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intersection

intersection

intersection Sentence Examples

  • From every point of the curve of intersection, perpendiculars are drawn to the axis.

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  • Surmounting all, at the intersection of the arches is a cross.

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  • He neared the intersection where the road branched to her house and his.

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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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  • She paused at the intersection with another narrow alley, not liking the smelly alleys at all.

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  • We caught two intersection videos of the van traveling in the direction of route 154.

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  • having a resultant in the direction PO, where P is the intersection of an ellipse n with the hyperbola 13; and with this velocity the ellipse n can be swimming in the liquid, without distortion for an instant.

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  • the line of intersection forming a descending gutter which runs to the outlet.

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  • high, has double vaulted aisles and the transepts single aisles; and at the intersection of nave and transepts there is a cupola.

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  • Jenn chose a direction and paused at the first intersection to listen for anyone approaching.

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  • to the perpendicular distance from the line of intersection of the plane of the area with the free surface of the liquid.

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  • Brady reached the intersection and saw the tunnel running perpendicular opened into a crowded underground city.

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  • From its intersection with A'A' arcs are struck cutting B in two points.

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  • Adjoining the town hall is the Anglican cathedral of St Andrew, in the Perpendicular style; it has two towers at the west end and a low central tower above the intersection of the nave and transepts, with a very handsome chapter house.

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  • The line adopted starts from Lake Suches, the source of a small river of that name flowing into the north of Lake Titicaca, crosses the Cordillera by the Palomani to the Tambopata river, follows that stream to the mouth of the Lanza, thence crosses to the source of the Heath river, which forms the dividing line down to its junction with the Madre de Dios, descends that river to the mouth of the Torosmonas, thence in a straight line north-westerly to the intersection of the Tahu.amanu river by the 69th meridian, and thence north on that meridian to the Brazilian frontier.

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  • Just west of the intersection, he pulled up to Cimarron Books, a small combination bookstore and coffee shop.

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  • It is at the intersection of two branches of the Boston & Maine railway, and is served by several interurban electric lines.

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  • He slowed as he reached an intersection and made his way through the town to the outskirts, where small houses lined the street.

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  • She paused at an intersection to let a group of Immortals through, uninterested in talking to anyone just now.

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  • to enclose the basin of the Essequibo and its tributaries, thence it turns east and north of east along the Serra Acaria to unite with the unsettled boundary line of Dutch Guiana near the intersection of the 2nd parallel north with the 56th meridian.

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  • Situated at the intersection of two roads - from Kulja to Tashkent, and from Semipalatinsk to Kashgar - Vyernyi carries on an active trade in wheat, rice, corn, tea, oil and tobacco.

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  • Hannah stopped at an intersection, and Katie took her hand again, continuing down the hall toward the second stairwell.

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  • The provisional line, representing the Brazilian claim, begins at the termination of the Bolivian section (the intersection of the 11th parallel with the meridian of 72° 26' W.

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  • The afternoon sun was high in the sky, baking the revelers in summer warmth as they clustered around the intersection of Sixth and Main Street, the site of the infamous water fight.

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  • The borough is built on nearly level ground in the fertile valley of the Conewago, at the point of intersection of the turnpike roads leading to Baltimore, Carlisle, York and Frederick, from which places the principal streets - sections of these roads - are named.

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  • sphere are necessarily circles; if the cutting plane contains the centre, the section is said to be "meridional," the curve of intersection is a "great circle," and the solid cut off a "hemisphere."

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  • She glanced at the signs at the nearest intersection indicating the direction of the major department stores and the food court.

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  • The ordinates of this new briquette at the points of intersection of x =x 0, x = xi,.

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  • Fermat and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described.

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  • It was provided with a yard scale calculated with reference to height of site, and elevation was read by the intersection of the edge of the liquid with the graduation for the particular range.

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  • A.) Fleche (French for "arrow"), the term generally used in French architecture for a spire, but more especially employed to designate the timber spire covered with lead, which was erected over the intersection of the roofs over nave and transepts; sometimes these were small and unimportant, but in cathedrals they were occasionally of large dimensions, as in the fleche of Notre-Dame, Paris, where it is nearly ioo ft.

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  • As the lines of the surface which correspond to Ee, &c., slope downwards to their common intersection it follows that the alloy e has the lowest freezing-point of any mixture of the three metals; this freezing-point is 96° C., and the alloy e contains about 32% of lead, 15-5% of tin and 52.5% of bismuth.

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  • There is an entire underground city with several storeys of larger and smaller streets, squares and cross ways, cut out of the rock; at the intersection of the cross ways FIG.

