranking one of the writing levers, o'p', as shown in the plan of fig.
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  • As this position is approached the period of swing becomes greater and greater, and sensibility to slight tilting at right angles to the plane of o'o"m is increased.
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  • The movements of the apparatus, which when complete should consist of two similar pendulums in planes at right angles to each other, are recorded by means of a beam of light, which, after reflection from the mirror or mirrors, passes through a cylindrical lens and is focussed upon a moving surface of photographic paper.
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  • Fine ones of bronze are common in the XVIIIth Dynasty, and some with two eyes at right angles, one above the other, to carry two different threads.
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  • His schemes consisted of series of broad, straight streets, cutting one another at right angles.
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  • The main streets run from the angles of the triangular market-place, in which stands the market cross, dated 1642, but probably much older.
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  • Wollaston in the angles of the rhombohedra of the carbonates isomorphous with calc-spar, he observed that the angle in the case of calc-spar varied with the temperature.
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  • The tetraspores may arise by the simultaneous division of the contents of a sporangium, when they are arranged tetrahedrally, or they may arise by two successive divisions, in which case the arrangement may be zonate when the spores are in a row, or cruciate when the second divisions are at right angles to the first, or tetrahedral when the second divisions are at right angles to the first and also to one another.
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  • The eastern parts of Greece are composed almost entirely of Cretaceous beds, but nevertheless they must be considered to belong to the central area, for the folds which affect them are nearly at right angles to those of the western chains.
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  • These, as shown in the figure, are composed of a variable number of vertical triangular prisms, in contact with one another by two (or one) of their angles.
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  • The withdrawal of the Romans from Britain (410) left the northern part of the island as a prey to be fought for by warlike tribes, of whom the most notable were the Picts in the north, the Scots or Dalriads from Ireland in the west (Argyll), the Cymric or Welsh peoples in the south-west and between Forth and Tay, and the Teutonic invaders, Angles or English, in the south-east.
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  • Between Kala Wamar (6580 ft.) and Kala Khum (4400 ft.), where the Oxus again bends southwards, its course to the north-west is almost at right angles to the general strike of the Darwaz mountains, which is from north-east to south-west, following the usual conformation of all this part of high Asia.
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  • Another of about equal length, starting from the same, central water-parting of this mountain block, and included within the Oxus bend, follows a transverse direction at almost right angles to the Shiwa, and joins the Oxus valley near its debouchment into the more open Kolab plains, where the course of the Oxus has again assumed a direction parallel to the mountain strike.
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  • Any number of points on the parabola are obtained by taking any point E on the directrix, joining EG and EF and drawing FP so that the angles PFE and DFE are equal.
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  • General Soimonov, with the Sevastopol column, after assembling his troops before dawn on the 5th, led them on to the upland east of Careenage Ravine, while the field army column, under General Pavlov, crossed the Tchernaya near its mouth, almost at right angles to Soimonov's line of advance.
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  • The medullary rays extend radially from the centre of the tree to the bark at right angles to the grain of the wood, and serve during life to bind the whole together as well as to convey nourishment from one part of the tree to another.
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  • Sigebert, king of the East Angles, founded a monastery here about 633, which in 903 became the burial place of King Edmund, who was slain by the Danes about 870, and owed most of its early celebrity to the reputed miracles performed at the shrine of the martyr king.
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  • But when curving occurs In different planes at right or other angles (hollowing), the metal has to be drawn or extended on the outside, and important differences arise.
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  • Up or down this plain, at opposite seasons, sweep the monsoon winds, in a direction at right angles to that of their nominal course; and thus vapour which has been brought by winds from the Bay of Bengal is discharged as snow and rain on the peaks and hillsides of the Western Himalayas.
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  • Hindus wind the pagri in various ways as described for Mussulmans, but the angles are formed over the ears and not from front to back.
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  • Thomas Digges, in his Stratioticus, p. 359, published in 1579, states that his father, Leonard Digges, "among other curious practices had a method of discovering by perspective glasses set at due angles all objects pretty far distant that the sun shone upon, which lay in the country round about," and that this was by the help of a manuscript book of Roger Bacon of Oxford, who he conceived was the only man besides his father who knew it.
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  • In its simplest form the mounting of an equatorial telescope consists of an axis parallel to the earth's axis, called" the polar axis "; a second axis at right angles to the polar axis called" the declination axis "; and the telescope tube fixed at right angles to the declination axis.
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  • Its lower extremity terminates in a fork on which is mounted a mirror C D, capable of turning about A on an axis at right angles to A B, the plane of the mirror being parallel to this latter axis.
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  • Within the focus of the object-glass is a right-angled prism of total reflection, which diverts the converging rays from the object-glass at right angles to the axis of the telescope, and permits the observing micrometer n to be mounted in the very convenient position shown in the figure.
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  • The interval between the true trails, measured at right angles to the direction of the trails, obviously corresponds to the difference of zenith distance of the two stars.
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  • When the line of centres is at right angles to our line of sight, the stars present to us their greatest apparent surface, and therefore send us the maximum light.
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  • Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.
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  • Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.
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  • A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.° Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.
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  • Towers also surmount the angles of the terraces of the two upper stages.
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  • For this equation merely states that m turnings of a line through successive equal angles, in one plane, give the same result as a single turning through m times the common angle.
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  • But, instead of dealing with points on a line, and then wandering out at right angles to it, as Buee and Argand had done, he chose to look on algebra as the science of " pure time," 1 and to investigate the properties of " sets " of time-steps.
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  • Again, the product of two lines at right angles to one another cannot, even in part, be a number.
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  • But Grassmann distinctly states in his preface that he had not had leisure to extend his method to angles in space.
