nth

(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.

10In the extensive calculus of the nth category, we have, first of all, n independent " units," el, e2, ...

10nth species.

13Gyula-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.

00Young 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.

00He 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.

00In 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.

00He 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.

00His 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.

00The papal bulls granting the use of mitres before the nth century are all forgeries (Liturgische Gewandung, 431-448).

00At last, on the nth of April, he wrote the deed of abdication.

00Finally, we reach a complex number of the nth order.

00On 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.

00As 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.

00bnn Mult ply the i st, 2nd nth rows by b 11, b 12, ...

00For in this case the n equations are not independent since identically Alï¿½ft+ A2ï¿½ f2+...+Anï¿½fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

00If 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.

00In 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.

00Hence the formula (2) is also true for the nth power of A-I-a.

00The (r+1)th figurate number of the nth order, i.e.

00the (r+ i) th number in the nth diagonal row, is n(n-}-1).

00But the nth term is (3n-I)(3n+2)=18nr 21 -6nr 11 - 2.

00(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.

00Thus the nth term of the series 2.5+5.8+8.11+...

00(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.

00(and, when necessary, of the nth category).

00Thus, 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

00If, 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.

00Local 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.

00(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).

000= {(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.

00But 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.

00de 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.

00The first raises its potential to v, the second to v' and so on, and the nth to V.

00(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.

00It 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.

00nth August.

00On 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.

00On the nth of August the wind, which had been westerly, turned to the S.E., giving him the weather gage.

00The 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.

00n, as the nth term of a new series, we obtain the series 1+2+3+..

00Taking this sum as the nth term, we obtain the series 1+3+6+10+..

00This 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) ...

00In the nth century a burgrave (chatelain, castellanus), who was an episcopal officer, is found exercising jurisdiction in the city as well as the Vogt.

00LOUIS BERTRAND CASTEL (1688-1757), French mathematician, was born at Montpellier on the nth of November 1688, and entered the order of the Jesuits in.

00It 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.

00The 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.

00For the first time we have a correct and convenient expression for Laplace's nth coefficient."

00The 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 ").

00123, of nth cent.; (4) Rome, Vatican Library, 2010; (5) Vienna, Hofu.

00There 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.

00- Clarke's it sinks to A), or nth under proof (as when it Hydrometer.

00emerges 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.

00The small divisions on the scale corresponded to differences of nth of a grain in the weight of the instrument.

00In 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.

00If 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.

00The 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.'

00The geometrical mean of n quantities is the nth root of their product.

00And, 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.

00The Norman kingdom, which had conquered Sicily and southern Italy at the end of the nth century, was almost as grave a source of anxiety to the popes of this period.

00In the nth century the town and district passed to the counts of Nassau, fell to the Walram line in 1255, and in 1355 Wiesbaden became with Idstein capital of the county Nassau-Idstein.

00A similar cement is a mixture of dried fresh curd with i nth of its weight of quicklime and a little camphor; it is made into a paste with water when employed.

00It belongs probably to the nth century.

00Normandy was the best-governed part of France in the nth century; and the Danes in East Anglia and the Five Burgs were in many regards a model to their Saxon neighbours (Steenstrup, op. cit.

00Beadnell, An Egyptian Oasis (London, 1909); Murray's Handbook for Egypt, nth ed.

00It is situated on the right bank of the river Theiss, and is historically known for the decisive victory won in its vicinity by Prince Eugene of Savoy over the Turks on the nth of September 1697.

00He has given by means of it a simple proof of the existence of n roots, and no more, in every rational algebraic equation of the nth order with real coefficients.

00Landing at Reggio di Calabria he hastened to Monza, where he conducted with firmness and tact the preparations for the burial of King Humbert and for his own formal accession, which took place on the 9th and nth of August 1900.

00In the early middle ages Assisi was subject to the dukes of Spoleto; but in the nth century it seems to have been independent.

00Our knowledge of the process and materials employed in niello-work is derived mainly from four writers,- Eraclius the Roman (a writer probably of the nth century), Theophilus the monk, who wrote in the 12th or 13th century,' and, in the 16th century, Benvenuto Cellini 2 and Giorgio Vasari.3 The design was cut with a sharp graving tool on the smooth surface of the metal, which was usually silver, but occasionally gold or even bronze.

00He ascertained the distribution of electricity among several spheres (whether equal or unequal) placed in contact in a straight line; and he measured the distribution of 2 In 1878 Clerk Maxwell repeated Cavendish's experiments with improved apparatus and the employment of a Kelvin quadrant electrometer as a means of detecting the absence of charge on the inner conductor after it had been connected to the outer case, and was thus able to show that if the law of electric attraction varies inversely as the nth power of the distance, then the exponent n must have a value of 2 t Isua.