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  • This shows that the C.P. is the antipole of the line of intersection of its plane with the free surface with respect to the momental ellipse at the C.G.

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  • The fish is also said to be represented in the oval-shaped figure, pointed at both ends, and formed by the intersection of two circles.

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  • wide, whose south-eastern extremity is the intersection of the 32nd meridian with the Alabama boundary, is characterized by beds of aluminous grey and white sandstone, aluminous and siliceous clay-stone, quartzitic sandstone, and green sand and marls.

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  • from the mouth of the Great Miami river to the Canadian boundary, if there were to be three states, or to its intersection with an E.

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  • (12) The Mausolea of Alexander (Soma) and the Ptolemies in one ring-fence, near the point of intersection of the two main streets.

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  • Then the locus of the intersection of PQ and OM is the quadratrix of Dinostratus.

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  • In the west the frontier is as follows: From the point of intersection of 1 ° S.

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  • Its name shows that it was of Roman origin, and its importance was no doubt due to its position at the intersection of the road leading west to the Via Popillia and north-east to the Via Appia, with the Via Herculia.

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  • the Columbia river separates it from Oregon from the mouth of that river to the point of the upper intersection with the 46th parallel of N.

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  • QUATREFOIL, in Gothic architecture, the piercing of tracery in a window or balustrade with small semicircular openings known as "foils"; the intersection of these foils is termed the cusp.

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  • Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.

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  • It was practically certain that by following up this pavement to its point of intersection with the road from Sicyon the agora would be discovered.

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

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

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  • Just as he neared the intersection, Dean recognized Corday and Fitzgerald driving toward Ouray.

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  • Two needles (for some letters, one only) were acted upon at the same time, and the letter at the point of intersection of the direction of the indexes was read.

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  • The eye-end of the tube is closed by a metal plate having a small hole at its centre near the intersection of the glass plates.

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  • The principal building is the state capitol (completed in 1857) in a square of ten acres at the intersection of High and Broad streets.

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  • In consequence of this composite formation, amethyst is apt to break with a rippled fracture, or to show "thumb markings," and the intersection of two sets of curved ripples may produce on the fractured surface a pattern something like that of "engine turning."

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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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  • By the time he neared the woman, she'd crossed the intersection where the water fight would be held later, and was passing the bank in the heart of town.

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  • How do I compute the intersection of two arrays?

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  • Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.

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  • The light was green and she accelerated across the intersection.

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  • How I love the open country, away from city police and cameras at every intersection.

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  • They made it several doors before three of Romas's clan charged around the corner of a nearby intersection.

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

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  • in a French text-book thus: " The layer, keeping his eye about a foot from the collimateur and working the elevating wheel, makes the hori z ontal line dance about the landscape until it dances on to the target; then working the traversing gear he does the same with the vertical line, then bringing his eye close, he brings the intersection on to the target."

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  • determined by the intersection of the two lines, one beginning at A, and the other at E.

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  • This stream enters the state near the centre of the northern boundary, pursues a winding south-easterly course, and from its intersection with the 43rd parallel of N.

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  • It is situated among wooded hills on the Savoureuse at the intersection of the roads and railway lines from Paris to Basel and from Lyons to Mizlhausen and Strassburg, by which it maintains considerable trade with Germany and Switzerland.

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  • A relation which is of historical interest connects the logarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.

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  • Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (f - f')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.

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  • 36 it is seen that the line joining the points A and B is the locus of the intersection of equal tangents, for if P be any point on AB and PC and PD the tangents to the circles, then PA PB = PC 2 = PD 2, and therefore PC = PD.

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  • A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis - considered as a circle of infinite radius.

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  • In the case of a coaxal system having real points of intersection the limiting points are imaginary.

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  • A coaxal system having real points of intersection has imaginary limiting points; 3.

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  • A coaxal system having imaginary points of intersection has real limiting points; 4.

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  • For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

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  • De Rationis Sectione had for its subject the resolution of the following problem: Given two straight lines and a point in each, to draw through a third given point a straight line cutting the two fixed lines, so that the parts intercepted between the given points in them and the points of intersection with this third line may have a given ratio.

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  • Its design was that of a Jerusalem cross, with two flanking towers at the east end, two at the west end, and one in the centre, at the intersection of the roofs of the nave and transepts.

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  • There are a number of theatres, but the city had no large theatre of architectural merit previous to the construction of the Municipal Theatre at the intersection of the Avenida Central with Rua 13 de Maio, with an elegant marble facade in the French Renaissance style.