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  • But his claims, however great they may be, can in no way conflict with those of Hamilton, whose mode of multiplying couples (in which the " inner " and " outer " multiplication are essentially involved) was produced in 1833, and whose quaternion system was completed and published before Grassmann had elaborated for press even the rudimentary portions of his own system, in which the veritable difficulty of the whole subject, the application to angles in space, had not even been attacked.
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  • There are towers at the angles of the enceinte, and others at intervals, and two at each of the four gates, making a total of twenty towers altogether.
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  • Consisting of red sandstones, mudstones and conglomerates, they are inclined at high angles usually away from the granite massif and the encircling metamorphic rocks.
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  • Here there is an ascending sequence from the Calciferous Sandstone, through the Carboniferous Limestone with thin coals formerly worked, to the Coal Measures, the strata being inclined at high angles to the north.
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  • The upper end of the suspension is turned till the axis of the magnet is at right angles to the magnetic meridian.
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  • To record the variations of the vertical component use is made of a magnet mounted on knife edges so that it can turn freely about a horizontal axis at right angles to its 1 Report British Association, Bristol, 18 9 8, P. 741.
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  • With the exception of the old quarter, Kolozsvar is generally well laid out, and contains many broad and fine streets, several of which diverge at right angles from the principal square.
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  • The north and south streets cross these at right angles, and the blocks thus formed are like great terraces.
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  • Two divisions under Di Giorgio had been dispatched to hold this line, but their march, at right angles to the line of the retreat and athwart the long streams of retiring troops and civilians, had been very difficult.
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  • They include many particulars of what purports to be the history of the royal houses, not only of the Gautar and the Danes, but also of the Swedes, the continental Angles, the Ostrogoths, the Frisians and the Heathobeards, besides references to matters of unlocalized heroic story such as the exploits of Sigismund.
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  • When he grew up he reigned over the Angles at " Slaswic."
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  • As the name of Beaw appears in the genealogies of English kings, it seems likely that the traditions of his exploits may have been brought over by the Angles from their continental home.
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  • While, however, it thus appears that the mythic part of the Beowulf story is a portion of primeval Angle tradition, there is no proof that it was originally peculiar to the Angles; and even if it was so, it may easily have passed from them into the poetic cycles of the related peoples.
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  • For all we know, the intercourse of the Angles with Scandinavia, which enabled their poets to obtain new knowledge of the legends of Danes, Gautar and Swedes, may not have ceased until their conversion to Christianity in the 7th century.
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  • Although the heathen Angles had their own runic alphabet, it is unlikely that any poetry was written down until a generation had grown up trained in the use of the Latin letters learned from Christian missionaries.
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  • If, as is usually most convenient, the two assigned directions are at right angles, the two components of a force P will be P cos 0, P sin 0, where 0 is the inclination of P to the direction of the p former component.
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  • The construction is neatest if the two arbitrary directions are taken at right angles to one another.
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  • If AB, AC represent infinitesimal rotations about intersecting axes, the consequent displacement of any point 0 in the plane BAC will be at right angles to this plane, and will be represented by twice the sum of the areas OAB, OAC, taken with proper signs.
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  • We examine first the case where the axes of the two screws are at right angles and intarsect.
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  • The displacement of G is at right angles to JG; this shows that for equilibrium JG must be vertical.
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  • The simplest case is that of a frame of three bars, when the three joints A, B, C fall into a straght line; a small displacement of the joint B at right angles to AC would involve changes in the lengths of AB, BC which are only of the second order of small quantities.
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  • When the body is twisted through an angle 0 the threads make angles aC/i, be/I with the vertical, and the moment of the tensions about the vertical through G is accordingly Kg, where K = M gab/i.
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  • At the instant t+t, Ox, Oy, Os will no longer coincide with Ox, Oy, Os; in particular they will make with Ox angles whose cosines are, to the first order, I, rot, qOt, respectively.
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  • And from this, and from the property of a rigid body, already stated in 29, it follows, that the components along a is ne of connection of all the points traversed by that line, whether -in the driver or in the follower, are equal; and consequently, that the velocities of any pair of points traversed by a line of connection are to each other inversely as the cosines, or directly as the secants, of the angles made by the paths of those points with the line of connection.
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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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  • In skew-bevel wheels the properties of a line of connection are not possessed by every line traversing the line of contact, but only by every line traversing the line of contact at right angles.
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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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  • Set off ab = ac = 1/2p. Draw radii bd, Ce; draw fb, cg, making angles of e 753/4 with those radii.
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  • If a helix be described round the screw, crossing each turn of the thread at right angles, the distance between two corresponding points on two successive turns of the same thread, measured along this normal helix, may be called the normal pitch; and when the screw has more than one thread the normal pitch from thread to thread may be called the normal divided pitch.
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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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  • 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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  • To obviate the unsteadiness of motion which this tends to cause, the shafts are provided with a second set of cranks at right angles to the first, connected by means of a similar coupling-rod, so that one set of cranks pass their dead points at the instant when the other set are farthest from theirs.
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  • To obviate this evil a short intermediate shaft is introduced, making equal angles with the first and last shaft, coupled with each of them by a Hookes joint, and having its own two forks in the same plane.
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  • It can be proved that the point C always moves in a straight line at right angles to the line EF.
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  • To find the instantaneous centre for a particular link corresponding to any given configuration of the kinematic chain, it is only necessary to know the direction of motion of any two points in the link, since lines through these points respectively at right angles to their directions of motion.
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  • Hence set out the possible direction of Bs motion in the velocity diagram, namely cbi, at right angles to CB.
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  • But tile point B must also move at right angles to AB in the case under consideration.
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