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intersect

intersect

intersect Sentence Examples

  • Several important roads intersect the province; among them are - I.

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  • The broad streets of the city intersect at right angles.

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  • The broad streets of the city intersect at right angles.

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  • The axes will not be parallel, nor will they intersect each other.

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  • The axes will not be parallel, nor will they intersect each other.

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  • intersect in the instantaneous centre.

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  • These plateaus, with an average elevation of Boo to 1000 ft., are mostly covered with forests of oak, beech and lime, and are deeply cut by river valleys, some being narrow and craggy, and others broad, with gentle slopes and marshy bottoms. Narrow ravines intersect them in all directions, and they often assume, especially in the east, the character of wild, impassable, woody and marshy tracts.

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  • These plateaus, with an average elevation of Boo to 1000 ft., are mostly covered with forests of oak, beech and lime, and are deeply cut by river valleys, some being narrow and craggy, and others broad, with gentle slopes and marshy bottoms. Narrow ravines intersect them in all directions, and they often assume, especially in the east, the character of wild, impassable, woody and marshy tracts.

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  • The tunnel widened, and his pace slowed as he saw another tunnel intersect it.

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  • They intersect regularly at right angles, dividing the town into square blocks, like modern Mannheim or Turin, according to a Roman system usual in both Italy and the provinces: plainly they were laid out all at once, possibly by Agricola (Tac. Agr.

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  • - and nearly all intersect at right angles; they are paved with brick and asphalt, and many in the residential quarters are shaded with fine elms and maples.

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

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  • In these thoroughfares and in several of the streets which intersect them are the offices of the mining companies, the banks, clubs, newspaper offices, hotels and shops, the majority being handsome stone or brick buildings, while the survival of some wooden shanties and corrugated iron buildings recalls the early character of the town.

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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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  • In these thoroughfares and in several of the streets which intersect them are the offices of the mining companies, the banks, clubs, newspaper offices, hotels and shops, the majority being handsome stone or brick buildings, while the survival of some wooden shanties and corrugated iron buildings recalls the early character of the town.

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  • In 1754 Prome was besieged by the king of Pegu, who was again defeated by Alompra, and the war was transferred from the upper provinces to the mouths of the navigable rivers, and the numerous creeks and canals which intersect the lower country.

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  • With the same feeling with which he had galloped across the path of a wolf, Rostov gave rein to his Donets horse and galloped to intersect the path of the dragoons' disordered lines.

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  • These equations show that the circles touch where they intersect the lines x 2 +y 2 = o, i.e.

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  • In obtaining the minor Aik in the form of a determinant we erased certain rows and columns, and we would have erased in an exactly similar manner had we been forming the determinant associated with A2:8, since the deleting lines intersect rk in two pairs of points.

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  • Such a rule of the two diameters not only guides us toward the sun in the system and the heart in man, but draws lines through the length and breadth of the aggregate of a man's particular daily behaviors and waves of life into his coves and inlets, and where they intersect will be the height or depth of his character.

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  • We may observe that the asymptotes intersect this circle in the same points as the directrices.

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  • A number of gold reefs intersect the surrounding district and in some of the reefs gold is mined.

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  • Numerous canals intersect the district, affording ample means of irrigation.

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  • Electric tramways intersect the town, and are continued for 3 m.

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  • Paris is served by the Vandalia, and the Cleveland, Cincinnati, Chicago & St Louis (New York Central system) railways; the main line and the Cairo division of the latter intersect here, and the city is the transfer point for traffic from the E.

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  • The state constitution adopted in 1802 followed the enabling act in accepting this line, but made the proviso that if it should not intersect Lake Erie east of the mouth of the Miami river, then the northern boundary should be a line from the southern end of Lake Michigan to the most northern cape of Maumee Bay and thence to the Territorial line, and to the Pennsylvania line.

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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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  • 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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  • With variation of temperature, the surfaces of equal pressure and density need not coincide; but, taking the pressure, density and temperature as connected by some relation,such as the gas-equation, the surfaces of equal density and temperature must intersect in lines lying on a surface of equal pressure.

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  • The central zone includes Hejaz (or Hijaz), Nejd and El Hasa; much of it is a dry, stony or sandy steppe, with few wells or watering-places, and only occupied by nomad tribes; but the great wadis which intersect it contain many fertile stretches of alluvial soil, where cultivation is possible and which support a considerable settled population, with several large towns and numerous villages.