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  • Other notable buildings are the ornate Monroe palace at the intersection of the Central and Beira-Mar avenues, the Praca do Commercio (Commercial Exchange) on Rua 1 ° de Margo, the Caixa da Amortizagao on the Avenida Central, the custom-house with its extensive warehouses, the terminal station of the Central railway at the N.W.

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  • The angle between a line and a curve (mixed angle) or between two curves (curvilinear angle) is measured by the angle between the line and the tangent at the point of intersection, or between the tangents to both curves at their common point.

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  • Section through Intersection.

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  • Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him.

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  • The situation of Axminster at the intersection of the two great ancient roads, Iknield Street and the Fosse Way, and also the numerous earthworks and hill-fortresses in the neighbourhood indicate a very early settlement.

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  • The eye end of the telescope tube is removed - a counterpoise to the object end being substituted in its place - and a prism is inserted at the intersection of the visual axis with the transit axis, so that the rays from the object-glass may be reflected through one of the tubes of the transit axis to an eye-piece in the pivot of this tube.

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  • coast of Africa at the intersection of 32° N.

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  • of the Ezbekia is the Place Atabeh, the chief point of intersection of the electric tramways which serve the newer parts of the town.

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  • In other cases it is secured by the intersection of joints, whereby a rock, in itself hard and durable, is divided into small angular blocks, which are separated by the action of the elements and slide down the declivities.

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  • A small section of this line terminating on the Pacific coast is also in dispute, Ecuador claiming the main channel of the Mira as the dividing line, and Colombia claiming a small district south of that channel, the line running due west from the mouth of the most southern outlet of the Mira opening into Panguapi Bay, to a point of intersection with that river.

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  • The peculiar form of the tube is eminently suited for rigid preservation of the relative parallelism of the axes of the two telescopes, so that,;i the image of a certain selected star is retained on the intersection of two wires of the micrometer, by means of the driving clock, aided by small corrections given by the observer in right ascension and declination (required on account of irregularity in the clock movement, error in astronomical adjustment of the polar axis, or changes in the star's apparent place produced by refraction), the image of a star will continue on the same spot of the photographic film during the whole time of exposure.

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  • arranged, and are all necessary for the quick and easy working raised and lowered nearly in an arc of a circle of which the point of intersection of the polar and declination axes is the centre.

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  • They then meet a small plane mirror supported at the point of intersection of the polar and declination axes, whence they are reflected down through the hollow polar axis as shown in fig.

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  • These branches are now below the point of intersection, part of the lower Ganges canal system.

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  • Similarly, when these lines are produced to meet the screen, their points of intersection with it form a line which separates the illuminated from the non-illuminated parts of the screen.

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  • quarter (especially the four at the intersection of its two main streets), which was added by Ercole (Hercules) I.

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  • of Des Moines, at the intersection of two lines of the Chicago & North-Western railway.

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  • Since the sun moves in the ecliptic, it is in the last-named sense the point of intersection of the ecliptic and the celestial equator.

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  • At nearly every intersection of two avenues is a circle or square in which is the statue of some notable American whose name the square bears.

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  • At the intersection of a street with an avenue there is usually the reservation of a small triangular grass plot at least.

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  • Instead of this the mall extends from the Capitol to Washington Monument, which stands near the intersection of lines west from the Capitol and south from the White House.

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  • The Public Library, a gift of Andrew Carnegie, is a white marble building in the Mount Vernon Square, at the intersection of Massachusetts and New York avenues.

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  • If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.

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  • (ii) Two forces in intersecting lines may be replaced by a force which is their geometric sum, acting through the intersection.

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  • If R be the intersection of these sides, FIG.

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  • We have only to construct the line of action of the resultant for each of two arbitrary directions of the forces; the intersection of the two lines gives the point required.

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  • Successive halfturns about intersecting axes a, b are equivalent to a rotation about the common perpendicular to a, b at their intersection, Of amount equal to twice the acute angle between them, in the direction from a to b.

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  • But it may be reduced to simpler elements in a variety of ways., For example, it may be reduced to two forces in perpendicular skew lines, For consider any plane, and let each force, at its intersection with the plane, be resolved into two components, one (P) normal to the plane, the other ~ in the plane.

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  • Thus, let the plane of the paper be perpendicular to the planes of two couples, and therefore perpendicular to the line of intersection of these planes.

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  • the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.

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  • Again, the locus of G is an arc of an ellipse whose centre is in the intersection of the planes; since this arc is convex upwards the equilibrium is unstable.

