## 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. **Ac**paioipwv vi)oot: Lat., Fortunatae Insulae), in Greek mythology a group of islands near the edge of the Western Ocean, peopled not by the dead, but by mortals upon whom the gods had conferred immortality.- 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... - (III.) Again in (I.) transposing a x (bc) to the other side and squaring, we obtain 2(
**ac**) (bc)axbx = (bc) 2 a'+(**ac**) 2 bx- (ab) 2 c1. - (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 . - Put M 1 For M, N I For N, And Multiply Through By (Ab); Then { (F, C6) } = (Ab) A X 2A Y B X 1 M N I 2 (Xy), ?) 2, = (A B)Ax 1B X 2B Y L I Multiply By Cp 1 And For Y L, Y2 Write C 2, C1; Then The Right Hand Side Becomes (Ab)(Bc)Am Lbn 2Cp 1 M I C P (F?) 2 M { N2 X, Of Which The First Term, Writing C P =, ,T, Is Mn 2 A B (Ab)(Bc)Axcx 1 M 2 N 2 P 2 2222 2 2 _2 A X B X C (Bc) A C Bx M N 2 2 2 M2°N 2 N 2 M 2 2 A X (Bc) B C P C P (Ab) A B B(
**Ac**) Ax Cp 2 = 2 (04) 2 1 (F,0) 2.4 (F,Y') 2 ï¿½?; And, If (F,4)) 1 = Km " 2, (F??) 1 1 M N S X X X Af A _Af A Ax, Ax Ax Ax1 Observing That And This, On Writing C 2, C 1 For Y 11 Y 21 Becomes (Kc) K X 'T 3C X 1= (F,0 1 ', G 1; ï¿½'ï¿½1(F,O) 1 M 1=1 M 2 0`,4)) 2 0, T (Fm 2.4 (0,0 2 .F ' And Thence It Appears That The First Transvectant Of (F, (P) 1 Over 4) Is Always Expressible By Means Of Forms Of Lower Degree In The Coefficients Wherever Each Of The Forms F, 0, 4, Is Of Higher Degree Than The First In X 1, X2. - 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. - 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. - 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. **Ac**cording to Molengraaff it includes the two following series: - An upper group including the auriferous conglomerates of the Rand: Witwatersrand Series.**Ac**. xxv.; W.- 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. - Lands with an
**acreage**below 246**ac**. are not expropriated. - 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. - 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.- 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).