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vertex

vertex

vertex Sentence Examples

  • My cousin built his house on the vertex of the highest hill in the county.

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  • The vertex of my roof needs some serious repair.

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  • It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

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  • It may be noticed that if the scales of x and be properly adjusted, the curve of positions in the present problem is the portion of a cycloid extending from a vertex to a cusp.

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  • It may be noticed that if the scales of x and be properly adjusted, the curve of positions in the present problem is the portion of a cycloid extending from a vertex to a cusp.

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  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

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  • The vertex of the Washington Monument is made of aluminum, an extremely expensive material at the time of its construction.

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  • The [ox's] horns are of nearly equal size in both sexes, are placed on or near the vertex of the skull, and may be either rounded or angulated, while their direction is more or less outwards, with an upward direction near the tips, and conspicuous knobs or ridges are never developed on their surface.

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  • Each vertex is singly enclosed by the five faces; the centre of each face is doubly enclosed by the succession of faces about the face; and the centre of the solid is doubly enclosed by the faces.

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  • Each vertex is singly enclosed by the five faces; the centre of each face is doubly enclosed by the succession of faces about the face; and the centre of the solid is doubly enclosed by the faces.

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  • To comprehend more exactly the discovery of Apollonius, imagine an oblique cone on a circular base, of which the line joining the vertex to the centre of the base is the axis.

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  • To comprehend more exactly the discovery of Apollonius, imagine an oblique cone on a circular base, of which the line joining the vertex to the centre of the base is the axis.

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  • The cube may have originated by placing three equal squares at a common vertex, so as to form a trihedral angle.

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  • Each vertex is singly enclosed by the succession of faces about it; and the centre of the solid is quadruply enclosed by the faces.

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  • If three equilateral triangles be placed at a common vertex with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

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  • If three equilateral triangles be placed at a common vertex with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

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  • With a vertex much more distant the desired effect would be impaired, and with one nearer neither of the poles would be seen, whilst the exaggeration of China would have been too gross for a professed representation of the hemisphere.

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  • With a vertex much more distant the desired effect would be impaired, and with one nearer neither of the poles would be seen, whilst the exaggeration of China would have been too gross for a professed representation of the hemisphere.

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  • Each vertex is doubly enclosed by the succession of covertical faces, while the centre of the solid is triply enclosed by the faces.

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  • "Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.

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  • Above is the crown (vertex or epicranium), on which or on the " front " may be seated three simple eyes (ocelli).

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  • Most insects possess a pair of compound eyes, and many have, in addition, three simple eyes or ocelli on the vertex.

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  • or " vertex," the compound eyes and the front divisions of the genae are formed by the cephalic lobes of the embryo (belonging membrane analogous to the amnion of higher Vertebrates andto the ocular segment), while the mandibular and maxillary segments known by the same term.

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  • 23 should have a common vertex in the middle of the neck with a semi-vertical angle of 54° 44', while the condition for a uniform field is satisfied when the cones have a semivertical angle of 39° 14'; in the latter case the magnetic force in the air just outside is sensibly equal to that within the neck.

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  • It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays.

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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

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  • x The involute of the catenary is called the tractory, tractrix or antifriction curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix.

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  • Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.

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  • - If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.

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  • - A, Front of head of Sawfly (Pachynematus); a, labrum; b, clypeus; c, vertex; d, d, antennal cavities.

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  • The head of a hymenopterous insect bears three simple eyes (ocelli) on the front and vertex in addition to the large compound FIG.

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  • Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.

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  • Another method of verifying the formula is to take a point Q in the mid-section, and divide up the prismoid into two pyramids with vertex Q and bases ABCD ...

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  • respectively, and a series of tetrahedra having Q as one vertex.

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  • In the case of a pyramid, of height h, the area of the section by a plane parallel to the base and at distance x from the vertex is clearly x 2 /h 2 X area of base.

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  • As the load travels, the shear at the head of the train will be given by the ordinates of a parabola having its vertex at A, and a maximum F max.

