## Conjugate Sentence Examples

- The hyperbola which has for its transverse and
**conjugate**axes the transverse and**conjugate**axes of another hyperbola is said to be the**conjugate**hyperbola. - The centre is a
**conjugate**point (or acnode) and the curve resembles fig. - Of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)ï¿½x4; and it can be shown that 0, x, 1P are the three
**conjugate**quadratic factors of t above mentioned. - If we put qo= Sq' - Vq', then qo is called the
**conjugate**of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'. - If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are
**conjugate**foci, but also that the foci are exempt from the most important term in the aberration. - 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. - Y If the motion is irrotational, u=-x-- dy' 2' d y = dx' y y so that :(, and 4' are
**conjugate**functions of x and y, 0+4,i = f(x + y i), v 2 4 =o, v 2 0 =o; or putting 0+0=w, +yi=z, w=f(z). - - By the use of the complex variable and its
**conjugate**functions, an attempt can be made to give a mathematical interpretation of problems such as the efflux of water in a jet or of smoke from a chimney, the discharge through a weir, the flow of water through the piers of a bridge, or past the side of a ship, the wind blowing on a sail or aeroplane, or against a wall, or impinging jets of gas or water; cases where a surface of discontinuity is observable, more or less distinct, which separates the running stream from the dead water or air. - Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as
**conjugate**functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q. - All objects, therefore, which lie beyond a certain point (the
**conjugate**focus of the dioptric system of the eye, the far point) are indistinctly seen; rays from them have not the necessary divergence to be focused in the retina, but may obtain it by the interposition of suitable concave lenses. - 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. - Ramsden's dioptric micrometer consists of a divided lens placed in the
**conjugate**focus of the innermost lens of the erecting eye-tube of a terrestrial telescope. - An important notion is that of
**conjugate**partitions. - Thus a partition of 6 is 42; writing this in the form z 11' and summing the columns instead of the lines, we obtain the
**conjugate**partition 2211; evidently, starting from 2211, the**conjugate**partition is 42. - In this article the equations to the more important circles - the circumscribed, inscribed, escribed, self-
**conjugate--will**be given; reference should be made to the article Triangle for the consideration of other circles (nine-point, Brocard, Lemoine, &c.); while in the article Geometry: Analytical, the principles of the different systems are discussed. - The self-
**conjugate**circle is a 2 sin 2A +0 2 sin 2 B +y 2 sin 2C = o, or the equivalent form a cosAa 2 +bcosB(2 +ccosCy 2 = o, the centre being sec A, sec B, sec C. - In length, the
**conjugate**diameter being 12 in. - 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 two nuclei when once associated are termed"
**conjugate**"nuclei, and they always divide at the same time, a half of each passing into each cell. - This
**conjugate**condition is finally brought to a close by the nuclear fusion in the basidium. - From one cell to another or C, A further stage in which whether two daughter nuclei from sm l the first aecidiobecome
**conjugate**in one cell, spore (a) and the intercalary is not yet clear. - Although in the forms without aecidia the two generations are not sharply marked off from one another, we may look up the generation with single nuclei in the cells as the gametophyte and that with
**conjugate**nuclei as the sporophyte. - Idium), a reduced fertilization which denotes their derivation, through the Uredineae, from more typically sexual forms. No one has yet t.-ade out in any form the exact way in which the association of nuclei tr -.-es place in the group. The mycelium is always found to contain
**conjugate**nuclei before the formation of basidia, but the point at which the**conjugate**condition arises seems very variable. - Mycelium ircdospores otachY' ar Mycelium aecidi'spores teleutospores (young) - mycelium SporoNtyte with
**conjugate**nuclei GametohyEe with single nuclei teleutospores ?