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intersection

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

65057Surmounting all, at the intersection of the arches is a cross.

13782He neared the intersection where the road branched to her house and his.

7856It 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.

6666She paused at the intersection with another narrow alley, not liking the smelly alleys at all.

5938We caught two intersection videos of the van traveling in the direction of route 154.

4426having 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.

2618the line of intersection forming a descending gutter which runs to the outlet.

2212Jenn chose a direction and paused at the first intersection to listen for anyone approaching.

2021high, has double vaulted aisles and the transepts single aisles; and at the intersection of nave and transepts there is a cupola.

1818to the perpendicular distance from the line of intersection of the plane of the area with the free surface of the liquid.

1613From its intersection with A'A' arcs are struck cutting B in two points.

1510Adjoining 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.

1510The 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.

1512Brady reached the intersection and saw the tunnel running perpendicular opened into a crowded underground city.

1515Just west of the intersection, he pulled up to Cimarron Books, a small combination bookstore and coffee shop.

1410It is at the intersection of two branches of the Boston & Maine railway, and is served by several interurban electric lines.

1410He slowed as he reached an intersection and made his way through the town to the outskirts, where small houses lined the street.

1414She paused at an intersection to let a group of Immortals through, uninterested in talking to anyone just now.

1414to 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.

137to 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.

137Situated 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.

1310Hannah stopped at an intersection, and Katie took her hand again, continuing down the hall toward the second stairwell.

1317The 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.

125The 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.

1210The 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.

1211sphere 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."

1211She glanced at the signs at the nearest intersection indicating the direction of the major department stores and the food court.

1219The ordinates of this new briquette at the points of intersection of x =x 0, x = xi,.

1267Fermat 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.

118It 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.

1010A.) 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.

1012As 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.

1056There 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.

95This 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.

85The fish is also said to be represented in the oval-shaped figure, pointed at both ends, and formed by the intersection of two circles.

87wide, 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.

88QUATREFOIL, 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.

88from 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.

88(12) The Mausolea of Alexander (Soma) and the Ptolemies in one ring-fence, near the point of intersection of the two main streets.

88Then the locus of the intersection of PQ and OM is the quadratrix of Dinostratus.

88In the west the frontier is as follows: From the point of intersection of 1 ° S.

88Its 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.

88the 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.

88Its 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.

88Thus 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.

77It was practically certain that by following up this pavement to its point of intersection with the road from Sicyon the agora would be discovered.

77If the plane does not contain the centre, the curve of intersection is a "small circle," and the solid cut off is a "segment."

77Two 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.

77Thus 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.

77If the plane does not contain the centre, the curve of intersection is a "small circle," and the solid cut off is a "segment."

77Two 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.

65The 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.

65Just as he neared the intersection, Dean recognized Corday and Fitzgerald driving toward Ouray.

613Just as he neared the intersection, Dean recognized Corday and Fitzgerald driving toward Ouray.

613The principal building is the state capitol (completed in 1857) in a square of ten acres at the intersection of High and Broad streets.

54In 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."

54In 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.

55By 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.

59Newton 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.

213The light was green and she accelerated across the intersection.

00How I love the open country, away from city police and cameras at every intersection.

00They made it several doors before three of Romas's clan charged around the corner of a nearby intersection.

00For 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.

00in 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."

00determined by the intersection of the two lines, one beginning at A, and the other at E.

00This 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.

00It 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.

00A 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.

00Obviously 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.

0036 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.

00A 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.

00In the case of a coaxal system having real points of intersection the limiting points are imaginary.

00A coaxal system having real points of intersection has imaginary limiting points; 3.

00A coaxal system having imaginary points of intersection has real limiting points; 4.

00For 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.

00De 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.

00Its 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.

00There 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.

00Other 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.

00The 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.

00Section through Intersection.

00Leonhard 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.

00The 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.

00The 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.

00coast of Africa at the intersection of 32° N.