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  • Remembering that in this case the centre bending moment Ewl will be equal to wL 2 /8, we see that the horizontal tension H at the vertex for a span L (the points of support being at equal heights) is given by the expression 1..

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  • H = wL2/8y, or, calling x the distance from the vertex to the point of support, H = wx2/2y.

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  • 70, at a distance x from the vertex, the horizontal component of the resultant (tangent to the curve) will be unaltered; the vertical component V will be simply the sum of the loads between 0 and F, or wx.

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  • The value of R, the tension at any point at a distance x from the vertex, is obtained from the equation R 2 = H2 +V2 = w2x4 /4Y 2 +w2x2, or, 2.

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  • R=wx (I+x2/4Y2) Let i be the angle between the tangent at any point having the co-ordinates x and y measured from the vertex, then 3..

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  • At the vertex A, where y =H, we have t = t' =1-T, so that (33) H = sgT2, which for practical purposes, taking g= 32, is replaced by (34) H = 4T 2, or (2T)2.

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  • To share the S between and 0, the vertex A is taken as the point of half-time (and therefore beyond half-range, because of the continual diminution of the velocity), and the velocity vo at A is calculated from the formula (38) T(vo) = T(V) - = z {T(V) -T (v)}; and now the degree table for D(v) gives (39) 4=C{D(V)-D(v0)}, =CID (vo) -D(v)}.

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  • Largest of all is Sivatherium, typically from the Lower Pliocene of Northern India, but also recorded from Adrianople, in which the skull of the male is short and wide, with a pair of simple conical horns above the eye, and a huge branching pair at the vertex.

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  • The line CD passing through the focus and perpendicular to the directrix is the axis or principal diameter, and meets the curve in the vertex G.

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  • parallel to the tangent at the vertex of the diameter and is equal P A B to four times the focal distance of the vertex.

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  • The simplest equation to the parabola is that which is referred to its axis and the tangent at the vertex as the axes of co-ordinates, when it assumes the form y 2 = 4ax where as = semilatus rectum; this may be deduced directly from the definition.

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  • An equation of similar form is obtained when the axes of co-ordinates are any diameter and the tangent at the vertex.

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  • The pedal equation with the focus as origin is p 2 =ar; the first positive pedal for the vertex is the cissoid and for the focus the directrix.

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  • The funicular or link polygon has its vertices on the lines of action of the given forces, and its sides respectively parallel to the lines drawn from 0 in the force-diagram; in particular, the two sides meeting in any vertex are respectively parallel to the lines drawn from 0 to the ends of that side of the force-polygon which represents the corresponding force.

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  • The two diagrams being supposed constructed, it is seen that each of the given systems of forces can be replaced by two components acting in the sides of the funicular which meet at the corresponding vertex, and that the magnitudes of these components will be given by the corresponding triangle of forces in the force-diagram; thus the force 1 in the figure is equivalent to two forces represented by 01 and 12.

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  • In a similar manner, for systems used in photography, the vertex of the colour curve must be placed in the position of the maximum sensibility of the plates; G'; and to accomplish this the F and violet mercury lines are united.

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  • i I); the internal pressure is equal to the external pressure, and the tension along the axis is equal to 27rTm where m is the distance of the vertex from the focus.

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  • The b co-ordinates of any point R on the a ?/' t11®V1 a cycloid are expressible in the form x=a(8-}-sin 0); y=a (I -cos 0), M where the co-ordinate axes are the tangent at the vertex 0 and the axis of the curve, a is the radius of the generating circle, and 0 the angle R'CO, where RR' is parallel to LM and C is the centre of the circle in its symmetric position.

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  • When measured R from the vertex the results may be expressed in the forms s= 4a sin 20 and s = (8ay); the total length of the curve is 8a.

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  • In the first place, it is out of of the question to allow the water to rise to the vertex a Factors .

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  • Stated in regard to the cone, we have there the fundamental theorem that there are two different kinds of sheets; viz., the single sheet, not separated into two parts by the vertex (an instance is afforded by the plane considered as a cone of the first order generated by the motion of a line about a point), and the double or twin-pair sheet, separated into two parts by the vertex (as in the cone of the second order).