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  • The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

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  • 52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

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  • If a+~+7 =0, G is at infinity; if a=~=y, G is at the intersection of the median lines ofthetriangle; jfa:: y=a: b: c,Gisatthecentreofthe inscribed circle.

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  • It is seen that for a given direction of p this moment is least when p passes through the intersection X of the first and last sides of the funicular; i.e.

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  • Considering, in the first place, the case in which the load and the two resistances by which each piece is balanced meet in one point, which may be called the centre of load, there will be as many such points of intersection, or centres of load, as there are pieces in the structure; and the directions and positions of the resistances or mutual pressures exerted between the pieces will be represented by the sides of a polygon joining Pi h2 ~, ~ those points, as in fig.

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  • 92), when the rolling will be towards the opposite hand; and at a given instant let T be the line of coptact of the two cylindrical surfaces, which is at their commor intersection with the plane AB traversing the two axes of figure.

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  • That for a pair of turning pieces with intersecting axes the line of contact is also straight, and traverses the~ point of intersection of the axes; and hence that the rolling surfaces are conical, with a common apex (the term conical including all surfaces generated by the motion of a straight line which traverses a fixed point).

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  • 97 and g8).Let 0 be the apex orpoint of intersection of the two axes OC1, 0C2.

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  • The line of intersection of the planes perpendicular to the paths of the two connected points at a given instant is the instantaneous axis of the link at that instant; and the velocities of the connected points are directly as their distances from that axis.

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  • Let 0 be the point of intersection of the axes OCf, 0C2,

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  • moves at right angles to the central plane of its shaft and (ork, therefore the line of intersection of the central planes of the two forks at any instant is the instantaneous axis of the cross, and the velocity ratio of the points Ff, F2 (which, as the forks are equal, is also the angular velocity ratio of the shafts) is equal to the ratio of the distances of those points from that instantaneous axis.

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  • Julesburg, in the extreme north-east corner, at the intersection of the Platte valley and the overland wagon route, became transiently important during the rush of settlers that followed.

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  • on that parallel to its intersection with the 111th meridian of longitude west of Greenwich, from that point of intersection in a straight line to the Colorado river, 20 m.

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  • Among the islands formed by the intersection and confluence of the rivers is Majuli, or the Great Island, as it is called by way of pre-eminence.

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  • The tower, at the intersection of the nave and transepts, is of unusually massive proportions, being 30 ft.

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  • of Berlin by the main railway to Gorlitz, and at the intersection of the lines Halle-Sagan and GrossenhainFrankfort-on-Oder.

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  • In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (with infinitely distant objects: with a finite height of incidence the same distance of intersection, and the same sine ratio as to one neighbouring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system).

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  • The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called "zones," and the constructor endeavours to reduce these to a minimum.

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  • there are " chromatic differences " of the distances of intersection, of magnifications, and of monochromatic aberrations.

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  • The church itself was a cruciform structure with a choir, nave and transepts, and a tower surmounting the centre of intersection.

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  • north of Fort Olimpo and run south-west in a straight line to an intersection with the Pilcomayo in long.

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  • Thence it continues north to an intersection with the Desaguadero, in about 16° 45' S.

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  • Hence T, the point of intersection of Pp and Qq, must be the centre of similitude and must be on the common directrix.

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  • long., at the junction of the navigable river Mukhovets with the Bug, and at the intersection of railways from Warsaw, Kiev, Moscow and East Prussia.

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  • van Eetvelde, administrator-general of the foreign affairs of the Congo State, informed the French minister at Brussels that the International Association had not intended in 1884 that the right subsequently gave rise to considerable discussions with France, and eventually a protocol, signed at Brussels on the 29th of April 1887, continued the boundary along the Congo to its confluence with the Ubangi (Mobangi), whence it followed the thalweg of that river to its intersection with the 4th parallel of north latitude, below which parallel it was agreed that the northern boundary of the Congo Free State should in no case descend.

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  • 3) are horizontal in direction, being parallel to the edges of intersection between the prism and pyramid faces, and are due to the frequent oscillatory combination of these faces.

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  • The faces s are striated parallel to their edge of intersection with r; this serves to distinguish r and z, and thus, in the absence of x faces, to distinguish leftor right-handed crystals.

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  • In the simplest case of a single mountain valley to be used for the supply of an impounding reservoir, the rainfall should be known at five points, three being in the axis of the valley, of which one is near the point of intersection of that axis with the boundary of the watershed.