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  • Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.

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  • The best soils when abundantly irrigated yield from 50to 60-fold, and the water for this purpose is supplied by the innumerable streams which intersect the province.

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  • If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.

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  • Consider the case of two circles, and in the first place suppose them to intersect in two real points A and B.

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  • The circles intersect in real or imaginary points according to the lower or upper sign of k 2, and the limiting points are real for the upper sign and imaginary for the lower sign.

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  • When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental.

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  • Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.

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  • When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental.

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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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  • 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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  • The greater part of the country is hilly and irregular, though there are considerable plains; but besides Rhodope two other tolerably definite chains intersect it, one of which descends from Haemus to Adrianople, while the other follows the coast of the Euxine at no great distance inland.

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  • Deep gorges, through which tributaries of the Chorokh force their passage to the main river, intersect these highlands, forming most picturesque gorges.

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  • Two of the principal thoroughfares, Federal and Ohio streets, intersect at a central square, in which are the city hall, public library, post office and the marketplace; and surrounding the main business section on the E., N.

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  • The existence of this route, which traverses the Darwaz mountains from east to west, cutting off the northern bend of the Oxus, and connecting those easterly routes which intersect the Pamirs by means of the Ghund and Shakhdara (and which concentrate about Lake Shiwa) with Kolab in eastern Bokhara, is important.

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  • intersect, the velocity ratio of the Ci - - - - -

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  • Again, imagin d fixed, then the instantaneous centre Obd of b with regard n d is found by producing the links c and a to intersect in Obd and the shapes of the centroids belonging respectively to thi links Ii and d can be found as before.

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  • The greater part of the country is hilly and irregular, though there are considerable plains; but besides Rhodope two other tolerably definite chains intersect it, one of which descends from Haemus to Adrianople, while the other follows the coast of the Euxine at no great distance inland.

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  • The soft shales or clays of the hills bounding the valley render these hills especially subject to the action of denudation, and the result, in rounded slopes and easily accessible crests, determines the nature of the easy tracks and passes which intersect them.

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  • Two canals, the Oude and the Nieuwe Gracht, intersect the town from end to end.

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  • The soft shales or clays of the hills bounding the valley render these hills especially subject to the action of denudation, and the result, in rounded slopes and easily accessible crests, determines the nature of the easy tracks and passes which intersect them.

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  • At its northern edge, where the waterless forest tract of the Bhabar ends, a series of springs burst from the surface, and these, increasing and uniting in their progress, form the numerous streams that intersect the Tarai.

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  • The points where axes intersect the plane of section are called centres; the point where the line of contact intersects it, the poini of contact, or pitch-point; and the wheels are described as circular, elliptical, &c., according to the forms of their sections made by that plane.

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  • Naming the central ray passing through the entrance pupil the " axis of the pencil " or " principal ray," we can say: the rays of the pencil intersect, not in one point, but in two focal lines, which we can assume to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and FIG.

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  • Hence the tangents at A and B to the upper catenary must intersect above the directrix, and the tangents at A and B to the lower catenary must intersect below the directrix.

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  • Does one group include, or exclude, or intersect another with which it is compared ?

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  • It bears a strong resemblance to a Dutch town, for the houses are built in the style of those of Amsterdam, and the narrow channel separating it from its western suburb of Overzijde and the waters of the Waigat, which intersect it, recall the canals.

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

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  • If funiculars be drawn for two positions 0,0 of the pole in the force-diagram, their corresponding sides will intersect on a straight line parallel to 00.

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  • Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the directrix; for since any catenary with its directrix is a similar figure to any other catenary with its directrix, if the directrix of the one coincides with that of the other the centre of similitude must lie on the common directrix.

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  • This catenoid, however, is in stable equilibrium only when the portion considered is such that the tangents to the catenary at its extremities intersect before they reach the directrix.

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  • 1), they intersect one another at different angles, producing an intricate network which it is almost impossible to reduce to any system.

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  • But in many parts deep transverse valleys intersect the prevailing direction of the ridges, and facilitate the passage of man, plants and animals, as well as of currents of air which mitigate the contrast that would otherwise be found between the climates of the opposite slopes.

