In order that (ab)i(ac)j(bc)k...
Thus, if the molecule of a substance in solution is represented by AB, Grotthus considered a chain of AB molecules to exist from one electrode to the other.
Possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...
A young senator (ab actis senatus) was chosen to draw up these Acta, which were kept in the imperial archives and public libraries.
We may write (AB)i(AC)j(BC)k...
The eyepiece ab consists of two plano-convex lenses a, b, of nearly the same focal length, and with the two convex sides facing each other.
Now, if CD is pressed by its weight or by a spring on the surface AB, the effect of wear will be to produce a symmetrical grinding away of both surfaces, which may be represented thus, fig.
Some see the guarantee, or at least the indication, of infallibility in the consensus of the Church (quod semper, ubique, et ab omnibus) expressed from time to time in general councils; others see it in the special grace conferred upon St Peter and his successors, the bishops of Rome, as heads of the Church; others again see it in the inspired Scriptures, God's Word.
Quintus Curtius was largely used for the Alexandreis (c. 1180) of Gaultier de Lille or de Chatillon (Galtherus ab Insulis or de Castellione).
It was destroyed in 1260 by Llewellyn ab Gruffydd, prince of Wales, with the supposed connivance df Mortimer, but its site was reoccupied by the earl of Lincoln in 277, and a new castle at once erected.
Leading examples may be found in the various prosecutions of St Athanasius, in whose case also there is the germ of an appeal, tanquam ab abusu.
The appellatio tanquam ab abusu (appel comme d'abus) in France was an application of a like nature.
Censures were as follows: (i) Suspension from attending divine offices or ab ingressu ecclesiae, more appropriate for a layman.
(1) The taking away of all matrimonial, testamentary and ab intestate jurisdiction by 20 & 21 Vict.
Roman Catholic writers, 4 however, have explained the prohibition to apply to matters of faith only, and in that case the Tridentine decree is little else than another form of the Vincentian canon which has been widely accepted in the Anglican communion: curandum est ut id teneamus quod ubique, quod semper, quod ab omnibus creditum est.
Philastrius, however, says: hominem autem ab angelis factum asserit, while according to Epiphanus xxiv.
In that case, all who accept a revelation without professing to understand its content would require to be ranked as mystics; the fierce sincerity of Tertullian's credo quia ab-' surdum, Pascal's reconciliation of contradictions in Jesus Christ, and Bayle's half-sneering subordination of reason to faith would all be marks of this standpoint.
Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.
His father belonged to the class of Dihkans (the old native country families and landed proprietors of Persia, who had preserved their influence and status under the A ab rule), and possessed an estate in the neighbourhood of Cus (in Khorasan).
Ab, Abdominal ganglion or site pe, The right pedal nerve.
Ab, g, The limpet breeds upon the southern English coast in the early part of April, but its development has not been followed.
As there is a break ab, Abdominal ganglion.
434; quod ubique, quod semper, quod ab omnibus creditum est).
In the year 1147, we have the bard testifying to the supereminence of the Cid among his country's heroes: "Ipse Rodericus Mio Cid semper vocatus, De quo cantatur quod ab hostibus haud superatus, Qui domuit Mauros, comites domuit quoque nostros."
Among these posts were various procuratorships (chief of which was that of the imperial fisc), and the offices ab epistulis, a rationibus and a libellis (secretary, accountant, receiver of petitions).
Schurz, De mutationibus in imperio ordinando ab imp. Hadr. factis, i.
Let the curve represent an elliptic orbit, AB being the major axis, DE the minor axis, and F the focus in which the centre of attraction is situated, which centre we shall call the sun.
These early fortifications of the Acropolis, ascribed to the primitive non-hellenic Pelasgi, must be distinguished from the Pelasgicum or Pelargicum, which was in all prob ab i l i ty an encircling wall, built round the base of the g citadel and furnished with nine gates from which it derived the name of Enneapylon.
6), be the axes of temperature and pressure, and A corresponds to the transition point (95.6°) of rhombic sulphur, we may follow out the line AB which shows the elevation of the transition point with increasing pressure.
In nonflowering plants the works usually followed are for ferns, Hooker and Baker's Synopsis filicum; for mosses, Muller's Synopsis muscorum frondosorum, Jaeger & Sauerbeck's Genera et species muscorum, and Engler & Prantl's Pflanzenfamilien; for algae, de Toni's Sylloge algarum; for hepaticae, Gottsche, Lindenberg and Nees ab Esenbeck's Synopsis hepaticarum, supplemented by Stephani's Species hepaticarum; for fungi, Saccardo's Sylloge fungorum, and for mycetozoa Lister's monograph of the group. For the members of large genera, e.g.
In it he discusses the "notes" which distinguish Catholic truth from heresy, and (cap. 2) lays down and applies the famous threefold test of orthodoxy - quod ubique, quod semper, quod ab omnibus credi-tum est.
Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.
It should be noticed that the real function denoted by (ab) 2 is not the square of a real function denoted by (ab).
For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.
In either case (AB) =A 1 B 2 -A 2 B 1 = (A/2)(ab); and, from the definition, (ab) possesses the invariant property.
Since (ab) = a l b 2 -a 2 b l, that this may be the case each form must be linear; and if the forms be different (ab) is an invariant (simultaneous) of the two forms, its real expression being aob l -a l b 0.
This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.
When either of the forms is of an order higher than the first (ab), as not being expressible in terms of the actual coefficients of the forms, is not an invariant and has no significance.
(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...
= t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...
The expression (ab) 4 properly appertains to a quartic; for a quadratic it may also be written (ab) 2 (cd) 2, and would denote the square of the discriminant to a factor pres.