Locus sentence example

locus
  • The locus of these intersections is the quadratrix.
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  • By means of this expression we may trace the locus of a band of given order as b varies.
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  • Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.
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  • In the third-order complex the centre locus becomes a finite closed quartic surface, with three (one always real) intersecting nodal axes, every plane section of which is a trinodal quartic. The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic scalar finds no place among them, and in consequence Q:1 is meaningless.
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  • Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is constant, &c., &c.
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  • Genetic characterization of the legs at odd angles angles locus, a new mutation causing motor neuron degeneration in a gene dose dependent manner.
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  • We found evidence that recombination contributed to sequence divergence within at least one gene locus.
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  • Reading speed improves if a new trained retinal locus (TRL) is established in an area that is more favorable for reading.
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  • People either have an external or internal locus of control.
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  • The definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two fixed points is constant); such definitions and other special properties are treated in the articles Ellipse, Hyperbola and Parabola.
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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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  • In the latest version you completely lose the locus of control, you have limited chances of stopping breakaways.
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  • We have evidence for point mutations, recombination, gene conversions, and unequal crossing-over within and between homologs at this complex locus.
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  • Summary An indifference curve is a locus of points about which the individual feels indifferent.
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  • These results have quite important meaning in the survey of genomic locus which is responsible for radiation hypersensitivity.
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  • While the chicken locus looks similar to the mammalian beta-globin loci at first glance, there are some major differences.
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  • Other yet undiscovered genes outside the prion protein gene locus might also confer susceptibility.
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  • Let PP1P2 be the path of the moving point, and let OT, OT 1, OT2, be drawn from the fixed point 0 parallel and equal to the velocities at P, P 1, respectively, then the locus of T is the hodograph of the orbits described by P (see figure).
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  • ` Quapropter locus est intactus, inane, vacansque Q uod si non esset, nulla ratione moveri Res possent; namque, officium quod corporis exstat, Officere atque obstare, id in omni tempore adesset Omnibus: haud igitur quicquam procedere posset, Principium quoniam cedendi nulla daret res.'
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  • A genome-wide scan for human obesity genes reveals a major susceptibility locus on chromosome 10.
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  • Of course, as luck would have it, she is the locus of the change that they have come back to repair - in normal time, she is killed in a traffic accident.
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  • I pop over to Locus on a regular basis, and SciFiWire, but that's about it.
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  • Also the auxiliarly circle is the locus of the feet of the perpendiculars from the foci on any tangent.
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  • The expression " wisdom," as it is employed in the locus classicus, Prov.
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  • Then the locus of the intersection of PQ and OM is the quadratrix of Dinostratus.
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  • The Asiatic story then died away, but the name remained, and the royal presbyter was now assigned a locus in Ethiopia.
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  • The pursuit of mechanical methods furnished a stimulus to the study of mechanical loci, for example, the locus of a point carried on a rod which is caused to move according to a definite rule.
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  • This was sometimes known as the parlour, colloquii locus, the monks having the privilege of conversation here.
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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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  • A system of circles is coaxal when the locus of points from which tangents to the circles are equal is a straight line.
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  • 36 it is seen that the line joining the points A and B is the locus of the intersection of equal tangents, for if P be any point on AB and PC and PD the tangents to the circles, then PA PB = PC 2 = PD 2, and therefore PC = PD.
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  • Tyndall's own summary of the course of research on the subject was as follows: The idea of semi-fluid motion belongs entirely to Rendu; the proof of the quicker central flow belongs in part to Rendu, but almost wholly to Agassiz and Forbes; the proof of the retardation of the bed belongs to Forbes alone; while the discovery of the locus of the point of maximum motion belongs, I suppose, to me.
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  • It may be defined as a section of a right circular cone by a plane parallel to a tangent plane to the cone, or as the locus of a point which moves .so that its distances from a fixed point and a fixed line are equal.
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  • The instantaneous centre will have a certain locus in space, and a certain locus in the lamina.
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  • Hence the locus of J relative to AB, and the locus relative to CD are equal ellipses of which A, B and C, D are respectively the foci.
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  • Again, that wrenches of arbitrary amounts about two given screws compound into a wrench the locus of whose axis is a cylindroid.
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  • Since the given wrench can be replaced by a force acting through any assigned point P, and a couple, the locus of the null-lines through P is a plane, viz, a plane perpendicular to the vector which represents the couple.
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  • The complex is therefore of the type called linear (in relation to the degree of this locus).
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  • Again, any plane w is the locus of a system of null-lines meeting in a point, called the null-point of c. If a plane revolve about a fixed straight line p in it, its ntill-point describes another straight line p, which is called the conjugate line of p. We have seen that the wrench may be replaced by two forces, one of which may act in any arbitrary line p. It is now evident that the second force must act in the conjugate line p, since every line meeting p, p is a null-line.
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  • Again, the locus of G is an arc of an ellipse whose centre is in the intersection of the planes; since this arc is convex upwards the equilibrium is unstable.
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  • Further, it is known from the theory of roulettes that the locus of G will be concave or convex upwards according as cos 4, 1 i ~p~p (8)
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  • The locus of the point V is called the hodograp/z (q.v.); and it appears that the velocity of the point V along the hodograph represents in magnitude and in directon tbt acceleration in the original orbit.
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  • Let a be the radius of the rolling sphere, c that of the spherical surface which is the locus of its centre, and let x, y, I be the co-ordinates of this centre relative to axes through 0, the centre of the fixed sphere.