00But though situated at a central point on Lake Malar, it was destroyed, apparently before the beginning of the nth century (exactly when or by whom is uncertain); and it never recovered.

00The difference between the continued fraction and the nth convergent is less than, and greater than a n+2 These limits qn may be replaced by the following, which, though not so close, are simpler, viz.

00In this case the sum to n terms of the series is equal to the nth convergent of the fraction.

00It has been sought at under the names of ` quinti-clave ' and ` ophicleide, ' they bear a great resemblance to those submitted to the Academy in the sitting of the nth of March 1811 by M.

00The Breviary rightly so called, however, only dates from the nth century; the earliest MS. containing the whole canonical office is of the year 1099 and is in the Mazarin library.

00Ricardo died on the nth of September 1823, at his seat (Gatcomb Park) in Gloucestershire, from a cerebral affection resulting from disease of the ear.

00The king died of this disease on the nth of November 1861, and two of his brothers, D.

00Thus, by the nth century, the Lombard cities had become "communes," commonalties, republics, managing their own affairs, and ready for attack or defence.

00Beginning with the examples of the nth and 12th centuries, we find the subjects generally of an archaic style, which is evidence of an early stage of the art.

00He died on the nth of November 1886.

00The average date of the first killing frost at Dover is the 4th of October, and of the last, the loth of May; at Atlantic City, on the sea-coast, these dates are respectively the 4th of November and the nth of April.

00The bones of St Kilian, the patron saint of Wiirzburg, are preserved in the Neumiinster church, which dates from the nth century; Walther von der Vogelweide is buried in the adjoining cloisters.

00MACEDONIO MELLONI (1798-1854), Italian physicist, was born at Parma on the nth of April 1798.

00He died at Portici near Naples of cholera on the nth of August 1854.

00His professional income as a lawyer was estimated at $ioo,000 per annum shortly before his death at Washington, D.C., on the nth of January 1893.

00The only countries where the order plays a distinctly subordinate part are some extra-tropical regions of the southern hemisphere, Australia, the Cape, Chili, &c. The proportion of graminaceous species to the whole phanerogamic flora in different countries is found to vary from nearly 4th in the Arctic regions to about 2 nth at the Cape; in the British Isles it is about y2th.

00Notre-Dame du Fort, the chief church, dates from the nth and 12th' centuries; irregular in plan, it is remarkable for a fine Romanesque tower and spire, and for the crenellated wall which partly surrounds it.

00Suppose that the weight of the goods on the platform is (p) lb, and that nth of this weight is transmitted by the long body lever to the point A, so that I l i lb is the pull at A.

00He died at Guadalajara on the nth of January 1495.

00On the nth of September the advance-guard of their army crossed the Drave under the command of Jellachich.

00They consist essentially of a galvanometer of which the needle or coil has such a short natural periodic time that it can follow all the variations of a current which runs through its cycle in say i;nth second.

00MINT PASTY (Traditional recipe from Nth England) 2 cups fine chopped mint 2 cups currants 2 cups brown sugar Pastry.

00nth degree.

00nth root of R without causing problems.

00nth term of a sequence.

00nth word ).

00nth time about me.

00nth dimension is selected for vectorization.

00At 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.

00For in this case the n equations are not independent since identically AlÃ¯¿½ft+ A2Ã¯¿½ f2+...+AnÃ¯¿½fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

00If 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 +Ã¯¿½Ã¯¿½Ã¯¿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.

00(a+r+ p - i Ã¯¿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.

00than 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.

00(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 Ã‚° - z=klog po - z= - k log(1 - k) - zt12 k (20) Po as before in 17).

00over an ellipsoid, so that its density is everywhere proportional to the thickness of a shell formed by describing round ' The solution of the problem of determining the distribution en an ellipsoid of a fluid the particles of which repel each other with a force inversely as the nth power of the distance was first given by George Green (see Ferrer's edition of Green's Collected Papers, p. 119, 1871).

00The plummet is now placed in distilled water at 15Ã‚°, 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.

00Early in the nth century Sigmund or Sigismund Bresterson, whose family had flourished in the southern islands but had been almost exterminated by See Hans von Post, "Om FarOarnes uppkomst," Geologiska Foreningens i Stockholm FOrhandlingar, vol.

00Canned and frozen vegetables may not contain even an nth of the vitamins they naturally have.

00Scholars 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.

01

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