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  • We find on the left-hand scale of yield that the height of the ordinate drawn to the 50-inch mean rainfall curve from 200,000 on the capacity scale, is 1457 gallons per day per acre; and the straight radial line, which cuts the point of intersection of the curved line and the co-ordinates, tells us that this reservoir will equalize the flow of the two driest consecutive years.

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  • In the most general case two points may be chosen on the line of intersection of the diametral planes, and tangents drawn to the pitch circles of the pulleys.

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  • On an elevated site at the Intersection of Washington Place - a continuation of N.

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  • As so used it may be defined as not only the Mason and Dixon Line proper, but also the line formed by the Ohio River from its intersection with the Pennsylvania boundary to its mouth, thence the eastern, northern and western boundaries of Missouri, and thence westward the parallel 36° 30' - the line established by the Missouri Compromise to separate free and slave territory in the " Louisiana Purchase," except as regards Missouri.

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  • of New York city by rail, and at the intersection of the boundary lines of the states of New York, New Jersey and Pennsylvania.

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  • Dallin, was unveiled in 1897, at the intersection of Main and Brigham Streets.

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  • the elimination from the two equations of y (or x) gives for x (or y) an equation of a certain order, say the resultant equation; and then to each value of x (or y) satisfying this equation there corresponds in general a single value of y (or x), and consequently a single point of intersection; the number of intersections is thus equal to the order of the resultant equation in x (or y).

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  • The theorem of the m intersections has been stated in regard to an arbitrary line; in fact, for particular lines the resultant equation may be or appear to be of an order less than m; for instance, taking m= 2, if the hyperbola xy - 1= o be cut by the line y=0, the resultant equation in x is Ox- 1 = o, and there is apparently only the intersection (x 110, y =0); but the theorem is, in fact, true for every line whatever: a curve of the order in meets every line whatever in precisely m points.

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  • It is, moreover, to be noticed that the points at infinity may be all or any of them imaginary, and that the points of intersection, whether finite or at infinity, real or imaginary, may coincide two or more of them together, and have to be counted accordingly; to support the theorem in its universality, it is necessary to take account of these various circumstances.

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  • this projection is the intersection of the given plane with the plane through the centre and the given line.

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  • Say the projection is always a line, then if the figure is such that the two planes are parallel, the projection is the intersection of the given plane by a parallel plane, or it is the system of points at infinity on the given plane, that is, these points at infinity are regarded as situate on a given line, the line infinity of the given plane.

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  • 1 1 In solid geometry infinity is a plane - its intersection with any given plane being the right line which iš the infinity of this given plane.

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  • Consider two circles partially drawn so that it does not appear whether the circles, if completed, would or would not intersect in real points, say two arcs of circles; then we can, by means of a third circle drawn so as to intersect in two real points each of the two arcs, determine a right line, which, if the complete circles intersect in two real points, passes through the points, and which is on this account regarded as a line passing through two (real or imaginary) points of intersection of the two circles.

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  • The construction in fact is, join the two points in which the third circle meets the first arc, and join also the two points in which the third circle meets the second arc, and from the point of intersection of the two joining lines, let fall a perpendicular on the line joining the centre of the two circles; this perpendicular (considered as an indefinite line) is what Gaultier terms the " radical axis of the two circles "; it is a line determined by a real construction and itself always real; and by what precedes it is the line joining two (real or imaginary, as the case may be) intersections of the given circles.

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  • Mag., 1858; considering the m - 2 points in which any tangent to the curve again meets the curve, he showed how to form the equation of a curve of the order (m - 2), giving by its intersection with the tangent the points in question; making the tangent touch this curve of the order (m - 2), it will be a double tangent of the original curve.

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  • To develop the theory, consider the curve corresponding to any particular value of the parameter; this has with the consecutive curve (or curve belonging to the consecutive value of the parameter) a certain number of intersections and of common tangents, which may be considered as the tangents at the intersections; and the so-called envelope is the curve which is at the same time generated by the points of intersection and enveloped by the common tangents; we have thus a dual generation.

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  • Many well-known derivative curves present themselves in this manner; thus the variable curve may be the normal (or line at right angles to the tangent) at any point of the given curve; the intersection of the consecutive normals is the centre of curvature; and we have the evolute as at once the locus of the centre of curvature and the envelope of the normal.

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  • And we thus see that the two hyperbolic legs belong to a simple intersection of the curve by the line infinity.

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  • We may from each of the circular points draw tangents to a given curve; the intersection of two such tangents (belonging of course to the two circular points respectively) is a focus.

