# Aa Sentence Examples

- The circles A'A', which are struck with 2-inch radius, define the first portion of the knuckle.
- The southeastern corner of the province is traversed by the Westerwolde
**Aa**, which discharges into the Dollart. - +na n _ i
**aa**n = 0. - HELMOND, a town in the province of North Brabant, Holland, on the small river
**Aa**, and on the canal (Zuid-Willems Vaart) between 'sHertogenbosch and Maastricht, 241 m. - "Join
**AA**," I answered. - CH(NH 2) ï¿½ Cooh, arginin or guanidine-a-amino-n-valerianic acid, (NH)(NH2)Cï¿½NHï¿½ (CH 2) 3 ï¿½CH(NH 2)ï¿½Cooh, ornithin or
**aa-diamino**valerianic acid, ï¿½ (CH 2) 3 ï¿½ CH(NH 2) ï¿½ Coon, -(3-imidazol propionic acid, [[Hoocï¿½ Ch(Nh 2) ï¿½Ch 2 ï¿½ C: Chï¿½N:Chï¿½Nh]], proline or a-pyrrolidin carboxylic acid, [[Hoocï¿½ Ch. - = 0; and such functions satisfy the differential equation aoaa i +2a0a 2 +3a 2
**aa**3 +... - The two quadratic forms f, 4); the two discriminants (f, f')2,(0,4')2, and the first and second transvectants of f upon 4, (f,, >) 1 and (f, 402, which may be written (
**aa**)a x a x and (**aa**) 2 . - By March 18 the Bolsheviks were thrown back over the
**Aa**river. - A 1, A2 ï¿½ Ai, A 1 A 2, A2 and then Ao = al Ai+2a1a2AIA2+a2 A2 - (a1A1+a2A2) 2 = a?, A l = (a 1 A 1 +a2A2) (alï¿½l +a2ï¿½2) =
**aAa**ï¿½, A 2 = (alï¿½l +a2/-12) 2 = aM; so that A =**aa**l +2a A a u 152+aM5 2 = (aA6+a,e2)2; whence A1, A 2 become a A, a m, respectively and ?(S) = (a21+a,E2) 2; The practical result of the transformation is to change the umbrae a l, a 2 into the umbrae a s = a1A1 +a2A2, a ï¿½ = a1/ï¿½1 + a21=2 respectively. - 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-+... - = wj,
**aa**1**aa**2 a a 3 the complete system of equations satisfied by an invariant. - +a"
**aa**"-1 have been much studied by Sylvester, Hammond, Hilbert and Elliott (Elliott, Algebra of Quantics, ch. - L
**aa**k -x 2 d d- = 0; Z(nk)ak+l adk - x ldd2=0; or in the form d d 52-x 2(7 =0, O - x1ax2 = 0; where 0 = ao d a l + 2a 1 -?...+na,,_id an, 0 = nal dao -? - Thus (A +a) 2 = (A +a) (A+a) =A(A+a) +a(A+a)=
**AA**+**Aa**+**aA**+**aa**; and the grouping of the second and third terms as 2Aa involves treating**Aa**and**aA**as identical. - Thus (A +a) 2 = (A +a) (A+a) =A(A+a) +a(A+a)=
**AA**+**Aa**+**aA**+**aa**; and the grouping of the second and third terms as 2Aa involves treating**Aa**and**aA**as identical. - (b) In the same way, for the expansion of (
**Aa**)", let o, denote uo-u 1 +. **Aa**18 18- For the symbol which was used at Ephesus and other places in Asia Minor and elsewhere for the sound represented by -
**aa**- in Ionic Greek, by -TT- in Attic, see ALPHABET. - By similarly transforming the binary n ic form ay we find Ao = (aI A 1 +a2 A2) n =
**aAn**A l = (alAi - I -a 2 A 2) n1 (a1ï¿½1 +a2m2) =**aa**a ï¿½ - A i n-1 A2, n-k k n-k k n-k k A = (al l+a2A2) (alï¿½1+a2ï¿½2) = a A ï¿½ =A 1 A2, so that the umbrae A1, A 2 are a A, a ï¿½ respectively. - If a, a be the linear forms, above defined, he raises the identity ax(0) =ax(aJ3) - (3x(
**aa**) to the fifth power (and in general to the power n) obtaining (**aa**) 5 f = (a13) 5 az - 5 (a0) 4 (**aa**) ax?3 -F... - - (
**aa**) and then expresses the coefficients, on the right, in terms of the fundamental invariants. - 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. - Van der
**Aa**, Biographisch woordenboek der Nederlanden (22 vols., Haarlem, 1852-1878). - The sides of the square are 6 in., and the centres
**AA**are taken at 2 in. - Acetonyl-acetophenone, C6H5.CO.CH2.CH2.CO.CH3, is produced by condensing phenacyl bromide with sodium acetoacetate with subsequent elimination of carbon dioxide, and on dehydration gives
**aa-phenyl-methyl-furfurane**. - The minor Aik is
**aa**, and is itself a determinant of order n-t. - If 0 be the degree of an invariant j - aj aj a; oj =a ° a a o +al
**aa**l +... - V., established the important result that in the case of a form in n variables, the concomitants of the form, or of a system of such forms, involve in the aggregate n-1 classes of
**aa**=5135 4 +4B8 3 p) =0, =5(135 4 - 4A 2 p 4) =0, P yield by elimination of S and p the discriminant D =64B-A2. - From its intersection with A'A' arcs are struck cutting B in two points.
- (ab),
**aa**, ab, (xa), ax, xx. - These semicircles and the circles A'A' are joined by tangents and short arcs struck from the centre of the figure.
- Operation upon J results as follows D
**AA**J = wJ; D A J=0; D ï¿½A J =0;D ï¿½ï¿½ J = wJ.