00of the Ezbekia is the Place Atabeh, the chief point of intersection of the electric tramways which serve the newer parts of the town.

00In 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.

00A 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.

00The 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.

00arranged, 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.

00They 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.

00These branches are now below the point of intersection, part of the lower Ganges canal system.

00Similarly, 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.

00quarter (especially the four at the intersection of its two main streets), which was added by Ercole (Hercules) I.

00of Des Moines, at the intersection of two lines of the Chicago & North-Western railway.

00Since the sun moves in the ecliptic, it is in the last-named sense the point of intersection of the ecliptic and the celestial equator.

00At 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.

00At the intersection of a street with an avenue there is usually the reservation of a small triangular grass plot at least.

00Instead 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.

00The 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.

00If, 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.

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

00If R be the intersection of these sides, FIG.

00We 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.

00Successive 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.

00But 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.

00Thus, 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.

00the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.

00Again, 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.

00The 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.

0052, 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.

00If 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.

00It 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.

00Considering, 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.

0092), 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.

00That 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).

0097 and g8).Let 0 be the apex orpoint of intersection of the two axes OC1, 0C2.

00The 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.

00Let 0 be the point of intersection of the axes OCf, 0C2,

00moves 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.

00Julesburg, 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.

00on 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.

00Among 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.

00The tower, at the intersection of the nave and transepts, is of unusually massive proportions, being 30 ft.

00of Berlin by the main railway to Gorlitz, and at the intersection of the lines Halle-Sagan and GrossenhainFrankfort-on-Oder.

00In 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).

00The 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.

00there are " chromatic differences " of the distances of intersection, of magnifications, and of monochromatic aberrations.

00The church itself was a cruciform structure with a choir, nave and transepts, and a tower surmounting the centre of intersection.

00north of Fort Olimpo and run south-west in a straight line to an intersection with the Pilcomayo in long.

00Thence it continues north to an intersection with the Desaguadero, in about 16° 45' S.

00Hence T, the point of intersection of Pp and Qq, must be the centre of similitude and must be on the common directrix.

00long., at the junction of the navigable river Mukhovets with the Bug, and at the intersection of railways from Warsaw, Kiev, Moscow and East Prussia.

00van 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.

003) 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.

00The 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.

00In 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.

00We 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.

00In 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.

00On an elevated site at the Intersection of Washington Place - a continuation of N.

00As 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.

00of New York city by rail, and at the intersection of the boundary lines of the states of New York, New Jersey and Pennsylvania.

00Dallin, was unveiled in 1897, at the intersection of Main and Brigham Streets.

00the 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).

00The 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.

00It 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.

00this projection is the intersection of the given plane with the plane through the centre and the given line.

00Say 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.

001 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.

00Consider 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.

00The 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.

00Mag., 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.

00To 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.

00Many 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.

00And we thus see that the two hyperbolic legs belong to a simple intersection of the curve by the line infinity.

00We 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.

00To 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.

00It 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.

008, 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.

00Hardy, 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.

00of the latter, about the intersection of 7° E.

00It is a peak of the Himalayas situated in Nepal almost precisely on the intersection of the meridian 87 E.

00the radius which passes through the intersection of 115° E.

00It 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.

00Draw 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.

00Let 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.

00(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.

00Then the intersection of EB and DB' determines a point P on the (true) curve.

00In 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.

00If 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.

00M is therefore the intersection of the principal rays.

00In 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.

00The intersection of the principal rays in this case lies in the middle of the entrance pupil or of the exit pupil.

00The 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.

00the 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).

00The point of intersection, i.e.

00In 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.

00The light was green and she accelerated across the intersection.

00How I love the open country, away from city police and cameras at every intersection.

00We strolled back to my stolen car and drove away, taking back street to avoid intersection cameras.

00We caught two intersection videos of the van traveling in the direction of route 154.

00He slowed as he reached an intersection and made his way through the town to the outskirts, where small houses lined the street.