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  • To find the ratio of these velocities, produce C1T~, C2T, till they intersect in K; K is the instantaneous axis of the connecting rod, and the velocity ratio is ci :v2 ::KTi :KT2.

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  • - the city is divided into these four parts by North Capitol, East Capitol and South Capitol streets, which intersect at the Capitol.

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  • A tunnel differs from a drift in that it is driven across the strata to intersect the deposit.

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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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  • d o, dx dy dz dx dy dz so that, at any instant, the surfaces over which tk and m are constant intersect in the vortex lines.

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  • Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.

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  • Four small streams - the Sagarmati, Saraswati, Khari and Dai - also intersect the district.

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  • In the latter case the sign is determined by -I raised to the same power as before, with the exception that Tux., replaces Tusk; but if one of these numbers be even the other must be uneven; hence A ik = - Ais� rk Moreover aik a,, aikarsAik +aisarkAis Aik, rk aik ars rs where the determinant factor is giyen by the four points in which the deleting lines intersect.

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  • Through any point in the field one such line can be drawn, but not more than one, for the force obviously cannot have more than one direction; the lines therefore never intersect.

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  • wide, the principal thoroughfares, intersect.

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  • At Sao Joao da Chapada, in Minas Geraes, diamonds occur in a clay interstratified with the itacolumite, and are accompanied by sharp crystals of rutile and haematite in the neighbourhood of decomposed quartz veins which intersect the itacolumite.

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  • The condition of stability of a catenoid is therefore that the tangents at the extremities of its generating catenary must intersect before they reach the directrix.

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  • A number of smaller streets intersect the Hauptstrasse at right angles and run down to the river,which is crossed by two fine bridges.

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  • Plucker finally (Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice.

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  • Lesser canals intersect the others radially, thus virtually dividing the city into a number of islands; whence it has been compared with Venice.

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  • The country which they thus enclose and intersect forms the delta of Bengal.

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  • The navigable streams which fall into the Ganges intersect the country in every direction and afford great facilities for internal communication.

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  • Steep and rugged ravines intersect the plains, opening into small bays or coves on the shore, fenced with masses of compact and cellular lava; and all over the island are found products of volcanic action.

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  • and S., intersect; from this point buildings on these two streets are numbered N., S., E.

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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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  • And we have then the theorem, two odd circuits intersect in an odd number of points; an odd and an even circuit, or two even circuits, in an even number of points.

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  • There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.

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  • taking P, P' as the corresponding points in an (a, a') correspondence on a curve of deficiency D, and supposing that when P is given the corresponding points P' are found as the intersections of the curve by a curve o containing the co-ordinates of P as parameters, and having with the given curve k intersections at the point P, then the number of united points is a = a+a' +2kD; and more generally, if the curve 0 intersect the given curve in a set of points P' each p times, a set of points Q' each q times, &c., in such manner that the points (P,P') the points (P, Q') &c., are pairs of points corresponding to each other according to distinct laws; then if (P, P') are points having an (a, a') correspondence with a number=a of united points, (P, Q') points having a (0,0') correspondence with a number =b of united points, and so on, the theorem is that we have p(a-a-a')+q(b-(3-(')+ ...

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  • A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

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  • The streets intersect at right angles, are from 60 to 120 ft.

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  • If we conceive a pole to each of these orbits, determined by the points in which lines perpendicular to their planes intersect the celestial sphere, the pole of the satellite orbit will revolve around the pole of the planetary orbit precisely as the pole of the earth does around the pole of the ecliptic, the inclination of the two orbits remaining unchanged.

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  • In the south, the Lee and the Blackwater intersect the mountains of Kerry and Cork flowing east, and turn abruptly into estuaries opening south.

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  • The railways, which are all owned and managed by the Hungarian state, intersect most parts of the country except the mountains south of Ogulin, where there is, nevertheless, a considerable traffic over the passes into Dalmatia and Bosnia.

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  • Let this arc on the reverse side to P intersect a line through 0 parallel to the major axis in a point H.

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  • Let JO intersect the major axis in 0 1.

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  • It has 12 pentagonal faces, and 30 edges, which intersect in fives to form 12 vertices.

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  • The great dodecahedron is determined by the intersections of the twelve planes which intersect the Platonic icosahedron in five of its edges; or each face has the same boundaries as the basal sides of five covertical faces of the icosahedron.

