# Xy sentence example

xy
• Now f = (xy 1 - x i y) (xy 2 - x 2 y) ...
• If three equations, each of the second degree, in three variables be given, we have merely to eliminate the six products x, 2, z 2, yz, zx, xy from the six equations u = v = w = o = oy = = 0; if we apply the same process :to thesedz equations each of degree three, we obtain similarly a determinant of order 21, but thereafter the process fails.
• (II.) Similarly in (I.), writing for c l, c 2 the cogredicnt pair -y2, +y1, we obtain axb5-a5bx=(ab)(xy)..
• Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...
• For instance, x+y = x+xy and xy = x(x+y) are reciprocal.
• In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.
• When the plane zx is not a plane of symmetry, we have to consider the terms in xy, 2 y, and y 3 .
• If the direction of motion makes an angle 0' with Ox, tan B' = d0 !dam _ ?xy 2 = tan 20, 0 =-10', (9) dy/ y and the velocity is Ua2/r2.
• Venn, in his Symbolic Logic, proposes the four forms, xy = o, xy = o, xy>o, xy> o (where y means " not-y "), but only as alternative to the ordinary forms. Bradley says that " ` S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that " ` is ' never stands for anything but ` exists ' "; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as " that which affirms the existence of its subject, or, in other words, asserts a fact."
• In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.
• He had now the following expression for the product of any two directed lines: xx' - yy - zz' +i(yx'+ xy')+ j(xz' '+zx') +ij(yz' - zy').
• There is, however, considerable evidence in support of the view that Greek va representing the sound arising from Ky, xy, Ty, By was pronounced as sh (s), while representing gy, dy was pronounced in some districts zh (z).4 On an inscription of Halicarnassus, a town which stood in ancient Carian territory, the sound of vv in `AXoKapvaao-Ewv is represented by T, as it is also in the Carian name Panyassis (IIavvfiTcos, geni tive), though the ordinary is also found in the same inscription.
• Taking this as the plane xy, with the axis of x drawn horizontally, and that of y vertically upwards, we have X=o, Y= mg; so that d2x ~
• C02H+C 2 [[Hsoh+Ch(Xy)ï¿½Cooh]]; (where X and Y =alkyl groups).
• The cartesian equation, if A be taken as origin and AB (= 2a) for the axis of x, is xy 2 =4a2(2a - x).
• The 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.
• Stating the theorem in regard to a conic, we have a real point P (called the pole) and a real line XY (called the polar), the line joining the two (real or imaginary) points of contact of the (real or imaginary) tangents drawn from the point to the conic; and the theorem is that when the point describes a line the line passes through a point, this line and point being polar and pole to each other.
• The most simple example is in the two systems of equations x': y': z' = yz: zx: xy and x: z'x': x'y'; where yz =0, zx =0, xy = o are conics (pairs of lines) having three common intersections, and where obviously either system of equations leads to the other system.
• By taking this plane, which is that of the orbit in which the planet performs its revolution, as the plane of xy, we have only two co-ordinates to consider.
• In all such cases, there is no component to plan convexity, any curvature being entirely orthogonal to the xy plane.
• In some South American field mice and the Scandinavian wood lemming, XY females are commonplace.
• Rather than columns running along a 2D x axis, a city scape consists of square columns at xy locations.
• For the simple case of a tensile stress sigma x combined with a shear stress tau xy.
• So far as (7) is concerned the alternative supposition that AD vanishes would answer equally well, if we suppose the vibrations to be executed in the plane of polarization; but let us now revert to (5), which gives w 3 = _ PAN y z - = + PAN xy _ PAN z 2 - x2 8 N r 2 N r2' W 2 + N r2 (8) from 0 along which there is no scattered light, - two along the axis According to these equations there would be, in all, six directions of y normal to the original ray, and four (y z = =x) at angles of 45Ã‚° with that ray.
• In quantitative judgments we may think x = y, or, as Boolero oses x = v Ã‚° p p y = - Ã‚° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.