00The shockwaves faded, and she stood in the middle of an intersection, stretching out with her Guardian senses to find some kind of life.

00She glanced at the signs at the nearest intersection indicating the direction of the major department stores and the food court.

00By 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.

00The 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.

00She paused at the intersection with another narrow alley, not liking the smelly alleys at all.

00She paused at an intersection to let a group of Immortals through, uninterested in talking to anyone just now.

00Hannah stopped at an intersection, and Katie took her hand again, continuing down the hall toward the second stairwell.

00They made it several doors before three of Romas's clan charged around the corner of a nearby intersection.

00Just west of the intersection, he pulled up to Cimarron Books, a small combination bookstore and coffee shop.

00Brady reached the intersection and saw the tunnel running perpendicular opened into a crowded underground city.

00He neared the intersection where the road branched to her house and his.

00Jenn chose a direction and paused at the first intersection to listen for anyone approaching.

00compute the intersection of two arrays?

00conical intersection, many unusual quantum effects take place.

00intersection of three planes.

00intersection of gender, technology and media in Asia.

00intersection of a row and a column is called a cell.

00intersection of the celestial circles with the circle of the Horizon at the equinox.

00intersection of advertising, marketing and product design, with particular applicability to fast-moving consumer goods.

00How do I compute the intersection of two arrays?

00When she reached an intersection she turned away from the flight path of the UFO and toward Dayton where the three of them lived.

00God forbid we should hamper a car from crossing an intersection!

00A countable intersection of open dense sets is the intersection of a countable number of open dense sets.

00In the vicinity of a conical intersection, many unusual quantum effects take place.

00She had been brought in last night by a man who found her in a busy intersection.

00At the major intersection with The Avenue, continue straight on along Burgess Road.

00Now I'm walking on the wasteland of a motorway intersection.

00From the exit of Sewers West, go straight until you get to a T intersection.

00Eight of the holes drilled on Oleninskoye intersected pegmatite within the area where the vein intersection was anticipated.

00The new raster should be the intersection of the two input rasters.

00roundabouts at a major intersection.

00The vortex patterns correspond to the intersection of the laser sheet with the trailing, helical vortices from the turbine blades.

00If 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.

00The 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.

00At 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.

00To 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.

00Now 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.

00Fermat 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.

00A.) 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.

00The 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.

00Two 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.

00The principal building is the state capitol (completed in 1857) in a square of ten acres at the intersection of High and Broad streets.

00The 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.

00In 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."

00the line of intersection forming a descending gutter which runs to the outlet.

00It then followed this line of longitude to its intersection with N.

00From its intersection with A'A' arcs are struck cutting B in two points.

00The fish is also said to be represented in the oval-shaped figure, pointed at both ends, and formed by the intersection of two circles.

00wide, 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.

00QUATREFOIL, 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.

00Surmounting all, at the intersection of the arches is a cross.

00From 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.

00from 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.

00In 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.

00(12) The Mausolea of Alexander (Soma) and the Ptolemies in one ring-fence, near the point of intersection of the two main streets.

00There 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.

00It is at the intersection of two branches of the Boston & Maine railway, and is served by several interurban electric lines.

00The provisional line, representing the Brazilian claim, begins at the termination of the Bolivian section (the intersection of the 11th parallel with the meridian of 72Ã‚° 26' W.

00The Colombian claim included the left bank of the Amazon eastward to the Auahy or Avahy-parana channel between the Amazon and Yapura, whence the line ran northward to the Negro near the intersection of the 66th meridian.

00Adjoining 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.

00For 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.

00to the perpendicular distance from the line of intersection of the plane of the area with the free surface of the liquid.

00This 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.

00having 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.

00Situated 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.

00From every point of the curve of intersection, perpendiculars are drawn to the axis.

00Then the locus of the intersection of PQ and OM is the quadratrix of Dinostratus.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.