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  • It may be mentioned that the single sheet is a sort of wavy form, having upon it three lines of inflection, and which is met by any plane through the vertex in one or in three lines; the twin-pair sheet has no lines of inflection, and resembles in its form a cone on an oval base.

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  • Thus the general curve of three bar-motion (or locus of the vertex of a triangle, the other two vertices whereof move on fixed circles) is a tricircular sextic, having besides three nodes (m = 6, 6 = 3+3+3, = 9), and having the centres of the fixed circles each for a singular focus; there is a third singular focus, and we have thus the remarkable theorem (due to S.

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  • The cissoid is the first positive pedal of the parabola y2+8ax=o for the vertex, and the inverse of the parabola y 2 = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion.

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  • The following table gives these constants for the regular polyhedra; n denotes the number of sides to a face, n 1 the number of faces to a vertex: - Archimedean Solids.

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  • (By the truncation of a vertex or edge we mean the cutting away of the vertex or edge by a plane making equal angles with all the faces composing the vertex or with the two faces forming the edge.) It is bounded by 4 triangular and 4 hexagonal faces; there are 18 edges, and 12 vertices, at each of which two hexagons and one triangle are covertical.

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  • Ann., 119, p. 406) as a semi-circle, but it is really a parabola with its axis parallel to the axis of E, and its vertex at the point t= -b/2c, which gives the neutral temperature.

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  • He discriminated the three species of conics as follows: - At one of the two vertices erect a perpendicular (talus rectum) of a certain length (which is determined below), and join the extremity of this line to the other vertex.

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  • Then the square of the ordinate intercepted between the diameter and the curve is equal to the rectangle contained by the portion of the diameter between the first vertex and the foot of the ordinate, and the segment of the ordinate intercepted between the diameter and the line joining the extremity of the latus rectum to the second vertex.

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  • The conics are distinguished by the ratio between the latus rectum (which was originally called the latus erectum, and now often referred to as the parameter) and the segment of the ordinate intercepted between the diameter and the line joining the second vertex with the extremity of the latus rectum.

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  • In modern notation, if we denote the ordinate by y, the distance of the foot of the ordinate from the vertex (the abscissa) by x, and the latus rectum by p, these relations may be expressed as 31 2 for the hyperbola.

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

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  • For shaded polygons, the color keyword can specify an array that contains the color index at each vertex.

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  • boron hydrides is the twelve vertex B 12 H 12 2- anion that displays perfect icosahedral geometry.

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  • METHODS: This prospective cohort study included 275 women in labor with live, singleton fetuses at term in vertex presentations.

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  • For an undirected graph, the number of edges incident to a vertex is its degree.

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  • Abstract In 1977, Appel and Haken proved that every planar graph is four vertex colourable.

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  • The upper limit for the binary boron hydrides is the twelve vertex B 12 H 12 2- anion that displays perfect icosahedral geometry.

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  • This category includes the 13-atom icosahedron, which can be decomposed into twenty tetrahedra sharing a common vertex.

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  • Structure 69C has a vertex atom missing from the underlying Mackay icosahedron like 38A.

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  • Note: It's not possible to change drawing attributes (color, ...) in the middle of a vertex pipeline in Ygl.

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  • pixel pipelines and 2 vertex units, apart from their clock speeds.

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  • The other vertex stars use different arrangements of the thick and thin rhombs.

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  • An inflation force is used at each vertex to inflate the overall model, while surface tension attempts to keep the mesh spherical.

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  • There is no vertex for the trivial subgroup (yet ).

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  • These came slightly undersized compared to the Vertex, apart from that they were identical.

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  • undirected graph, the number of edges incident to a vertex is its degree.

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  • vertex of the polygon.

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  • If this entry is not available you have failed to select vertex G.

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  • find the neighboring vertex with the largest number of incident edges.

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  • If it returns fail the new vertex or edge is not generated!

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  • Merge Classes This menu entry merges all classes within each level that contain a selected vertex.

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  • I am not asking you to take a psychiatric vertex at this point - it is too early.

