## XA Sentence Examples

- Ukx(n-2) ï¿½ Taking the first polar with regard to y (n - k) (a f)
**xa**x -k-l ay+ k (af) k-l ay -k (ab) (n -1) b12by n kn-2k-1 n-1 k(n-2) =k(n- 2)a u x u5+nax ayux and, writing f 2 and -f l for y1 and 3,21 (n-k)(a f) k+ta i k-1 + k (n - 1)(ab)(a f) k-1 (b f)4 1 k by-2 = (uf)u xn-2k-1? - The name probably means "very holy" = apt - ayvr,; another (Cretan) form 'Apt67)
**Xa**(_ Oavepa) indicates the return to a "bright" season of nature. - Now D A
**xA**k = (n - k) A k; Aï¿½ A k = k A?1; D ï¿½A A k = (n - k) A k+1;D mï¿½ A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, ï¿½ 1, ï¿½2 have arbitrary values, and therefore when the values are such that J =j, A k =akï¿½ Hence °a-do +(n -1)71 (a2aa-+... - The existence of such forms seems to have been brought to Sylvester's notice by observation of the fact that the resultant of of and b must be a factor of the resultant of
**Xax**+ 12 by and X'a +tA2 for a common factor of the first pair must be also a common factor so we obtain P: = of the second pair; so that the condition for the existence of such common factor must be the same in the two cases. - Then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i =
**Xa**i +,ia2, A2= - ï¿½ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (**XA**) = X i A2 - X2 Ai = (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (**xa**) possess the invariant property. - Then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i =
**Xa**i +,ia2, A2= - ï¿½ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (**XA**) = X i A2 - X2 Ai = (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (**xa**) possess the invariant property. - Then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i =
**Xa**i +,ia2, A2= - ï¿½ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (**XA**) = X i A2 - X2 Ai = (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (**xa**) possess the invariant property. - (ab), aa, ab, (
**xa**), ax, xx. - X (
**xa**) ki (xb) k2 (xc) k3...axibx2cx3...xx = (AB) hi (AC) h2 (BC) h3...A11 4 13 A1,14131 A B I ?C"' B C "' X (**XA**) ki (XB) k2 (XC) k3...AXB122cCk...X If this be of order e and appertain to an nie L Eke-/1+2m =e, h i+h2+ï¿½ï¿½ï¿½+221+ji+j2+ï¿½ï¿½ï¿½+kl+li =n, hi+h3+..ï¿½+222+ji+j3+ï¿½ï¿½ï¿½+k2+12 = n, h2+h3+ï¿½ï¿½ï¿½+223+j2+%3+ï¿½.ï¿½+k3+13 =n; viz., the symbols a, b, c,... - X (
**xa**) ki (xb) k2 (xc) k3...axibx2cx3...xx = (AB) hi (AC) h2 (BC) h3...A11 4 13 A1,14131 A B I ?C"' B C "' X (**XA**) ki (XB) k2 (XC) k3...AXB122cCk...X If this be of order e and appertain to an nie L Eke-/1+2m =e, h i+h2+ï¿½ï¿½ï¿½+221+ji+j2+ï¿½ï¿½ï¿½+kl+li =n, hi+h3+..ï¿½+222+ji+j3+ï¿½ï¿½ï¿½+k2+12 = n, h2+h3+ï¿½ï¿½ï¿½+223+j2+%3+ï¿½.ï¿½+k3+13 =n; viz., the symbols a, b, c,... - For the quadratic aoxi +2a i x i x 2 +a 2 x, we have (i.) ax = 7/1x1+2aixix2-I-7/24, (ii.) xx=xi+xzi (ab) 2 =2(aoa2 - ai), a a = a o+712, _ (v.) (
**xa**)ax= i'?- (a2 - ao)xix2 - aix2. - 4), and issues in a jet between two edges A and A'; the wall
**xA**being bent at a corner B, with the external angle (3= 2Wr/n. - If there are more B corners than one, either on
**xA**or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1! - If there are more B corners than one, either on
**xA**or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1! - Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.
- Two corners B 1 and in the wall
**xA**, with a' = -00, and n =I, will give the solution, by duplication, of a jet issuing by a reentrant mouthpiece placed symmetrically in the end wall of the channel; or else of the channel blocked partially by a diaphragm across the middle, with edges turned back symmetrically, problems discussed by J. - The velocity of the ellipsoid defined by X =o is then U= - 2 __ M ((ro b J o (a2 =ab (i -A0), (20) with the notation A or A a a= a (a2bc+ = - 2abc d -- so that in (4)
**xA**x 'UxA x A' 4)' 1 -Ao' (22) in (I) for an ellipsoid. - ZUy2BB0 Bll; reducing, when the liquid extends to infinity and B 3 =0, to =
**xA**o' _ - zUy 2B o so that in the relative motion past the body, as when fixed in the current U parallel to xO, A 4)'=ZUx(I+Bo), 4)'= zUy2(I-B o) (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting b 2 =pa, A = A'a, and proceeding to the limit where a = oo, we find for a paraboloid of revolution P B - p (7) B = 2p +A/' Bo p+A y2 i =p+A'- 2x, (8) p+? - The line XZ consists of a series of lengths, as
**XA**, AB ... - The weight load was pushing downwards, causing pressure on the strut.
- Hruschka's extractor, first brought to public
**xa**cto s.X? - =x d,b,c d ', c', , d "b" c",, original determinant is = o, and therefore the determinant itself is = o; that is, the linear equations give x'a,b,c - d,b,c =o; a', b', c' d', b', c' a", b', c" d", b", c" which is the result obtained above.
- Amongst them, actually or potentially, are the grand steward (0yas oircovo,uos), who serves him as deacon in the liturgy and presents candidates for orders; the grand visitor (µryas oaKEAAaptos), who superintends the monasteries; the sacristan (o - KEvocAuAa); the chancellor (X apr041,
**Xa**), who superintends ecclesiastical causes; the deputyvisitor (o rou caKEAAiov), who visits the nunneries; the protonotary (7rpwrovorapcos); the logothete (Aoy06Erns), a most important lay officer, who represents the patriarch at the Porte and elsewhere outside; the censer-bearer, who seems to be also a kind of captain of the guard (Kavarpio-cos or Kavvrp11vQLos); the referendary (pEckpevSapcos); the secretary (i)7rown L uoyp x4wv); the chief syndic (7rpwrEK&Kos), 1 The numbers have varied from time to time. - 7) that "he emptied himself and took upon him the form of a servant" (EauTOv µop4 v OovXoD
**Xa**(3c7.v). - The various forms in areal co-ordinates may be derived from the above by substituting
**Xa**for 1, µb for m and vc for n, or directly by expressing the condition for tangency of the line x+y+z = o to the conic expressed in areal coordinates. - 67 a) in a fitting position to represent part of the polygon of forces at Xefa; beginning with the upward thrust EX, continuing down
**XA**, and drawing AF parallel to AF in the frame we complete the polygon by drawing EF parallel to EF in the frame.