## Ellipse Sentence Examples

- But since an
**ellipse**can always be constructed with a given centre so as to touch a given line at a given point, and to have a given value of ab(=h/-~ u) we infer that the orbit will be elliptic whatever the initial circumstances. - Hence the path is approximately, an
**ellipse**, and the period is 2sr ~/ (l/g). - The star thus appears to describe a small
**ellipse**in the sky, and the nearer the star, the larger will this**ellipse**appear. - Msh2(n-a); (3) so that this
**ellipse**can be rotating with this angular velocity R for an instant without distortion, the**ellipse**a being fixed. - It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an
**ellipse**of very small eccentricity, and a true parabolic figure can thus be obtained. - Now in a conic whose focus is at 0 we have where 1 is half the latus-rectum, a is half the major axis, and the upper or lower sign is to be taken according as the conic is an
**ellipse**or hyperbola. - This merely shows that a particular
**ellipse**may be described under the law of the direct distance provided the circumstances of projection be suitably adjusted. - Of the wedge of immersion and emersion, will be the C.P. with respect to FF' of the two parts of the water-line area, so that b 1 b 2 will be conjugate to FF' with respect to the momental
**ellipse**at F. - If the forks are not of exactly the same frequency the
**ellipse**will slowly revolve, and from its rate of revolution the ratio of the frequencies may be determined (Rayleigh, Sound, i. - The latter completely encloses a large area of ground in a semicircle of which Besancon itself is the centre, and the whole of the newer works taken together form an irregular
**ellipse**of which the major axis, lying north-east by south-west, is formed by the Doubs. - This shows that the C.P. is the antipole of the line of intersection of its plane with the free surface with respect to the momental
**ellipse**at the C.G. - Within which the C.P. must lie when the area is immersed completely; the boundary of the core is therefore the locus of the antipodes with respect to the momental
**ellipse**of water lines which touch the boundary of the area. - The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal
**ellipse**, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area. - Having a resultant in the direction PO, where P is the intersection of an
**ellipse**n with the hyperbola 13; and with this velocity the**ellipse**n can be swimming in the liquid, without distortion for an instant. - An
**ellipse**interior to n = a will move in a direction opposite to the exterior current; and when n = o, U = oo, but V = (m/c) sh a sin 13. - The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the
**ellipse**; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the**ellipse**n to infinity. - Sca, through,, u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the
**ellipse**and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other. - If the two forks have the same frequency, it is easily seen that the figure will be an
**ellipse**(including as limiting cases, depending on relative amplitude and phase, a circle and a straight line). - If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in F, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an
**ellipse**, or circle with centre F and radius FA; while the time-curve will be a sinusoid. - Proposition 14 shows how to draw an
**ellipse**through five given points, and Prop. 15 gives a simple construction for the axes of an**ellipse**when a pair of conjugate diameters are given. - The greatest displacement of the star from its mean position (the semi-axis major of the
**ellipse**) is called its parallax. - Thus Whewell mistook Kepler's inference that Mars moves in an
**ellipse**for an induction, though it required the combination of Tycho's and Kepler's observations, as a minor, with the laws of conic sections discovered by the Greeks, as a major, premise. - The line parallel to q' q-- 1 which intersects the axes of Q and Q'; the plane of the member contains a fixed line; the centre is on a fixed
**ellipse**which intersects the transversal; the axis is on a fixed ruled surface to which the plane of the**ellipse**is a tangent plane, the**ellipse**being the section of the ruled surface by the plane; the ruled surface is a cylindroid deformed by a simple shear parallel to the transversal. - 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. - Which may be called the momental
**ellipse**at 0. - The path is therefore an
**ellipse**of which a, b are conjugate semi-diameters, and is described in the period 24 Ju; moreover, the velocity at any point P is equal to ~ OD, where OD is the semi-diameter conjugate to OP. ~,This type of motion;,s called elliptic harmonic. If the co-ordinate axes are the principal axes of the**ellipse**, the angle ft in (I o) is identical with the excentric angle. - In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an
**ellipse**similar to the actual orbit. - The pole 0 of the hodograph is inside on or outside the circle, according as the orbit is an
**ellipse**, parabola or hyperbola. - In the course of constructions for surfaces to reflect to one and the same point (1) all rays in whatever direction passing through another point, (2) a set of parallel rays, Anthemius assumes a property of an
**ellipse**not found in Apollonius (the equality of the angles subtended at a. - We put e for the eccentricity of the
**ellipse**, represented P, by the ratio M CF: CA. - Thus the core of a circle or an
**ellipse**is a concentric circle or**ellipse**of one quarter the size.