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  • You need this option if you have moved a vertex without its class (holding down the SHIFT key ).

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  • The user is prompted for every selected vertex, which label it should have.

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  • Tracks are now coming from the same primary vertex.

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  • To achieve smooth results, any triangles which share a common vertex should have the same normal vector at that vertex.

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  • These events are represented by a single vertex in a Feynman diagram.

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  • You will get a new vertex 12 for an index 24 subgroup.

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  • By way of example, how to draw a triangle: DRAW MOVE to first vertex.

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  • vertex shaders, 3D maths.

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  • vertex shader information directly to the memory, allowing faster access time.

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  • vertex pipeline in Ygl.

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  • vertex detector is the Central Outer Tracker, a gas drift chamber which operates via the detection of charged ions.

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  • vertex v 1.

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  • vertex manipulation can be applied!

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  • For charged decays the detector is capable of reconstructing the position of the decay vertex.

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  • vertices of the icosahedron is 5% longer than the distance between a vertex and the center.

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  • "Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.

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  • These two lines may be pictured in the in solido definition as the section of a cone by a plane through its vertex and parallel to the plane generating the hyperbola.

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  • Above is the crown (vertex or epicranium), on which or on the " front " may be seated three simple eyes (ocelli).

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  • A, Front; B, side; C, back; v, vertex; f, frons; cl, clypeus; lbr, labrum; oc, compound eye; ge, gena; mn, mandible; ca, st, pa, ga, la, cardo, stipes, palp, galea, lacinia of first maxilla; sm, m, pa', pg, submentum, mentum, palp, galea of 2nd maxilla.

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  • Most insects possess a pair of compound eyes, and many have, in addition, three simple eyes or ocelli on the vertex.

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  • or " vertex," the compound eyes and the front divisions of the genae are formed by the cephalic lobes of the embryo (belonging membrane analogous to the amnion of higher Vertebrates andto the ocular segment), while the mandibular and maxillary segments known by the same term.

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  • 23 should have a common vertex in the middle of the neck with a semi-vertical angle of 54° 44', while the condition for a uniform field is satisfied when the cones have a semivertical angle of 39° 14'; in the latter case the magnetic force in the air just outside is sensibly equal to that within the neck.

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  • It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays.

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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

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  • x The involute of the catenary is called the tractory, tractrix or antifriction curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix.

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  • Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.

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  • The horns are of nearly equal size in both sexes, are placed on or near the vertex of the skull, and may be either rounded or angulated, while their direction is more or less outwards, with an upward direction near the tips, and conspicuous knobs or ridges are never developed on their surface.

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  • - If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.

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  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

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  • - A, Front of head of Sawfly (Pachynematus); a, labrum; b, clypeus; c, vertex; d, d, antennal cavities.

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  • The head of a hymenopterous insect bears three simple eyes (ocelli) on the front and vertex in addition to the large compound FIG.

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  • Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.

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  • Another method of verifying the formula is to take a point Q in the mid-section, and divide up the prismoid into two pyramids with vertex Q and bases ABCD ...

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  • respectively, and a series of tetrahedra having Q as one vertex.

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  • In the case of a pyramid, of height h, the area of the section by a plane parallel to the base and at distance x from the vertex is clearly x 2 /h 2 X area of base.

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  • A "spherical sector" and "spherical cone" may be also regarded as the solids of revolution of a circular sector about one of its bounding radii, and about any other line through the vertex respectively.

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  • He showed that the surface of a segment is equal to the area of the circle whose radius equals the distance from the vertex to the base of the segment; that the surface of the entire sphere is equal to the curved surface of the circumscribing cylinder, and to four times the area of a great circle of the sphere; and that the volume is twothirds that of the circumscribing cylinder.

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  • As the load travels, the shear at the head of the train will be given by the ordinates of a parabola having its vertex at A, and a maximum F max.

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  • Remembering that in this case the centre bending moment Ewl will be equal to wL 2 /8, we see that the horizontal tension H at the vertex for a span L (the points of support being at equal heights) is given by the expression 1..

