# XL Sentence Examples

- He describes the safe and happy establishment of the people in their own land.
**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lv.) we have no longer a Jewish but a foreign messiah.**Xl**.-lv.- + v ?
**xl**1 + u l U1+v1V 1 + w1W1) ï¿½ or T x0a,?_ (m-I) J+m(o . - ï¿½; S = r A F(a 0, 711, a2,ï¿½ï¿½ï¿½bo, b l, b 2,ï¿½ï¿½ï¿½9ï¿½ï¿½ï¿½;
**xl**, x2), viz. - For the substitution rr
**xl**=A 11 +1 2 12, 52=A21+ï¿½2E2, of modulus A1 ï¿½i = (Alï¿½.2-A2ï¿½1) = (AM), A 2 ï¿½2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A lï¿½l +ai(A1/.22+A2ï¿½1) +7,2X2/22, A2 = aoï¿½l +2a1ï¿½1/ï¿½2 +a 2ï¿½2 ï¿½ We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a? - =y la
**xl**-i-y2a x2 must also vanish for the root a, and thence ax, and a must also vanish for the same root; which proves that a is a double root of f, and f therefore a perfect square. - A 31 ...n !aï¿½, for a l, a 2, a 3 ...a n respectively; it then becomes a e xi +na l xi -I x 2 +n (n -1)a 9
**xl**-2 x2 +... - Taking the variables to be x, y and effecting the linear transformation x = X1X+1.11Y, y = X2X+It2Y, X 2 +Y2X Y
**Xl**- X2 y = _ x X I + AI R X 122 so that - ï¿½l b it is seen that the two lines, on which lie (x, y), (X, Y), have a definite projective correspondence. - Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution
**xl**= X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry. - In both cases ddl and dal are cogredient with
**xl**and x 2; for, in the case of direct substitution, dxi = cost dX i - sin 00-(2, ad2 =sin B dX i +cos O dX 2, and for skew substitution dai = cos B dX i +sin 0d2, c-&-- 2 n d =sin -coseax2. - In Aristotle the
**Xl**yos of a thing is its definition, including its formal cause, while the ultimate principles of a science are apxal, the "reasons" (in a common modern sense) which explain all its particular facts.' **XL**, in which case aA+0B+ ...**Xl**., and here Jehovah is six times changed to Elohim, while the opposite change happens but once.**Xl**., we have the striking assertion, which surely did not originate in the Temple, that God has no delight in sacrifice and offerings.- And
**xl**.-lxvi. - It was of the utmost importance to declare that (especially) Isaiah
**xl**.-lxvi. - Was a prophetic work of the highest order; this was reason sufficient (apart from any presumed phraseological affinities in
**xl**.-lxvi.) for ascribing them to the royal prophet Isaiah. - The question of the Isaianic or non-Isaianic origin of the disputed prophecies (especially
**xl**.-lxvi.) must be decided on grounds of exegesis alone. **Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-**xlviii**.**Xl**.-**xlviii**., and its appendix chaps.**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lxvi.**Xl**.-lxvi.