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  • It has 12 faces, which meet in 30 edges; these intersect in threes to form 20 vertices.

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  • Other less pronounced wrinkles run from southwest to north-east and intersect the former series at certain points, so that it is by alternate digressions from one to the other series that the irregular crest of the Pyrenees acquires its general direction.

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  • Good roads and byeways intersect it in every direction.

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  • Taramelli (Notizie degli Scavi, 1905, 41 seq.) rightly points out that the nucleus of the Roman municipium is probably represented by the present quarter of the Marina, in which the streets intersect at right angles and Roman remains are frequently found in the subsoil.

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  • An important property of confocal systems is that only two confocals can be drawn through a specified point, one being an ellipse, the other a hyperbola, and they intersect orthogonally.

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  • The first book deals with the generation of the three conics; the second with the asymptotes, axes and diameters; the third with various metrical relations between transversals, chords, tangents, asymptotes, &c.; the fourth with the theory of the pole and polar, including the harmonic division of a straight line, and with systems of two conics, which he shows to intersect in not more than four points; he also investigates conics having single and double contact.

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  • The principal rays, which on the object-side connect the object-points with the centre of the entrance pupil, intersect the axis on the image-side at the centre of rotation M of the eye.

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  • The aberration of rays in which the outer rays intersect the axis at a shorter distance than the central rays is known as " undercorrection."

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  • A cross-table is very convenient for this calculation, for with the aid of the two movable slides situated in the plane of the plate and at right angles to one another, the point where the two crystal edges intersect can be quickly and correctly brought into the revolving axis of the plate.

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  • The tunnel widened, and his pace slowed as he saw another tunnel intersect it.

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  • collinear points in the gradient image intersect in peaks in the Hough transform space.

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  • And where these two categories intersect, there lurks only one evil: video games.

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  • Although the hole did not intersect significant economic mineralization it did intersect three horizons of interest.

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  • intersect at the minimum point of the average cost curve.

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  • Such metabolic pathways are not linear but often intersect to form a complex network.

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  • You must not intersect more than two chords at the same point.

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  • The marginal cost curve must also intersect the average cost at its minimum.

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  • The boundaries of B - independent predicates not only intersect; they intersect wherever they have a point in common.

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  • Where Lines MO and NO intersect this semicircle read and values along the short curves on the scale of the inner semicircle.

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  • Simple algebraic operations are then used to intersect two spheres, or a line and a sphere.

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  • Numerous canals intersect the district, affording ample means of irrigation.

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  • Paris is served by the Vandalia, and the Cleveland, Cincinnati, Chicago & St Louis (New York Central system) railways; the main line and the Cairo division of the latter intersect here, and the city is the transfer point for traffic from the E.

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  • The curve does not appear to intersect the conjugate axis, but the introduction of imaginaries permits us to regard it as cutting this axis in two unreal points.

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  • We may observe that the asymptotes intersect this circle in the same points as the directrices.

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  • These contours intersect the ground at a given distance above or below the level of the sea, and thus bound a series of horizontal planes (see fig.

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  • 1), they intersect one another at different angles, producing an intricate network which it is almost impossible to reduce to any system.

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  • When a cleavage flake of mica is struck a sharp blow with a blunt needle-point a six-rayed star of cracks or "percussion figure" is developed: the rays intersect at angles of approximately 60°, and the pair most prominently developed are parallel to the plane of symmetry of the crystal.

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  • In obtaining the minor Aik in the form of a determinant we erased certain rows and columns, and we would have erased in an exactly similar manner had we been forming the determinant associated with A2:8, since the deleting lines intersect rk in two pairs of points.

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  • In the latter case the sign is determined by -I raised to the same power as before, with the exception that Tux., replaces Tusk; but if one of these numbers be even the other must be uneven; hence A ik = - Ais� rk Moreover aik a,, aikarsAik +aisarkAis Aik, rk aik ars rs where the determinant factor is giyen by the four points in which the deleting lines intersect.

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  • Through any point in the field one such line can be drawn, but not more than one, for the force obviously cannot have more than one direction; the lines therefore never intersect.

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  • On the other hand, among the Africans of Punt the waistcloth passes from each knee to the opposite thigh, and two sashes hang down to conceal the parts where they intersect (Miller, r08).

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  • A tunnel differs from a drift in that it is driven across the strata to intersect the deposit.