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  • H = wL2/8y, or, calling x the distance from the vertex to the point of support, H = wx2/2y.

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  • 70, at a distance x from the vertex, the horizontal component of the resultant (tangent to the curve) will be unaltered; the vertical component V will be simply the sum of the loads between 0 and F, or wx.

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  • The value of R, the tension at any point at a distance x from the vertex, is obtained from the equation R 2 = H2 +V2 = w2x4 /4Y 2 +w2x2, or, 2.

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  • R=wx (I+x2/4Y2) Let i be the angle between the tangent at any point having the co-ordinates x and y measured from the vertex, then 3..

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  • I), where the trajectory cuts the line of sight; so that IT is the time to the vertex A, where the shot is flying parallel to OB.

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  • At the vertex A, where y =H, we have t = t' =1-T, so that (33) H = sgT2, which for practical purposes, taking g= 32, is replaced by (34) H = 4T 2, or (2T)2.

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  • Thus, if the time of flight of a shell is 5 sec., the height of the vertex of the trajectory is about loo ft.; and if the fuse is set to burst the shell one-tenth of a second short of its impact at B, the height of the burst is 7.84, say 8 ft.

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  • To share the S between and 0, the vertex A is taken as the point of half-time (and therefore beyond half-range, because of the continual diminution of the velocity), and the velocity vo at A is calculated from the formula (38) T(vo) = T(V) - = z {T(V) -T (v)}; and now the degree table for D(v) gives (39) 4=C{D(V)-D(v0)}, =CID (vo) -D(v)}.

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  • Ingalls, U.S.A., for approximating to a high angle trajectory in a single arc, which assumes that the mean density of the air may be taken as the density at two-thirds of the estimated height of the vertex; the rule is founded on the fact that in an unresisted parabolic trajectory the average height of the shot is two-thirds the height of the vertex, as illustrated in a jet of water, or in a stream of bullets from a Maxim gun.

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  • Institution, 1888, employing Siacci's method and about twenty arcs; and Captain Ingalls, by assuming a mean tenuity-factor T=0.68, corresponding to a height of about 2 m., on the estimate that the shot would reach a height of 3 m., was able to obtain a very accurate result, working in two arcs over the whole trajectory, up to the vertex and down again (Ingalls, Handbook of Ballistic Problems).

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  • It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

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  • Largest of all is Sivatherium, typically from the Lower Pliocene of Northern India, but also recorded from Adrianople, in which the skull of the male is short and wide, with a pair of simple conical horns above the eye, and a huge branching pair at the vertex.

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  • The line CD passing through the focus and perpendicular to the directrix is the axis or principal diameter, and meets the curve in the vertex G.

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  • parallel to the tangent at the vertex of the diameter and is equal P A B to four times the focal distance of the vertex.

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  • To construct the parabola when the focus and directrix are given, draw the axis CD and bisect CF at G, which gives the vertex.

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  • The simplest equation to the parabola is that which is referred to its axis and the tangent at the vertex as the axes of co-ordinates, when it assumes the form y 2 = 4ax where as = semilatus rectum; this may be deduced directly from the definition.

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  • An equation of similar form is obtained when the axes of co-ordinates are any diameter and the tangent at the vertex.

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  • The pedal equation with the focus as origin is p 2 =ar; the first positive pedal for the vertex is the cissoid and for the focus the directrix.

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  • the second form; if above the vertex and oblique or parallel to the axis, the third form; if below the vertex and touching the surface, the fourth form, and if the plane contains the axis, the fifth form results (see Curve).

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  • The funicular or link polygon has its vertices on the lines of action of the given forces, and its sides respectively parallel to the lines drawn from 0 in the force-diagram; in particular, the two sides meeting in any vertex are respectively parallel to the lines drawn from 0 to the ends of that side of the force-polygon which represents the corresponding force.

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  • The two diagrams being supposed constructed, it is seen that each of the given systems of forces can be replaced by two components acting in the sides of the funicular which meet at the corresponding vertex, and that the magnitudes of these components will be given by the corresponding triangle of forces in the force-diagram; thus the force 1 in the figure is equivalent to two forces represented by 01 and 12.

