## 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.- 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~ **Xl**., 1901).- TABLE
**XL-Production**of Iron Ore (in thousands of long tons). - For the Scottish Excavations see Proceedings of the Society of Antiquaries of Scotland, xx.-
**xl**., and especially J. **Xl**.-**xlviii**., in which Cyrus is the anointed of Yahweh.- [[Table
**Xl**]] - Principal Days of the Mahommedan Calendar. - 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). - Count Gunther
**XL**., who died in 1552, was the last common ancestor of both lines. - [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]. **Xl**.), Sethites (Cainites) should also here be mentioned, and finally the Carpocratians.