In the extensive calculus of the nth category, we have, first of all, n independent " units," el, e2, ...
Gyula-Fehervar is the seat of a Roman Catholic bishop, and has a fine Roman Catholic cathedral, built in the 1 nth century in Romanesque style, and rebuilt in 5443 by John Hunyady in Gothic style.
At the close of the nth century the system of feudal states had been firmly established in the Netherlands under stable dynasties hereditary or episcopal, and, despite the The continual wars between them, civilization had begun to crusades.
Young advised them to call their state Vermont, and he also sent through them a circular letter, dated the nth of April 1777, urging the people to adopt a state constitution on the Pennsylvania model.
He was, however, sentenced to be hanged on the 12th of November; but on the nth he cut his throat with a penknife, and on the 19th of November 17 9 8 he died of the wound.
In Burma, on the other hand, where Pali was probably introduced from Ceylon, no writings in Pali can be dated before the nth century of our era.
He was instrumental in saving New York and Vermont from invasion by his brilliant victory of lake Champlain gained, on the nth of September 1814, with a flotilla of 14 vessels carrying 86 guns, over Captain George Downie's 16 vessels and 92 guns.
His system was' adopted by Abu'l-walid ibn Jannah, of Saragossa (died early in the nth century), in his lexicon (Kitab al-usul, in Arabic) and other works.
The papal bulls granting the use of mitres before the nth century are all forgeries (Liturgische Gewandung, 431-448).
At last, on the nth of April, he wrote the deed of abdication.
Finally, we reach a complex number of the nth order.
On the 12th of April Wellington advanced to invest Toulouse from the south, but Soult on the night of the nth had retreated towards Villefranque, and Wellington then entered the city.
As early as the nth century the Novgorodians had occasionally penetrated into Siberia; but the fall of the republic and the loss of its north-eastern dependencies checked the advance of the Russians across the Urals.
Bnn Mult ply the i st, 2nd nth rows by b 11, b 12, ...
THE Theory Of Binary Forms A binary form of order n is a homogeneous polynomial of the nth degree in two variables.
If the variables of the quantic f(x i, x 2) be subjected to the linear transformation x1 = a12Et2, x2 = a21E1+a2252, E1, being new variables replacing x1, x 2 and the coefficients an, all, a 21, a22, termed the coefficients of substitution (or of transformation), being constants, we arrive at a transformed quantic f% 1tn n n-1 n-2 52) = a S +(1)a11 E 2 + (2)a2E1 E 2 +ï¿½ï¿½ï¿½ in the new variables which is of the same order as the original quantic; the new coefficients a, a, a'...a are linear functions 0 1 2 n of the original coefficients, and also linear functions of products, of the coefficients of substitution, of the nth degree.
In 1861 he was appointed United States consul at Trieste, but ill-health compelled him to resign and remove to Florence, where he died on the nth of July 1865.
Hence the formula (2) is also true for the nth power of A-I-a.
The (r+1)th figurate number of the nth order, i.e.
The (r+ i) th number in the nth diagonal row, is n(n-}-1).
(ii.) In the same way, if we multiply the table by c, the sum of the first n numbers in any column is equal to the nth number in the next following column.
But the nth term is (3n-I)(3n+2)=18nr 21 -6nr 11 - 2.
(vi.) It follows that, if two multinomials of the nth degree in x have equal values for more than n values of x, the corresponding coefficients are equal, so that the multinomials are equal for all values of x.
Thus the nth term of the series 2.5+5.8+8.11+...
(a+r+ p - i ï¿½b), we divide the product of the p+1 factors which occur either in the nth or in the (n+i)th term by p+ 1, and by the common difference of the factors, and add to a constant, whose value is found by putting n= o.
Than the nth root of their product) we show that if any two are unequal their product may be increased, without altering their sum, by making them equal, and that if all the numbers are equal their arithmetic mean is equal to their geometric mean.
(and, when necessary, of the nth category).
Thus, for instance ei.e2e3 = l e 2 .e 3 = ele2e3 = - e2eie3 = e2e3e1; and, in general, the number of distinct units of the rth species in the nth category (r
If, in the extensive calculus of the nth category, all the units (including i and the derived units E) are taken to be homologous instead of being distributed into species, we may regard it as a (2'-I)-tuple linear algebra, which, however, is not wholly associative.
In the nth century Desiderius, abbot of Monte Casino, sent to Constantinople for workers in mosaic.
Local tradition attributes the establishment of a permanent camp at this spot to Julius Caesar, but Louvain only became important in the nth century as a place of residence for the dukes of Brabant.
And, again, if this transaction settled the investiture question, it did not solve the problem of the reconciliation of the universal power of the popes with the claims of the emperors to the government of Europe; and the conflict subsisted - slumbering, it is true, but ever ready to awake under other forms. Nevertheless, the two great Christian agitations directed by the papacy at the end of the nth century and the beginning of the 12th - the reformation and the crusade - were of capital importance for the foundation of the immense religious monarchy that had its centre in Rome; and it is from this period that the papal monarchy actually dates.
The geometrical mean of n quantities is the nth root of their product.
If on emergence the different portions he brought together at the focus it is obvious that the optical action must be in every respect similar to that of a grating when the nth order of spectrum is considered.
The optical effect as regards resolving power is the same as with a grating of N lines in the nth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders.'
Sir Thomas Wardle of Leek, in his handbook on silk published in 1887, showed by a series of measurements that the diameter of a single cocoon thread or bave varied from o oth to -nth part of an inch in diameter in the various species of Bombycides, whilst those of the Saturnides or wild species varied from - 0 oth to 3-0 0 th part of an inch.
In the nth century it became the seat of the Eppenstein family, who frequently bore the title of counts of Gorizia; and in the beginning of the 12th century the countship passed from them to the Lurngau family which continued to exist till the year 1500, and acquired possessions in Tirol, Carinthia, Friuli and Styria.
The small divisions on the scale corresponded to differences of nth of a grain in the weight of the instrument.
There are two other marks, A and B, at top and bottom of the stem, to show whether the liquor be nth above proof (as when FIG.
- Clarke's it sinks to A), or nth under proof (as when it Hydrometer.
Emerges to B), when a brass weight such as C has been screwed on to the bottom at There are a great many such weights, of different sizes, and marked to be screwed on instead of C, for liquors that differ more than nth from proof, so as to serve for the specific gravities in all such proportions as relate to the mixture of spirituous liquors, in all the variety made use of in trade.
123, of nth cent.; (4) Rome, Vatican Library, 2010; (5) Vienna, Hofu.