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  • To a given point (x', y', z') not on the curve u' =0 there corresponds, not a single point, but the system of points (x, y, z) given by the equations x': y': z' = X: Y: Z, viz., regarding x', y', z' as constants (and to fix the ideas, assuming that the curves X = o, Y =0, Z =o, have no common intersections), these are the points of intersection of the curves X: Y: Z, =x': y' : z', but no one of these points is situate on the curve u = o.

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  • It is a leading point in the theory that a curve in space cannot in general be represented by means of two equations U= o, V = o; the two equations represent surfaces, intersecting in a curve; but there are curves which are not the complete intersection of any two surfaces; thus we have the cubic in space, or skew cubic, which is the residual intersection of two quadric surfaces which have a line in common; the equations U= o, V= o of the two quadric surfaces represent the cubic curve, not by itself, but together with the line.

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  • 8, then we know that the star is exactly in the line of sight of the telescope, defined as the line joining the centre of the object glass, and the point of intersection of the cross threads.

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  • Hardy, a railway official, who planned a town at the intersection of the New Orleans & NorthEastern (which built a round house and repair shops here in 1885) and the Gulf & Ship Island railways.

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  • of the latter, about the intersection of 7° E.

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  • It is a peak of the Himalayas situated in Nepal almost precisely on the intersection of the meridian 87 E.

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  • the radius which passes through the intersection of 115° E.

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  • It is situated at the intersection of the Missouri, Kansas & Texas, and the Kansas City, Fort Scott & Memphis ("Frisco System") railways, in the midst of a lead a: d zinc region, extremely valuable deposits of these metals having been discovered in 1877.

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  • Draw any number of radii of the two circles, and from the points of intersection with the major circle draw lines parallel to the minor axis, and from the points of intersection with the minor circle draw lines parallel to the major axis.

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  • Let P be the intersection of the line SL with the line RAM, then it can be readily shown that P is a point on the ellipse.

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  • (4) If the axes be given, the curve can be approximately constructed by circular arcs in the following manner: - Let AA', BB' be the axes; determine D the intersection of lines through B and A parallel to the major and minor axes respectively.

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  • Then the intersection of EB and DB' determines a point P on the (true) curve.

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  • In Newton's method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin's method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section.

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  • If the instrument has a sensible lens diameter, and is arranged so that the centre of rotation of the eye can coincide with the intersection of the principal rays, the lens can then form with the eye a centred system.

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  • M is therefore the intersection of the principal rays.

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  • In most cases, and also in corrected systems, the intersection of the principal rays is no longer available for the centre of rotation of the eye, and this kind of observation is impossible.

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  • The intersection of the principal rays in this case lies in the middle of the entrance pupil or of the exit pupil.

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  • The centre of the entrance pupil is the point of intersection of the principal rays; and it is therefore determinative for the perspective representation on the plane focused for.

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  • the intersection of the principal rays lies in front of the object, and consequently objects in front of the plane focused for will be projected on E magnified and the objects lying behind it diminished (" hypercentric " transmission).

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  • The point of intersection, i.e.

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  • In the case of the negative eyepiece, on the other hand, the divergence of the principal rays through the eyepiece is also further augmented, but their point of intersection is not accessible to the eye.

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  • We strolled back to my stolen car and drove away, taking back street to avoid intersection cameras.

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  • The shockwaves faded, and she stood in the middle of an intersection, stretching out with her Guardian senses to find some kind of life.

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  • compute the intersection of two arrays?

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  • conical intersection, many unusual quantum effects take place.

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  • intersection of three planes.

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  • intersection of gender, technology and media in Asia.

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  • intersection of a row and a column is called a cell.

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  • intersection of the celestial circles with the circle of the Horizon at the equinox.

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  • intersection of advertising, marketing and product design, with particular applicability to fast-moving consumer goods.

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  • When she reached an intersection she turned away from the flight path of the UFO and toward Dayton where the three of them lived.

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  • God forbid we should hamper a car from crossing an intersection!

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  • A countable intersection of open dense sets is the intersection of a countable number of open dense sets.

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  • In the vicinity of a conical intersection, many unusual quantum effects take place.

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  • She had been brought in last night by a man who found her in a busy intersection.

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  • At the major intersection with The Avenue, continue straight on along Burgess Road.

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  • Now I'm walking on the wasteland of a motorway intersection.

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  • From the exit of Sewers West, go straight until you get to a T intersection.

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  • Eight of the holes drilled on Oleninskoye intersected pegmatite within the area where the vein intersection was anticipated.

