# Ac Sentence Examples

**Ac**. Soc., Paris, xiv., 1856; E.- Fraknoi, The Embassies of Cardinal Carvajal to Hungary (Hung., Budapest, 1889); Marzio Galeotti, De egregie sapienter et jocose dictis
**ac**factis Matthiae regis (Script. - In his extensive work Tractatus de legibus
**ac**deo legislatore (reprinted, London, 1679) he is to some extent the precursor of Grotius and Samuel Pufendorf. **According**to Juvenal the sons of such proselytes were apt to go farther and to substitute the Jewish Law for the Roman Romanas autem soliti contemnere leges; Judaicum ediscunt et servant**ac**metuunt ius Tradidit arcano quodcunque volumine Moyses.- Passenger steamship service was transferred to a new 5
**ac**. pier on the lake front, built at a cost of $500,000. - Hemlock Spruce (Tsuga caibu.
**ac**usw). **Ac**to pc, Mouth of the shell.**Ac**. Sc. Turin, ideas in this are said to have been taken from Illiger; but the two systems seem to be wholly distinct.- Herold's edition (Originum
**ac**Germanicarum antiquitatum libri, Basel, 1557), which has been reproduced by Karl von Richthofen in the Mon. - The university of Pittsburgh, established in 1908 by assembling the scattered departments of what was the Western University of Pennsylvania, and taking over 43
**ac**. near the Carnegie Institute for a campus, grew rapidly in its new location, and in 1920 numbered 4,979 students. - From meta-brombenzoicacid two nitrobrombenzoic
**ac**i ds are obtained on direct nitration; elimination of the bromine atom and the reduction of the nitro to an amino group in these two**acids**results in the formation of the same ortho-aminobenzoic**acid**. - The overheating curve of rhombic sulphur extends along the curve
**AC**, where C is the melting-point of monoclinic sulphur. - Coronelli, appointed cosmographer of the Venetian Republic, 1685, and founder of the
**Ac**. Cosmogr. - -
**Ac**ROT [[Retidae, Siphonotretidae, Trematidae, Discinidae, Craniidae]]. - Is transformed into the operator d 1 by the substitution (
**ac**, al, a2, ï¿½ï¿½ï¿½as, ï¿½ï¿½ï¿½) _ (ao, Xoai, X 6 X i a 2, ï¿½ï¿½ï¿½, XcX1..%s_las,ï¿½ï¿½ï¿½), so that the theory of the general operator is coincident with that of the particular operator d1. - We may write (AB)i(
**AC**)j(BC)k... - (ab)i(
**ac**)j(bc)k..., that the symbolic product (ab)i(**ac**)j(bc)k..., possesses the invariant property. - Notice, therefore, that the symbolic product (ab)i(
**ac**)j(bc)k... - In order that (ab)i(
**ac**)j(bc)k... - Possess the invariant property, and we may write (AB) i (
**AC**)'(BC) k ...A P E B C... - = t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(
**ac**)'(bc)k...aibxc2... - (IV.) and herein writing d 2, -d 1 for x l, x2, 2 (
**ac**) (bc) (ad) (bd) = (bc) 2 (ad) 2 +(**ac**) 2 (bd) 2 - (ab) 2 (cd) 2. - 2 (
**ac**)(bc)anx xibn-i -1 x = (bc)2anbn-2Cn-2 + (**ac**)2an x x x The weight of a term ao°a l l ...an n is defined as being k,+2k2+... - -2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may
**accordingly**write 2(**ac**) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ. - (ab)(
**ac**)bxcx = - (ab)(bc)axcx = 2(ab)c x {(**ac**)bx-(bc)axi = 1(ab)2ci; so that the covariant of the quadratic on the left is half the product of the quadratic itself and its only invariant. - To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(
**ac**)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically. - For two factors the standard form is (ab) 2; for three factors (ab) 2 (
**ac**); for four factors (ab) 4 and (ab) 2 (cd) 2; for five factors (ab) 4 (**ac**) and (ab) 2 (**ac**)(de) 2; for six factors (ab) 6, (ab) 2 (bc) 2 (ca) 2, and (ab) 2 (cd) 2 (ef) 2 . - If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (
**ac**) by c x and so on. - From (
**ac**) 2 (bd) 2 (ad)(bc) we obtain (bd) 2 (bc) cyd x +(**ac**) 2 (ad) c xdx - (bd) 2 (ad)axb x - (**ac**)2(bc)axbx =4(bd) 2 (bc)c 2. - When R =0, and neither of the expressions
