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hessian

But if the given curve has a node, then not only the Hessian passes through the node, but it has there a node the two branches at which touch respectively the two branches of the curve; and the node thus counts as six intersections; so if the curve has a cusp, then the Hessian not only passes through the cusp, but it has there a cusp through which it again passes, that is, there is a cuspidal branch touching the cuspidal branch of the curve, and besides a simple branch passing through the cusp, and hence the cusp counts as eight intersections.

98by the Prussian Rhine province and the Hessian province of Rhein-Hessen; on the E.

89This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.

67The Hessian in that case is a factor of f, and Q is the third power of u2,...

56The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.

56In 1864 he went as Hessian envoy to Vienna, retiring in 1872 when the post was abolished.

512Hundreds of acres of wheat are lost annually in America by the ravages of the Hessian fly; the fruit flies of Australia and South Africa cause much loss to orange and citron growers, often making it necessary to cover the trees in muslin tents for protection.

35Many reforms in ecclesiastical, educational, financial and administrative matters were introduced, and in general the grand-duchy may be said to have passed largely under the influence of Prussia, which, by an arrangement made in 1896, controls the Hessian railway system.

312This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic f.

22For it is easy to establish] the formula (yx) 2 0 4 = 2f.4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?

23-, reduce s x2ax1 -x10x2 to the form j Oz ON 2 1 1 j 2 i The Binary Quintic.-The complete system consists of 23 forms, of which the simplest are f =a:; the Hessian H = (f, f') 2 = (ab) 2axbz; the quadratic covariant i= (f, f) 4 = (ab) 4axbx; and the nonic co variant T = (f, (f', f") 2) 1 = (f, H) 1 = (aH) azHi = (ab) 2 (ca) axbycy; the remaining 19 are expressible as transvectants of compounds of these four.

23f= ai; the Hessian H = (ab) 2 azbx; the quartic i= (ab) 4 axb 2 x; the covariants 1= (ai) 4 ay; T = (ab)2(cb)aybyci; and the invariants A = (ab) 6; B = (ii') 4 .

23The Hessian is symbolically (abc) 2 azbzcz = H 3, and for the canonical form (1 +2m 3)xyz-m 2 (x 3 +y 3 +z 3).

23What this means is that the Hessian lines are managed by the Prussian department.

23For it is easy to establish] the formula (yx) 2 0 4 = 2f.4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?

23It was recovered by the landgrave of Thuringia in 1388, but soon reverted to Hesse, and it became the residence of one of the branches of the Hessian royal house, a branch which died out in 1655.

24The French army, similarly arrayed, but with a few battalions attached to the cavalry wings, was more heterogeneous than the German, being composed of French, Hessian, German mercenaries, and Liegeois.

11Prussia, on the other hand, announced its determination to carry out the principles of the Union and to maintain the Hessian constitution.

11The quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian vanishes identically; and conversely.

12Gordan has also shown that the vanishing of the Hessian of the binary n ic is the necessary and sufficient condition to ensure the form being a perfect n th power.

12When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

12from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.

12Chief among these is the barracks, erected by the colony in 1758 to mitigate the evils of billeting, and occupied by British troops during the Seven Years' War, and at different times by British, Hessian and American troops during the War of Independence.

12Intellectual interests of a high order have always characterized, Leipzig, and what Karl von Holtei once said of it is true to-day: "There is only one city in Germany that represents Germany; only a single city where one can forget that he is a Hessian, a Bavarian, a Swabian, a Prussian or a Saxon; only one city where, amid the opulence of the commercial world with which science is so gloriously allied, even the man who possesses nothing but his personality is honoured and esteemed; only one city, in which, despite a few narrownesses, all the advantages of a great, I may say a world-metropolis, are conspicuous !

12Gordan has also shown that the vanishing of the Hessian of the binary n ic is the necessary and sufficient condition to ensure the form being a perfect n th power.

12He first studied theology at Giessen, but after the campaign of 1814, in which, like his brother August, he took part as a Hessian volunteer, began the study of jurisprudence, and in 1818 established himself as Privatdocent of civil law at Giessen.