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  • The new raster should be the intersection of the two input rasters.

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  • roundabouts at a major intersection.

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  • The vortex patterns correspond to the intersection of the laser sheet with the trailing, helical vortices from the turbine blades.

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  • If the perpendiculars from the vertices to the opposite faces of a tetrahedron be concurrent, then a sphere passes through the four feet of the perpendiculars, and consequently through the centre of gravity of each of the four faces, and through the mid-points of the segments of the perpendiculars between the vertices and their common point of intersection.

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  • The central tower of a church over the intersection of the nave and chancel with the transepts is sometimes called the " rood tower "; an example is that at Notre Dame at Paris.

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  • At the focus of his telescope he placed fine silver wires at right angles to each other, which, by their intersection, formed a network of small squares.

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  • To use the instrument, it is well first to adjust the web moved by the screw S, so that its point of intersection with the web (commonly called the " position-web "), which is parallel to the axis of the screw, shall be nearly coincident with the axis of rotation of the micrometer box.

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  • Now direct the telescope to a star near the equator and so that the star's image in its diurnal motion shall pass across the intersection of the two webs which mark the axis of rotation of the micrometer box.

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  • The line starts at the intersection of the 23rd parallel with the 67th meridian and runs south-westerly and southerly to the mountain and volcano summits of Rincon, Socompa, Llullaillaco, Azufre, Aguas Blancas and Sierra Nevada, thence to the initial point of the British award.

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  • It then followed this line of longitude to its intersection with N.

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  • From the point of intersection of the 71st meridian with the 36th parallel of latitude, an unbroken range of mountain stretches on one side towards the north-east, up to the crest of the northern slope of the Tibetan plateau, and on the other nearly due west as far as the Caspian.

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  • The provisional line, representing the Brazilian claim, begins at the termination of the Bolivian section (the intersection of the 11th parallel with the meridian of 72° 26' W.

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  • As the lines of the surface which correspond to Ee, &c., slope downwards to their common intersection it follows that the alloy e has the lowest freezing-point of any mixture of the three metals; this freezing-point is 96° C., and the alloy e contains about 32% of lead, 15-5% of tin and 52.5% of bismuth.

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  • In the west the frontier is as follows: From the point of intersection of 1 ° S.

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  • the point of intersection of its diagonals.

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  • Other notable buildings are the ornate Monroe palace at the intersection of the Central and Beira-Mar avenues, the Praca do Commercio (Commercial Exchange) on Rua 1 ° de Margo, the Caixa da Amortizagao on the Avenida Central, the custom-house with its extensive warehouses, the terminal station of the Central railway at the N.W.

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  • coast of Africa at the intersection of 32° N.

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  • duced by euclidian methods from the definition include the following: the tangent at any point bisects the angle between the focal distance and the perpendicular on the directrix and is equally inclined to the focal distance and the axis; tangents at the extremities of a focal chord intersect at right angles on the directrix, and as a corollary we have that the locus of the intersection of tangents at right angles is the directrix; the circumcircle of a triangle circumscribing a parabola passes through the focus; the subtangent is equal to twice the abscissa of the point of contact; the subnormal is constant and equals the semilatus rectum; and the radius of curvature at a point P is 2 (FP) 4 /a 2 where a is the semilatus rectum and FP the focal distance of P.

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  • By directing the telescope to a distant object, or to the intersection of the webs of a fixed collimating telescope (see Transit Circle), it is easy to measure the effect of a small change of zenith distance of the axis of the telescope in terms both of the level and of the micrometer screw, and thus, if the levels are perfectly sensitive and uniform in curvature and graduation, to determine the value of one division of each level in terms of the micrometer screw.

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  • If these sides intersect, the resultant acts through the intersection, and its magnitude and direction are given by the line joining the first and last sides of the force-polygon (see fig.

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  • To define the moment of a force about an axis HK, we project the force orthogonally on a plane perpendicular to HK and take the moment of the projection about the intersection of ilK with the plane (see 4).

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  • It is situated at the intersection of four great railway systems-the Atchison Topeka & Santa Fe, the St Louis & San Francisco, the Kansas City Southern (which maintains shops here), and the Missouri Pacific, and is served by inter-urban electric railways.

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  • These points lie, therefore, upon a horizontal plane at a given elevation passing through the land shown on the map, and the contour-line is the intersection of that horizontal plane with the surface of the ground.

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  • In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component contains the amount due to each refracting surface (see Czapski-Eppenstein, op. cit.