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  • In 1754 Prome was besieged by the king of Pegu, who was again defeated by Alompra, and the war was transferred from the upper provinces to the mouths of the navigable rivers, and the numerous creeks and canals which intersect the lower country.

    0
    0
  • With variation of temperature, the surfaces of equal pressure and density need not coincide; but, taking the pressure, density and temperature as connected by some relation,such as the gas-equation, the surfaces of equal density and temperature must intersect in lines lying on a surface of equal pressure.

    0
    0
  • d o, dx dy dz dx dy dz so that, at any instant, the surfaces over which tk and m are constant intersect in the vortex lines.

    0
    0
  • Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.

    0
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  • The central zone includes Hejaz (or Hijaz), Nejd and El Hasa; much of it is a dry, stony or sandy steppe, with few wells or watering-places, and only occupied by nomad tribes; but the great wadis which intersect it contain many fertile stretches of alluvial soil, where cultivation is possible and which support a considerable settled population, with several large towns and numerous villages.

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  • Several important roads intersect the province; among them are - I.

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  • Two canals, the Oude and the Nieuwe Gracht, intersect the town from end to end.

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  • The best soils when abundantly irrigated yield from 50to 60-fold, and the water for this purpose is supplied by the innumerable streams which intersect the province.

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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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  • If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.

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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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  • wide, the principal thoroughfares, intersect.

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

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  • Deep gorges, through which tributaries of the Chorokh force their passage to the main river, intersect these highlands, forming most picturesque gorges.

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

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  • These equations show that the circles touch where they intersect the lines x 2 +y 2 = o, i.e.

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  • Consider the case of two circles, and in the first place suppose them to intersect in two real points A and B.

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  • The circles intersect in real or imaginary points according to the lower or upper sign of k 2, and the limiting points are real for the upper sign and imaginary for the lower sign.

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  • They intersect regularly at right angles, dividing the town into square blocks, like modern Mannheim or Turin, according to a Roman system usual in both Italy and the provinces: plainly they were laid out all at once, possibly by Agricola (Tac. Agr.

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  • Four small streams - the Sagarmati, Saraswati, Khari and Dai - also intersect the district.

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  • The state constitution adopted in 1802 followed the enabling act in accepting this line, but made the proviso that if it should not intersect Lake Erie east of the mouth of the Miami river, then the northern boundary should be a line from the southern end of Lake Michigan to the most northern cape of Maumee Bay and thence to the Territorial line, and to the Pennsylvania line.

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  • Electric tramways intersect the town, and are continued for 3 m.

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  • At its northern edge, where the waterless forest tract of the Bhabar ends, a series of springs burst from the surface, and these, increasing and uniting in their progress, form the numerous streams that intersect the Tarai.

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  • But in many parts deep transverse valleys intersect the prevailing direction of the ridges, and facilitate the passage of man, plants and animals, as well as of currents of air which mitigate the contrast that would otherwise be found between the climates of the opposite slopes.

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  • - and nearly all intersect at right angles; they are paved with brick and asphalt, and many in the residential quarters are shaded with fine elms and maples.

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  • At Sao Joao da Chapada, in Minas Geraes, diamonds occur in a clay interstratified with the itacolumite, and are accompanied by sharp crystals of rutile and haematite in the neighbourhood of decomposed quartz veins which intersect the itacolumite.

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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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  • It bears a strong resemblance to a Dutch town, for the houses are built in the style of those of Amsterdam, and the narrow channel separating it from its western suburb of Overzijde and the waters of the Waigat, which intersect it, recall the canals.

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  • Two of the principal thoroughfares, Federal and Ohio streets, intersect at a central square, in which are the city hall, public library, post office and the marketplace; and surrounding the main business section on the E., N.

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  • The existence of this route, which traverses the Darwaz mountains from east to west, cutting off the northern bend of the Oxus, and connecting those easterly routes which intersect the Pamirs by means of the Ghund and Shakhdara (and which concentrate about Lake Shiwa) with Kolab in eastern Bokhara, is important.

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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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  • Does one group include, or exclude, or intersect another with which it is compared ?

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  • - the city is divided into these four parts by North Capitol, East Capitol and South Capitol streets, which intersect at the Capitol.

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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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  • If funiculars be drawn for two positions 0,0 of the pole in the force-diagram, their corresponding sides will intersect on a straight line parallel to 00.