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  • In a similar manner, for systems used in photography, the vertex of the colour curve must be placed in the position of the maximum sensibility of the plates; G'; and to accomplish this the F and violet mercury lines are united.

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  • i I); the internal pressure is equal to the external pressure, and the tension along the axis is equal to 27rTm where m is the distance of the vertex from the focus.

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  • The b co-ordinates of any point R on the a ?/' t11®V1 a cycloid are expressible in the form x=a(8-}-sin 0); y=a (I -cos 0), M where the co-ordinate axes are the tangent at the vertex 0 and the axis of the curve, a is the radius of the generating circle, and 0 the angle R'CO, where RR' is parallel to LM and C is the centre of the circle in its symmetric position.

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  • When measured R from the vertex the results may be expressed in the forms s= 4a sin 20 and s = (8ay); the total length of the curve is 8a.

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  • In the first place, it is out of of the question to allow the water to rise to the vertex a Factors .

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  • Stated in regard to the cone, we have there the fundamental theorem that there are two different kinds of sheets; viz., the single sheet, not separated into two parts by the vertex (an instance is afforded by the plane considered as a cone of the first order generated by the motion of a line about a point), and the double or twin-pair sheet, separated into two parts by the vertex (as in the cone of the second order).

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  • It may be mentioned that the single sheet is a sort of wavy form, having upon it three lines of inflection, and which is met by any plane through the vertex in one or in three lines; the twin-pair sheet has no lines of inflection, and resembles in its form a cone on an oval base.

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  • Thus the general curve of three bar-motion (or locus of the vertex of a triangle, the other two vertices whereof move on fixed circles) is a tricircular sextic, having besides three nodes (m = 6, 6 = 3+3+3, = 9), and having the centres of the fixed circles each for a singular focus; there is a third singular focus, and we have thus the remarkable theorem (due to S.

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  • In the typical oxen, as represented by the existing domesticated breeds (see Cattle) and the extinct aurochs, the horns are cylindrical and placed on an elevated crest at the very vertex of the skull, which has the frontal region of great length.

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  • More distinct are the bisons, forming the sub-genus Bison, represented by the European and the American species (see Bison), the forehead of the skull being much shorter and wider, and the horns not arising from a crest on the extreme vertex, while the number of ribs is different (14 pairs in bisons, only 13 in oxen), and the hair on the head and neck is long and shaggy.

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  • The cissoid is the first positive pedal of the parabola y2+8ax=o for the vertex, and the inverse of the parabola y 2 = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion.

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  • The cube may have originated by placing three equal squares at a common vertex, so as to form a trihedral angle.

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  • Three pentagons may be placed at a common vertex to form a solid angle, and by forming several such sets and placing them in juxtaposition .a solid is obtained having 12 pentagonal faces, 30 edges, and 20 vertices.

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  • If F be the number of faces, n the number of edges per face, m the number of faces per vertex, and l the length of an edge, and if we denote the angle between two adjacent faces by I, the area by A, the volume by V, the radius of the circum-sphere by R, and of the in-sphere by r, the following general formulae hold, a being written for 21r/n, and a for 27r/m:- Sin z I =cos 1 3/sin a; tan II =cos l3/ (sin'- a -cos t R) 2.

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  • Each vertex is doubly enclosed by the succession of covertical faces, while the centre of the solid is triply enclosed by the faces.

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  • Each vertex is singly enclosed by the succession of faces about it; and the centre of the solid is quadruply enclosed by the faces.

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  • Poinsot gave the formula E 2k = eV + F, in which k is the number of times the projections of the faces from the centre on to the surface of the circumscribing sphere make up the spherical surface, the area of a stellated face being reckoned once, and e is the ratio " angles at a vertex /21r" as projected on the sphere, E, V, F being the same as before.

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  • The following table gives these constants for the regular polyhedra; n denotes the number of sides to a face, n 1 the number of faces to a vertex: - Archimedean Solids.