(mature) 8a ?; sporida ?m celium erm $ fertile cells Y sp (abortaitviae) (of aecidium) fertilized cells (of aecidium) and bears the basidiospores. - It is known that zoogametes, which usually
**conjugate**, may, when conjugation fails, germinate directly (Sphaerella). - Gametes which fail to
**conjugate**sometimes assume the appearance of zygospores and germinate in due course. - It also follows that a line half-way between a point and its polar and parallel to the latter touches the parabola, and therefore the lines joining the middle points of the sides of a self-
**conjugate**triangle form a circumscribing triangle, and also that the ninepoint circle of a self-**conjugate**triangle passes through the focus. - The orthocentre of a triangle circumscribing a parabola is on the directrix; a deduction from this theorem is that the centre of the circumcircle of a self-
**conjugate**triangle is on the directrix ("Steiner's Theorem"). - Try = o to be a parabola is lbc+mca+nab = o, and the conic for which the triangle of reference is self-
**conjugate**la 2 +143 2 +n7 2 =o is a 2 inn--+b 2 nl+c 2 lm=o. - As the two lesser roots are made more and more equal the oval shrinks in size and ultimately becomes a real
**conjugate**point, and the curve, the equation of which is y2= (x - a) 2 (x - b) (in which a > b) consists of this point and a bell-like branch resembling the right-hand member of fig. - Perceiving a molecular isonomy between them and the inorganic compounds of the metals from which they may be formed, he saw their true molecular type in the oxygen, sulphur or chlorine compounds of those metals, from which he held them to be derived by the substitution of an organic group for the oxygen, sulphur, &c. In this way they enabled him to overthrow the theory of
**conjugate**compounds, and they further led him in 1852 to publish the conception that the atoms of each elementary substance have a definite saturation capacity, so that they can only combine with a certain limited number of the atoms of other elements. - The composition of two such lines by the algebraic 1 Theory of
**Conjugate**Functions, or Algebraic Couples, with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time, read in 1833 and 1835, and published in Trans. - This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a
**conjugate**KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) 2(1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane. - Take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the
**conjugate**lines of those of the former. - 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. - Again, since the shortest distance between any two
**conjugate**lines cuts the central axis at right angles, the orthogonal projections of two**conjugate**lines on a plane perpendicular to the central axis will be parallel (fig. - If we take any polyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be
**conjugate**(in the above sense) to those of the former. - It may further be shown that if Binets ellipsoid be referred to any system of
**conjugate**diameters as co-ordinate axes, its equation will be ~2+~2+~-2I, (27) - 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. - If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of
**conjugate**centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum. - In (1,3) satisfy the
**conjugate**or orthogonal relations anaiai+aiiaiai+. - The problem is identical with that of finding the common
**conjugate**diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const. - If we combine the solutions corresponding to a pair of
**conjugate**complex roots, we obtain, in real form, - = Care ~ cos (ot+~er), (37) - The later "c-w-µ€v was at first a solecism, an attempt to
**conjugate**a " verb in µ.c " like the " verbs in w." - If we write r for PN, then y= r cos a, and equation 9 becomes 13.7,T - I) This relation between y and r is identical with the relation between the perpendicular from the focus of a conic section on the tangent at a given point and the focal distance of that point, provided the transverse and
**conjugate**axes of the conic are 2a and 2b respectively, where a= p, and b 2 = -. - In all these cases the internal pressure exceeds the external by 2T/a where a is the semi-transverse axis of the conic. The resultant of the internal pressure and the surface-tension is equivalent to a tension along the axis, and the numerical value of this tension is equal to the force due to the action of this pressure on a circle whose diameter is equal to the
**conjugate**axis of the ellipse. - The resultant of the internal pressure and the surface-tension is equivalent to a pressure along the axis equal to that due to a pressure p acting on a circle whose diameter is the
**conjugate**axis of the hyperbola. - When the
**conjugate**axis of the hyperbola is made smaller and smaller, the nodoid approximates more and more to the series of spheres touching each other along the axis. - When the
**conjugate**axis of the hyperbola increases without limit, the loops of the nodoid are crowded on one another, and each becomes more nearly a ring of circular section, without, however, ever reaching this form.