- Clebsch to take the form T= 2p(x12 +x22)+2p'x32 + q (xiyi +x2y2) +q'x3y3 +2r(y12+y22)+2r'y32 so that a fourth integral is given by dy 3 /dt = o, y = constant; dx3 (4 y) (q + y) _ (y y) dt -
**xl**'x2**xl**Y Y x l 2 - 1, y2 () = (x12 +x22) (y12 + y22) = (X 1 2 + X 2) +y22)-(FG-x3y3)2 = (x 1 y32-G2)-(Gx3-Fy3) 2, in which 2 = F 2 -x3 2, x l y l +x2y2 = FG-x3y3, Y(y1 2 +y2 2) = T -p(x12 +x22) -p'x32 -2q(xiyi 'x2y2)- 2 q ' x = (p -p') x 2 + 2 (- q ') x 3 y 3+ m 1, (6) m1 = T 2 i y 3 2 (7) so that dt3) 2 =X3, (8) where X3 is a quartic function of x3, and thus t is given by an elliptic (8) (6) (I) integral of the first kind; and by inversion x 3 is in elliptic function of the time t. - Now (x1 - x21) (y 1 +y21) =
**xl**l +x2y2 + - (' r 1 2 - x2y1) = FG-x3y3+iV X3, yi+3 7 21_FG-x3y3+2V X3**xl**+x21 X12 +X22 (x 1 +x 2 i) = - i{(q' - q)x3+r'y3]+irx3(y1+y21), = FG - x3y3 +ZJ X3 dt2log(x1+x22) - - (q g) x 3- r y3+rx3 F2x32 (12) d dl2 log V x1 ± x2 2 (q'-q)x3-(r'-r) y3FrFF2-x 2 3 ' (13) requiring the elliptic integral of the third kind; thence the expression of x1-f -x21 and yl-}-y21. - Introducing Euler's angles 0, c15, x1= F sin 0 sin 0, x 2 =F sin 0 cos 0,
**xl**+x 2 i =iF sin 0e_, x 3 = F cos 0; sin o t=P sin 4+Q cos 0, dT F sin 2 0d l - dy l + dy 2x = (qx1+ryi)**xl**+(qx2+ry2)x2 = q (x1 2 +x2 2) +r (xiyi +x2y2) = qF 2 sin 2 0-Fr (FG - x 3 y 3), (16) _Ft (FG _x 323 Frdx3 (17) F x3 X3 elliptic integrals of the third kind. - -
**xl**.) and 4 Ezra (x. **Xl**.-lxvi.- Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d
**xl**and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx. - Amongst his published works were a commentary on the Book of Job (1850), a translation of the Song of Songs (1852), an exposition of Isaiah
**xl**.-lxvi. **Xl**., 1884).- Thus arose the more developed system of Ezekiel's scheme (
**xl**.-**xlviii**.) and of the Priestercodex and the high dignity which became attached to the person of the High Priest (reflected in the narrative of Uzziah's leprosy in 2 Chron. **Xl**.-1v., chs.**Xl**.-lxvi., and by Photius, patriarch of Constantinople in the 9th century, who, according to Diestel (Gesch.**Xl**.-lxvi.; (3) the book of Daniel was written in the 2nd century s.c.; (4) the Priestly Code is post-exilic; (5) most of the Psalms are post-exilic. Now I, 2, 3 are absolutely independent - if 1 were proved false, 2 and 3 would still stand; and so with 2 and 3; so also 2 and 3 could be proved false without in any way affecting the validity of 4.**Xl**.), Sethites (Cainites) should also here be mentioned, and finally the Carpocratians.- [Aiy]EL ['1770-ODs 67r[oo idy W(rLV [0, ad E[io ]v i&Beol Kai [b]7rov E[IS] i(rTLV pOvoc, [
**Xl**]yw, iyc. EIpL pET' ailT[OU]. - Count Gunther
**XL**., who died in 1552, was the last common ancestor of both lines. - First comes a general theory of constitutions, right and wrong (Books A,B,F); and this part is afterwards referred to as " the first discourses " Ev Tois rpWTocs
**Xl**yocs). - [[Table
**Xl**]] - Principal Days of the Mahommedan Calendar. **Xl**.-**xlviii**., in which Cyrus is the anointed of Yahweh.- For the Scottish Excavations see Proceedings of the Society of Antiquaries of Scotland, xx.-
**xl**., and especially J. - TABLE
**XL-Production**of Iron Ore (in thousands of long tons). **Xl**., 1901).- If any other point 0, whose co-ordinates are x, y, z, be chosen in place of 0, as the point to which the forces are transferred, we have to write x1x, yiy, ZiZ for
**xl**, Yi, z1,and so on, in the preceding process. - The relation (44) is equivalent to
**Xl**X~