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  • (By the truncation of a vertex or edge we mean the cutting away of the vertex or edge by a plane making equal angles with all the faces composing the vertex or with the two faces forming the edge.) It is bounded by 4 triangular and 4 hexagonal faces; there are 18 edges, and 12 vertices, at each of which two hexagons and one triangle are covertical.

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  • Ann., 119, p. 406) as a semi-circle, but it is really a parabola with its axis parallel to the axis of E, and its vertex at the point t= -b/2c, which gives the neutral temperature.

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  • He discriminated the three species of conics as follows: - At one of the two vertices erect a perpendicular (talus rectum) of a certain length (which is determined below), and join the extremity of this line to the other vertex.

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  • Then the square of the ordinate intercepted between the diameter and the curve is equal to the rectangle contained by the portion of the diameter between the first vertex and the foot of the ordinate, and the segment of the ordinate intercepted between the diameter and the line joining the extremity of the latus rectum to the second vertex.

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  • The conics are distinguished by the ratio between the latus rectum (which was originally called the latus erectum, and now often referred to as the parameter) and the segment of the ordinate intercepted between the diameter and the line joining the second vertex with the extremity of the latus rectum.

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  • In modern notation, if we denote the ordinate by y, the distance of the foot of the ordinate from the vertex (the abscissa) by x, and the latus rectum by p, these relations may be expressed as 31 2 for the hyperbola.

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

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  • The other vertex stars use different arrangements of the thick and thin rhombs.

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  • Each vertex of the tree, except the leaves, might represent a speciation event.

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  • An inflation force is used at each vertex to inflate the overall model, while surface tension attempts to keep the mesh spherical.

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  • There is no vertex for the trivial subgroup (yet).

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  • These came slightly undersized compared to the Vertex, apart from that they were identical.

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  • The other problem comes when a hatch line passes through a vertex of the polygon.

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  • If this entry is not available you have failed to select vertex G.

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  • Find the neighboring vertex with the largest number of incident edges.

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  • If it returns fail the new vertex or edge is not generated !

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  • Merge Classes This menu entry merges all classes within each level that contain a selected vertex.

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  • I am not asking you to take a psychiatric vertex at this point - it is too early.

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  • You need this option if you have moved a vertex without its class (holding down the SHIFT key).

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  • The user is prompted for every selected vertex, which label it should have.

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  • Tracks are now coming from the same primary vertex.

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  • To achieve smooth results, any triangles which share a common vertex should have the same normal vector at that vertex.

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  • These events are represented by a single vertex in a Feynman diagram.

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  • You will get a new vertex 12 for an index 24 subgroup.

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  • By way of example, how to draw a triangle: DRAW MOVE to first vertex.

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  • Skills required: - C++, Object-oriented Design, DirectX, pixel & vertex shaders, 3D maths.

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  • Stream out allows the graphics card to output the pixel or vertex shader information directly to the memory, allowing faster access time.

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  • After the silicon vertex detector is the Central Outer Tracker, a gas drift chamber which operates via the detection of charged ions.

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  • Dijkstra 's algorithm is as follows: Input: A graph G and a specified vertex v 1.

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  • Well, our friend, vertex manipulation can be applied !

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  • For charged decays the detector is capable of reconstructing the position of the decay vertex.

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  • The distance between adjacent vertices of the icosahedron is 5% longer than the distance between a vertex and the center.

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  • My cousin built his house on the vertex of the highest hill in the county.

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  • The vertex of the Washington Monument is made of aluminum, an extremely expensive material at the time of its construction.

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  • The vertex of the Washington Monument is made of aluminum, an extremely expensive material at the time of its construction.

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  • Gamespot pegs this at around six vertex pipelines and 24 pixel pipelines.

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  • In this presentation, the baby's bottom is the presenting part instead of the head, which is called a vertex presentation.

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  • The risks of vaginal delivery with breech presentation are much higher than with a head-first (vertex) presentation.

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  • For reasons that are not fully understood, almost all unborn babies settle into a head down, or vertex, position.

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  • Vertex 42 has a series of debt reduction worksheets that you can use when taking the snowball approach to repaying your debts.

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  • vertex.

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