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  • Thence it continues north to an intersection with the Desaguadero, in about 16° 45' S.

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  • As so used it may be defined as not only the Mason and Dixon Line proper, but also the line formed by the Ohio River from its intersection with the Pennsylvania boundary to its mouth, thence the eastern, northern and western boundaries of Missouri, and thence westward the parallel 36° 30' - the line established by the Missouri Compromise to separate free and slave territory in the " Louisiana Purchase," except as regards Missouri.

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  • of the latter, about the intersection of 7° E.

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  • the radius which passes through the intersection of 115° E.

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  • Anchorage, Alaska, just opened its first two roundabouts at a major intersection.

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  • To keep those children safe, a house near a highway or main intersection would also be on that list.

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  • Located one mile east of the intersection of SR535 and Highway 192 are the Value Outlet Shops.

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  • This mall is located between St. Cloud, Minnesota, and Minneapolis, Minnesota at the intersection of I-94 and County Road 19.

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  • At this point, the small bit of skin in the intersection between the front and back needles will gently slough off.

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  • Bloom and his two unidentified female passengers were near the intersection of Fountain and Vista streets in Hollywood when another driver reportedly cut him off.

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  • November 2007 - Runs a red light at a busy intersection while using a cell phone (not on her ear, in front of her face) with her sleeping children in the back seat.

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  • While other cars had stopped to allow the boy to cross, Gayheart swerved her car around the others and proceeded through the intersection, hitting the boy on her way through.

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  • You'll generally place baffles at the intersection between the joists and the rafters.

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  • You should end up with an intersection in the center of the room the size of the square you plan on using.

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  • You can't know for sure if there's another car coming as you turn left at an intersection.

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  • Your teammates are holed up in the middle of an intersection, shooting bad guys in the face.

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  • In Franklin, NC, at the intersection of US Routes 23/441/64, take US Route 64 west for 12 miles to Wallace Gap/campground sign (Old Murphy Road.

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  • Route 67) Turn right onto Route 67 and drive 1.8 miles to the "Y" intersection.

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  • Roads - Don't locate your home at an intersection, especially if a road ends at the intersection directly across from your home.

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  • When complete, you will have two creases on the paper, with an intersection point in the center.

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  • The tip of the corner should meet the very center of the intersection point.

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  • A circle marks an intersection of creases where your folds should start or pass through.

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  • Dolores Place: Dolores Place is an affordable bed and breakfast in a great location, right at the intersection of 25th Street and Dolores.

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  • The score is calculated by the number of empty intersection points between a players pieces plus how many they have captured.

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  • You cannot build any villages on an intersection adjacent to an already existent village.

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  • The closest intersection is 21st Street and Mayflower Avenue.

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  • It's near the intersection of Meadow Lane and Dahlberg Drive off of Olson Memorial Highway.

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  • Full of bang and bling, Baby Phat purses mark the intersection of hip-hop style and high fashion.

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  • It seems to illustrate the intersection between graceful designs and jovial twists.

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  • But even more notable is the reflective piping added to the bag's exterior for "added visibility", you know, in case you're taking your three-month-old biking down a busy intersection during the late hours of night (?!!!).

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  • This narrows the point of intersection for the joining of two lives.

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  • The Celtic cross combines the crossed bars with a circle laid over the intersection to symbolize eternity.

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  • When you take both veins of symbolism into consideration, the intersection of the cross is viewed as a joining of forces.

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  • When laid over the intersection of the cross, the circle is believed to represent a place where the mystical and corporeal worlds meet.

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  • Celtic cross tattoos usually appear as a Latin cross shape with a circle around the intersection of the cross's four arms.

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  • The Celtic cross pattern is a basic cross shape with a circle which represents the sun incorporated at the cross' intersection.

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  • Provides nationwide searches by intersection, zip, station name, with information pricing for gasoline and diesel.

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  • Remember to use your turn signals any time you change lanes, turn at an intersection, or turn off the road into a driveway.

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  • However, the test gets a bit harder as you first must stop at a stop sign, make an appropriate turn, and then approach a four-way intersection.

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  • Whenever you come to an intersection and press on the brakes, do the wheels make an ear-piercing scraping sound?

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  • A driver runs a red light and strikes a car in the intersection, or is following too close and is involved in a rear-end collision.

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  • This rapid expansion has found a natural home in the intersection between fashion and lingerie.

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  • Intersection: This clue requires one team to partner up with another team until further notice.

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  • One strategy would be to add the words "NYC" to that search phrase, or the name of a particular neighborhood, intersection or area you would like to target.

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