# Nth Sentence Examples

- (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. - 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. - 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). - 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. - (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. - (2) (3) Suppose the density p varies as some
**nth**power of the depth below 0, then (7) and the lowering of the surface is 2 ° - z=klog po - z= - k log(1 - k) - zt12 k (20) Po as before in 17). - 0= {(n +I)Ar" - where P. denotes the zonal harmonic of the
**nth**order; also, in the exceptional case of =Ao cos 0, 4) = Ao/r; 4'= Bor, 49 = - Bo log tan 2B sh - lx/y. - But the military development and real importance of Pisa in the
**nth**century must be attributed to the continuous and desperate struggle it maintained against the tide of Saracenic invasion from Sicily. - De l'Afrique, &c., by Dozy and De Goeje, Leiden, 1866) belong to the loth,
**nth**and 12th centuries respectively; the history of Ibn Khaldun (Hist. - The first raises its potential to v, the second to v' and so on, and the
**nth**to V. - (17) in which c is a small quantity (expressing the defect from the ideal volume V =Re/p due to co-aggregation of the molecules) which varies inversely as the
**nth**power of 0, but is independent of p to a first approximation at moderate pressures. - It is not necessary to suppose that c varies inversely as the
**nth**power of the temperature, and that b is constant, as assumed in deducing the expressions for cp, E, and F. **Nth**August.- On the
**nth**of June he was included by the House of Commons, in spite of a recommendatory letter from Monk, among the twenty persons excepted from the act of indemnity and subject to penalties not extending to life. - On the
**nth**of August the wind, which had been westerly, turned to the S.E., giving him the weather gage. - The plummet is now placed in distilled water at 15°, and the beam brought to equilibrium by means of a rider, which we shall call I, hung on a hook; other riders are provided,;
**nth**and ii b th respectively of I. - N, as the
**nth**term of a new series, we obtain the series 1+2+3+.. - Taking this sum as the
**nth**term, we obtain the series 1+3+6+10+.. - This sum is taken as the
**nth**term of the next series, and proceeding in this way we obtain series having the following**nth**terms: I, n, n(n+1) /21, n(n+i) (n+2) /3 !,...n(n+1) ... - In the
**nth**century a burgrave (chatelain, castellanus), who was an episcopal officer, is found exercising jurisdiction in the city as well as the Vogt. - LOUIS BERTRAND CASTEL (1688-1757), French mathematician, was born at Montpellier on the
**nth**of November 1688, and entered the order of the Jesuits in. - After 1/
**nth**of a revolution, the two sets of perforations will again coincide, the lateral impulse of the air repeated, and hence the rapidity of rotation increased. - It was in this house that Lord Howe on the
**nth**of September 1776 held a peace conference with Benjamin Franklin, John Adams, and Edward Rutledge representing the Continental Congress. - The definition of the coefficients is that if (I-2h cos cp+h 2)-i be expanded in ascending powers of h, and if the general term be denoted by P„h', then P is of the Legendrian coefficient of the
**nth**order. - For the first time we have a correct and convenient expression for Laplace's
**nth**coefficient." - The Juarists were defeated outside the city of Mexico twice, in October 1858 and on the
**nth**of April 1859, On the second occasion the whole body of officers, who had surrendered, were shot with Miramon's authority, if not by his express orders, together with several surgeons (including one Englishman, Dr Duval) (the fifty-three " martyrs of Tacubaya "). - 123, of
**nth**cent.; (4) Rome, Vatican Library, 2010; (5) Vienna, Hofu. - 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. - The small divisions on the scale corresponded to differences of
**nth**of a grain in the weight of the instrument. - 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. - 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. - 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.' - The geometrical mean of n quantities is the
**nth**root of their product. - 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. **Nth**species.- Scholars desiring to explore for themselves the sources of Polish history from the
**nth**century to the 18th have immense fields of research lying open before them in the Acta historica res gestas Poloniae illustrantia (1878, &c.), the Scriptores rerum polonicarum (1872, &c.), and the Historical Dissertations (Pol., 1874, &c.), all three collections published, under the most careful editorship, by the University of Cracow.