# Xy Sentence Examples

- Referred to the asymptotes as axes the general equation becomes
**xy**2 obviously the axes are oblique in the general hyperbola and rectangular in the rectangular hyperbola. - 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. - Now f = (
**xy**1 - x i y) (**xy**2 - x 2 y) ... - 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),... - Since, If F = An, 4) = By, 1 = I (Df A4) Of A?) Ab A"'^1Bz 1=, (F, Mn Ax I Ax 2 Axe Ax1) J The First Transvectant Differs But By A Numerical Factor From The Jacobian Or Functional Determinant, Of The Two Forms. We Can Find An Expression For The First Transvectant Of (F, ï¿½) 1 Over Another Form Cp. For (M N)(F,4)), =Nf.4Y Mfy.4), And F,4, F 5.4)= (Axby A Y B X) A X B X 1= (
**Xy**)(F,4))1; (F,Ct)1=F5.D' 7,(**Xy**)(F4)1. - 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 . - Denoting them by x, y, so that AB is axis of y and a perpendicular through A the axis of x, and rationalizing (26), we have 2 ax 2 - V 2
**Xy**2 - V 2 aAy = o, which represents a hyperbola with vertices at 0 and A. - 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. - For in a rigid body, rotating about Oz with angular velocity the circulation round a curve in the plane
**xy**is x ds yds) ds = times twice the area. - Kirchhoff's expressions for X, Y, Z, the coordinates of the centre of the body, FX=y 1 cos
**xY--y**2 cos yY-{-y 3 cos zY, (18) FY = -y l cos xX -Hy2 cos yX+y 3 cos zX, (Ig) G=y 1 cos xZ+y 2 cos yZ+y 3 cos zZ, (20) (21) F(X+Yi) = Fy3-Gx3+i /) X 3epi. - In the general equation of the second degree the co-efficients of x 2 and y 2 are equal, and of
**xy**zero. - 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. - The three conditions of equilibrium arc therefore ~(X) = o, ~(Y) = o, ~(
**xY**yX) = o. - 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 ~ - R= __~~c_(xy_yx)+y, (24)
- Ketone hydrolysis,- CH3ï¿½COï¿½C(
**XY**)ï¿½C02C2H5-jCH3ï¿½COï¿½CH(**XY**)+C2HSOH+C02; Acid hydrolysis:- CH 3 ï¿½COï¿½C(**XY**) C02C2H5--)CH3. - 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 order of the curve is equal to that of the term or terms of highest order in the co-ordinates (x, y) conjointly in the equation of the curve; for instance,
**xy**- 1= o is a curve of the second order. - 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. - 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. **Xy**2 -4z 3 +g2x 2 y+g3x 3, and also the special form axz 2 -4by 3 of the cuspidal cubic. An investigation, by non-symbolic methods, is due to F.