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  • The points where axes intersect the plane of section are called centres; the point where the line of contact intersects it, the poini of contact, or pitch-point; and the wheels are described as circular, elliptical, &c., according to the forms of their sections made by that plane.

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  • intersect, the velocity ratio of the Ci - - - - -

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  • To find the ratio of these velocities, produce C1T~, C2T, till they intersect in K; K is the instantaneous axis of the connecting rod, and the velocity ratio is ci :v2 ::KTi :KT2.

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  • intersect in the instantaneous centre.

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  • Again, imagin d fixed, then the instantaneous centre Obd of b with regard n d is found by producing the links c and a to intersect in Obd and the shapes of the centroids belonging respectively to thi links Ii and d can be found as before.

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  • A number of gold reefs intersect the surrounding district and in some of the reefs gold is mined.

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  • Naming the central ray passing through the entrance pupil the " axis of the pencil " or " principal ray," we can say: the rays of the pencil intersect, not in one point, but in two focal lines, which we can assume to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and FIG.

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  • This catenoid, however, is in stable equilibrium only when the portion considered is such that the tangents to the catenary at its extremities intersect before they reach the directrix.

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  • Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the directrix; for since any catenary with its directrix is a similar figure to any other catenary with its directrix, if the directrix of the one coincides with that of the other the centre of similitude must lie on the common directrix.

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  • Hence the tangents at A and B to the upper catenary must intersect above the directrix, and the tangents at A and B to the lower catenary must intersect below the directrix.

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  • The condition of stability of a catenoid is therefore that the tangents at the extremities of its generating catenary must intersect before they reach the directrix.

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  • A number of smaller streets intersect the Hauptstrasse at right angles and run down to the river,which is crossed by two fine bridges.

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  • Plucker finally (Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice.

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  • Lesser canals intersect the others radially, thus virtually dividing the city into a number of islands; whence it has been compared with Venice.

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  • The country which they thus enclose and intersect forms the delta of Bengal.

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  • The navigable streams which fall into the Ganges intersect the country in every direction and afford great facilities for internal communication.

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  • Steep and rugged ravines intersect the plains, opening into small bays or coves on the shore, fenced with masses of compact and cellular lava; and all over the island are found products of volcanic action.

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  • and S., intersect; from this point buildings on these two streets are numbered N., S., E.

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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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  • And we have then the theorem, two odd circuits intersect in an odd number of points; an odd and an even circuit, or two even circuits, in an even number of points.

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  • There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.

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  • taking P, P' as the corresponding points in an (a, a') correspondence on a curve of deficiency D, and supposing that when P is given the corresponding points P' are found as the intersections of the curve by a curve o containing the co-ordinates of P as parameters, and having with the given curve k intersections at the point P, then the number of united points is a = a+a' +2kD; and more generally, if the curve 0 intersect the given curve in a set of points P' each p times, a set of points Q' each q times, &c., in such manner that the points (P,P') the points (P, Q') &c., are pairs of points corresponding to each other according to distinct laws; then if (P, P') are points having an (a, a') correspondence with a number=a of united points, (P, Q') points having a (0,0') correspondence with a number =b of united points, and so on, the theorem is that we have p(a-a-a')+q(b-(3-(')+ ...

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  • A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

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  • The streets intersect at right angles, are from 60 to 120 ft.

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  • If we conceive a pole to each of these orbits, determined by the points in which lines perpendicular to their planes intersect the celestial sphere, the pole of the satellite orbit will revolve around the pole of the planetary orbit precisely as the pole of the earth does around the pole of the ecliptic, the inclination of the two orbits remaining unchanged.

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  • In the south, the Lee and the Blackwater intersect the mountains of Kerry and Cork flowing east, and turn abruptly into estuaries opening south.

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  • The railways, which are all owned and managed by the Hungarian state, intersect most parts of the country except the mountains south of Ogulin, where there is, nevertheless, a considerable traffic over the passes into Dalmatia and Bosnia.

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  • Let this arc on the reverse side to P intersect a line through 0 parallel to the major axis in a point H.

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  • Let JO intersect the major axis in 0 1.

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  • It has 12 pentagonal faces, and 30 edges, which intersect in fives to form 12 vertices.