13For a short while he was at the head of the new Hessian administration; but his ambition was to share in the creation of a united Germany.

13American literature began as far back as 1788, when a report on the Hessian fly was issued by Sir Joseph Banks; in 1817 Say began his writings; while in 1856 Asa Fitch started his report on the " Noxious Insects of New York."

13For a short while he was at the head of the new Hessian administration; but his ambition was to share in the creation of a united Germany.

13The best-known dipterous pests are the Hessian fly (Cecidosnyia destructor), the pear midge (Diplosis pyrivora), the fruit flies (Tephritis Tyroni of Queensland and Halterophora capitata or the Mediterranean fruit fly), the onion fly (Phorbia cepetorum), and numerous corn pests, such as the gout fly (Chloropstaeniopus) and the frit fly (Oscinis frit).

15The Hessian 0 =A 2 is such that (f, 2 and if f is expressible in the form X(p x) 3 +,i(g x) 3, that is as the sum of two perfect cubes,.

17In general for a form in n variables the Hessian is 3 2 f 3 2 f a2f ax i ax n ax 2 ax " ï¿½ï¿½ ' axn and there is a remarkable theorem which states that if H =o and n=2, 3, or 4 the original form can be exhibited as a form in I, 2, 3 variables respectively.

110The badge is an open oval of gold with the Hessian lion in the centre.

116The badge is an open oval of gold with the Hessian lion in the centre.

116For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

00the Hessian (0 a 2 -al)xi + (a 0 a 3 -ala2)xlx2+ (a l a i - a2)x2.

00The second transvectant of a form over itself is called the Hessian of the form.

00When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

00The above approximation for the error bars rests on a gaussian approximation which assumes that the Hessian A is positive definite.

00Bought in this state, the wool arrived in 150 Kg hessian wrapped bales (not very moveable ).

00I worked the lid off and the ripping sound of hessian against hessian brought the old busybody bustling back down the stall.

00A hessian backed wool carpet square (2 ' x 2 ') is a very useful thing to have for many purposes.

00Derivatives of scalar fields: Gradient, directional derivatives of scalar fields: Gradient, directional derivative; applications including classification of max, min and saddle using Hessian.

00Hessian backed.

00This effect is fairly common if in addition the starting Hessian is also poorly defined.

00A number of mechanisms are available to define or calculate the initial Hessian: 1. On the VARIABLE definition lines of the ZMATRIX.

00Hessian used to protect brickwork.

00For Newton-Raphson calculations, the inverse Hessian is output after each exact recalculation, but not after updating.

00This may involve the application of damp Hessian or more usually a spray applied curing membrane.

00Hessian eigenmodes contribute with a weighting according to their eigenvalue.

00Hessian sack lined with straw.

00Topic: Hessian Type: Keyword Use: Causes details of the hessian matrix to be output.

00Hessian bag for kerbside collection.

00Hessian commands.

00Hessian element for the variable specified is set to this number.

00Correspondingly the minimiser will therefore default to BFGS starting from a unit Hessian.

00To address problems that arise in the resultant optimization we introduce a technique called spherical normalization that preconditions the Hessian matrix.

00As children they played by the Hessian bales of asbestos at the nearby railhead and played on the open tips around Harridge mill.

00Two ladies (Mrs Burgess and Mrs Hall) were employed to sew up and mend the Hessian sacks - quite a messy job.

00snuggled deeper in his hessian blanket and dreamed of rabbits fighting pirates on the high seas.

00He first studied theology at Giessen, but after the campaign of 1814, in which, like his brother August, he took part as a Hessian volunteer, began the study of jurisprudence, and in 1818 established himself as Privatdocent of civil law at Giessen.

00Already at the universities he had proclaimed his Liberal sympathies as a member of the Burschenschaft, and he now threw himself into open opposition to the unconstitutional spirit of the Hessian government, an attitude which led to his dismissal from the state service in 1833.

00In 1864 he went as Hessian envoy to Vienna, retiring in 1872 when the post was abolished.