**AC**- B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =**AC**- B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx. - Of the quadratic axe+2bxy+cy2, he discovered the two invariants
**ac-b**2, a-2b cos w+c, and it may be verified that, if the transformed of the quadratic be AX2=2BXY+CY2, sin w 2**AC**-B 2 =) (**ac-**b2), sin w A-2B cos w'+C = (sin w'1 2(a - 2bcosw+c). - Of the quadratic axe+2bxy+cy2, he discovered the two invariants
**ac-b**2, a-2b cos w+c, and it may be verified that, if the transformed of the quadratic be AX2=2BXY+CY2, sin w 2**AC**-B 2 =) (**ac-**b2), sin w A-2B cos w'+C = (sin w'1 2(a - 2bcosw+c). - The general form of covariant is therefore (ab) h i (
**ac**) h2 c) (b h3 a i bb2c'e3...abia?2b?3... - 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,... - On the surface of the carapace there are in both animals a pair of central eyes with simple lens and a pair of lateral eyetracts, which in Limulus consist of closely-aggregated simple eyes, forming a " compound" eye, whilst in Scorpio they present several
**AC**separate small eyes. **AC**, Arterial canal or foramen.- 16 1920); (b) about 40,000 owners of small holdings, averaging from 26 to 150
**ac**., formed the backbone of the Lettish middle class, and the liberal professions (nicknamed the " grey barons ") were partly supported by about 10,000 tenants of small farms; (c) the owners of very small holdings in Latgalia and Courland numbered some 10,600. - 4,091,490
**ac**., only 2,978,570 were under cultivation in 1920, with 473,410**ac**. under winter rye against 862,400 in 1913. - Lands with an
**acreage**below 246**ac**. are not expropriated. - To this list must be added: (I) the Satyricon of Martianus Capella, the greater part of which is a treatise on the seven liberal arts, the fourth book dealing with logic; (2) the De artibus
**ac**disciplinis liberalium literarum of Cassiodorus; (3) the Origines of Isidore of Seville (ob. **Ac**. xxv.; W.**Ac**cording to Molengraaff it includes the two following series: - An upper group including the auriferous conglomerates of the Rand: Witwatersrand Series.- Therwise, if A is positive rt= J y-s1 (A+2By+Cy') dy sh1 A'/ (A+2By+Cy 2) I ch1 A+By (26) -V A ch1 31, (B2--
**AC**) - A sh - 1 (B2-**AC**)' nd the axis falls away ultimately from its original direction. - Herold at Basel in 1557 (Originum
**ac**Germanicarum antiquitatum libri) from a MS. now lost, is founded on the second recension, but contains additions of considerably later date. - Everyone wants to come in and enjoy your
**AC**and play on your Wii. - Authore
**ac**Inventore Ioanne Nepero, Barone Merchistonii, &c., Scoto. - The cable is supposed to be worked duplex; but, if 5, C1, C2, and
**AC**are removed and the key connected directly with C3, the arrangement for simplex working is obtained. - The peculiar construction of
**AC**has been already referred to. - Endoderm, containing the st, Stomach, which in H
**ac**coelenteric cavity (cod), quires a secondary com while the outer layer munication with the diges furnishes the future ectotive cavity of the mother. - The spadix forms a gelatinous cyst, the so-called
**acrocyst**(**ac**), external to the gonotheca (gth), enclosing and protecting the embryos. - In B the spadix of the upper bud has protruded itself through the top of the gonoat the base of the theca and the
**acrocyst**(**ac**) is secreted round it. - The expectation entertained in many III.;
**ac**- quarters that great legislative changes would at once of be made in a liberal sense was not realized. **Ac**, Siphonal notch of the mouth of the shell.**Ac**. d.- Thus to obtain the resultant of aox 3 +a i x 2 +a 2 x+a 3, 4, =box2+bix+b2 we assume the identity (Box+Bi)(aox 3 +aix 2 +a2x+a3) = (Aox 2 +Aix+ A 2) (box2+bix+b2), and derive the linear equations Boa ° -
**Ac**b o = 0, Boa t +B i ao - A 0 b 1 - A 1 bo =0, Boa t +B 1 a 1 - A0b2 - A1b1-A2b° = 0, Boa3+Bla2 - A l b 2 -A 2 b 1 =0, B 1 a 3 - A 2 b 2 =0, = = (y l, y2,...ynl `x1, x2,...xnl for brevity.