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  • The great dodecahedron is determined by the intersections of the twelve planes which intersect the Platonic icosahedron in five of its edges; or each face has the same boundaries as the basal sides of five covertical faces of the icosahedron.

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  • It has 12 faces, which meet in 30 edges; these intersect in threes to form 20 vertices.

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  • Other less pronounced wrinkles run from southwest to north-east and intersect the former series at certain points, so that it is by alternate digressions from one to the other series that the irregular crest of the Pyrenees acquires its general direction.

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  • Good roads and byeways intersect it in every direction.

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  • Taramelli (Notizie degli Scavi, 1905, 41 seq.) rightly points out that the nucleus of the Roman municipium is probably represented by the present quarter of the Marina, in which the streets intersect at right angles and Roman remains are frequently found in the subsoil.

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  • An important property of confocal systems is that only two confocals can be drawn through a specified point, one being an ellipse, the other a hyperbola, and they intersect orthogonally.

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  • The first book deals with the generation of the three conics; the second with the asymptotes, axes and diameters; the third with various metrical relations between transversals, chords, tangents, asymptotes, &c.; the fourth with the theory of the pole and polar, including the harmonic division of a straight line, and with systems of two conics, which he shows to intersect in not more than four points; he also investigates conics having single and double contact.

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  • The principal rays, which on the object-side connect the object-points with the centre of the entrance pupil, intersect the axis on the image-side at the centre of rotation M of the eye.

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  • Through a suitable diaphragm in the back focal plane, banding can easily be produced in the image, which contains neither the vertical nor the horizontal lines of the two gratings, but there exist streaks, whose direction halves the angle under which the two gratings intersect (fig.

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  • The aberration of rays in which the outer rays intersect the axis at a shorter distance than the central rays is known as " undercorrection."

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  • The second aberration which must be removed from microscope objectives are the chromatic. To diminish these a collective lens of crown-glass is combined with a dispersing lens of flint; in such a system the red and the blue rays intersect at a point (see Aberration).

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  • A cross-table is very convenient for this calculation, for with the aid of the two movable slides situated in the plane of the plate and at right angles to one another, the point where the two crystal edges intersect can be quickly and correctly brought into the revolving axis of the plate.

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  • Where Lines MO and NO intersect this semicircle read and values along the short curves on the scale of the inner semicircle.

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  • Simple algebraic operations are then used to intersect two spheres, or a line and a sphere.

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  • Then, simply place the most important parts of your subject where the lines intersect.

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  • It requires dividing the viewfinder into nine equal parts and placing the most noteworthy parts of your subject where the lines intersect to create a more interesting composition.

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  • A high cross is a particular type of cross that is decorated with celtic knots or symbols and has a circle around the point where the two arms of the cross intersect.

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  • As you can see from this handful of shops, there are a lot of different definitions of what counts as sustainable that may not intersect with your ideas about organic products.

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  • As soon as your crosshairs intersect it, your gun will lock on to it.

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  • Then perpendicular lines are projected from these lines and the angle at which the lines intersect is measured.

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  • Fold the bottom corner up to reach the center point (where the two diagonal creases intersect).

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  • By following across and down to where the month and age intersect, the mother will find either a box containing a B for boy or a G for girl.

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  • Since all of the cable car lines intersect in front of the hotel, The Fairmont is also just a ride away from the city's most popular attractions.

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  • LoveToKnow Swimsuits was lucky enough to talk to CEO Houman Salem about swimwear, lingerie, lifestyles and how they all intersect at Forplay.

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  • Sauvage Swimwear is all about fashion, glamour, and how the two intersect at the beach.

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  • A cross is, quite simply, a pair of lines that intersect each other at a 90º angle.

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  • The basic shape, however, is a Latin cross, or crucifix, with a circle around the area where the lines intersect.

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  • When Apple announced the iPod nano 6G, I took one look at it and knew that this was where the two worlds I love can intersect."

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  • The cone marking the top of the vertical line should intersect the horizontal line at its center.

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  • The paths of Marcus, Selene, and Michael intersect when Marcus discovers Michael holds the key to William's tomb and Selene is the only remaining being who knows the whereabouts of the imprisoned werewolf.

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  • A twist on this trope is found in the NBC television series Chuck where the main character becomes the human computer known as Intersect, and must struggle against the Intersect’s ability to overwhelm his mind.

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