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  • The axode is hence the locus of the instantaneous axis, whilst the centrode is the locus of the instantaneous centre in any plane parallel to the plane of motion.
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  • To find the form of these surfaces corresponding to a particular pair of non-adjacent links, consider each link of the pair fixed in turn, then the locus of the instantaneous axis is the axode corresponding to the fixed link, or, considering a plane of motion only, the locus of the instantaneous centre is the ceotrode corresponding to the fixed link.
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  • The locus of any other carried point is an "epitrochoid" when the circle rolls externally, and a "hypotrochoid" when the circle rolls internally.
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  • Draw any line DE perpendicular to AB and meeting the circle in E, and take a point P on DE such that the line DP =arc BE; then the locus of P is the companion to the cycloid.
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  • The cartesian equation, referred to the fixed diameter and the tangent at B as axes may be expressed in the forms x= a6, y=a(I -cos 0) and y-a=a sin (x/afir); the latter form shows that the locus is the harmonic curve.
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  • When the refracting curve is a circle and the rays emanate from any point, the locus of the secondary caustic is a Cartesian oval, and the evolute of this curve is the required diacaustic. These curves appear to have been first discussed by Gergonne.
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  • There appears to be no locus poenitentiae for serious sins excepting in the case of catechumens, and there is a notable " perfectionist " tone in many of the prayers.
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  • Then the locus of P is the witch.
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  • Such a curve may be regarded geometrically as actually described, or kinematically as in the course of description by the motion of a point; in the former point of view, it is the locus of all the points which satisfy a given condition; in the latter, it is the locus of a point moving subject to a given condition.
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  • Thus the most simple and earliest known curve, the circle, is the locus of all the points at a given distance from a fixed centre, or else the locus of a point moving so as to be always at a given distance from a fixed centre.
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  • The Greek geometers invented other curves; in particular, the conchoid, which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the cissoid, which is the locus of a point such that its distance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point.
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  • In a machine of any kind, each point describes a curve; a simple but important instance is the " three-bar curve," or locus of a point in or rigidly connected with a bar pivoted on to two other bars which rotate about fixed centres respectively.
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  • Plucker first gave a scientific dual definition of a curve, viz.; " A curve is a locus generated by a point, and enveloped by a line - the point moving continuously along the line, while the line rotates continuously about the point "; the point is a point (ineunt.) of the curve, the line is a tangent of the curve.
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  • Secondly, as to the inflections, the process is a similar one; it can be shown that the inflections are the intersections of the curve by a derivative curve called (after Ludwig Otto Hesse who first considered it) the Hessian, defined geometrically as the locus of a point such that its conic polar (§ 8 below) in regard to the curve breaks up into a pair of lines, and which has an equation H = o, where H is the determinant formed with the second differential coefficients of u in regard to the variables (x, y, z); H= o is thus a curve of the order 3 (m - 2), and the number of inflections is =3m(m-2).
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  • Many well-known derivative curves present themselves in this manner; thus the variable curve may be the normal (or line at right angles to the tangent) at any point of the given curve; the intersection of the consecutive normals is the centre of curvature; and we have the evolute as at once the locus of the centre of curvature and the envelope of the normal.
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  • The Attic tradition, reproduced in Euripides (Ion 1002), regarded the Gorgon as a monster, produced by Gaea to aid her sons the giants against the gods and slain by Athena (the passage is a locus classicus on the aegis of Athena).
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  • Let APB be a semicircle, BT the tangent at B, and APT a line cutting the circle in and BT at T; take a point Q on AT so that AQ always equals PT; then the locus of Q is the cissoid.
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  • To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight line (the directrix) is constant and is less than unity.
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  • If the tangents be at right angles, then the locus of the point is a circle having the same centre as the ellipse; this is named the director circle.
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  • Bertin has shown that a useful picture of the form of these curves may be obtained by taking sections, parallel to the plate, of a surface that he calls the "isochromatic surface," and that is the locus of points on the crystal at which the relative retardation of two plane waves passing simultaneously through a given point and travelling in the same direction has an assigned value.
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  • One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the directrix) are in constant ratio.
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  • The gene has been identified at locus Xq27.
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  • The problem of the curves is solved by their reduction to a problem of straight lines; and the locus of any point is determined by its distance from two given straight lines - the axes of co-ordinates.
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  • And yet theism - or monotheism - constitutes a special locus in the history of religion.
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  • The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.
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  • But a little before Tertullian, Irenaeus, though he does not use the word ordo, anticipates in some measure Tertullian's abstract term, for he recognizes a magisterii locus, " a place of magistracy " or " presidency " in the church.
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  • In order that a large part of the field of view may be in focus at once, it is desirable that the locus of the focused spectrum should be nearly perpendicular to the line of vision.
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  • - As supplemental to the account of poetry may be mentioned here some of the chief collections of ancient verse, sometimes made for the sake of the poems themselves, sometimes to give a locus classicus for usages of grammar or lexicography, sometimes to illustrate ancient manners and customs. The earliest of these is the Mo'allakat.
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  • In the same preface is included (a) the famous problem known by Pappus's name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or (more generally) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones; (Pappus does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs - one of one set and one of another - of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position), (b) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by Pappus himself.
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  • (1900), 289 seq., on the discovery of an archaic altar of the Locus sacer of Florence, belonging to Ancharia (Angerona), the goddess of Fiesole.
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  • The manor, then called Bellus Locus or Beaulieu on account of its beautiful situation, was afterwards granted to the Mortimers, in whose family it continued until it was merged in the crown on the accession of Edward IV.
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