00American literature began as far back as 1788, when a report on the Hessian fly was issued by Sir Joseph Banks; in 1817 Say began his writings; while in 1856 Asa Fitch started his report on the " Noxious Insects of New York."

00The best-known dipterous pests are the Hessian fly (Cecidosnyia destructor), the pear midge (Diplosis pyrivora), the fruit flies (Tephritis Tyroni of Queensland and Halterophora capitata or the Mediterranean fruit fly), the onion fly (Phorbia cepetorum), and numerous corn pests, such as the gout fly (Chloropstaeniopus) and the frit fly (Oscinis frit).

00Hundreds of acres of wheat are lost annually in America by the ravages of the Hessian fly; the fruit flies of Australia and South Africa cause much loss to orange and citron growers, often making it necessary to cover the trees in muslin tents for protection.

00It was recovered by the landgrave of Thuringia in 1388, but soon reverted to Hesse, and it became the residence of one of the branches of the Hessian royal house, a branch which died out in 1655.

00Many reforms in ecclesiastical, educational, financial and administrative matters were introduced, and in general the grand-duchy may be said to have passed largely under the influence of Prussia, which, by an arrangement made in 1896, controls the Hessian railway system.

00For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

00the Hessian (0 a 2 -al)xi + (a 0 a 3 -ala2)xlx2+ (a l a i - a2)x2.

00The second transvectant of a form over itself is called the Hessian of the form.

00In general for a form in n variables the Hessian is 3 2 f 3 2 f a2f ax i ax n ax 2 ax " Ã¯¿½Ã¯¿½ ' axn and there is a remarkable theorem which states that if H =o and n=2, 3, or 4 the original form can be exhibited as a form in I, 2, 3 variables respectively.

00The Hessian 0 =A 2 is such that (f, 2 and if f is expressible in the form X(p x) 3 +,i(g x) 3, that is as the sum of two perfect cubes,.

00we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +Ã¯¿½(g x) 3 and immediately solved.

00This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic f.

00The Hessian in that case is a factor of f, and Q is the third power of u2,...

00The quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian vanishes identically; and conversely.

00This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.

00The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.

00-, reduce s x2ax1 -x10x2 to the form j Oz ON 2 1 1 j 2 i The Binary Quintic.-The complete system consists of 23 forms, of which the simplest are f =a:; the Hessian H = (f, f') 2 = (ab) 2axbz; the quadratic covariant i= (f, f) 4 = (ab) 4axbx; and the nonic co variant T = (f, (f', f") 2) 1 = (f, H) 1 = (aH) azHi = (ab) 2 (ca) axbycy; the remaining 19 are expressible as transvectants of compounds of these four.

00f= ai; the Hessian H = (ab) 2 azbx; the quartic i= (ab) 4 axb 2 x; the covariants 1= (ai) 4 ay; T = (ab)2(cb)aybyci; and the invariants A = (ab) 6; B = (ii') 4 .

00The Hessian is symbolically (abc) 2 azbzcz = H 3, and for the canonical form (1 +2m 3)xyz-m 2 (x 3 +y 3 +z 3).

00When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

00When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

00from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.

00denominator factors, that the complete system of the quadratic is composed of the form itself of degree order I, 2 shown by az 2, and of the Hessian of degree order 2, o shown by a2.

00Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.

00by the Prussian Rhine province and the Hessian province of Rhein-Hessen; on the E.

00In other directions also the expansion has been rapid; the village of Bornheim was incorporated in Frankfort in 1877, the former Hessian town of Bockenheim in 1895, and the suburbs of Niederrad, Oberrad and Seckbach in 1900.

00But at this critical moment the leading companies of the Hessian infantry arrived, re-established the equilibrium (though not before four Prussian batteries had been temporarily overrun by the enemy), and a most obstinate fight ensued.

00A third of the leading brigade (British) was killed and wounded in the vain attempt to break through the strong defences of the village, and some French squadrons charged upon it as it retired; a colour was captured in the melee, but a Hessian brigade in second line drove back the cavalry and retook the colour.

00Among his more famous hoaxes were the " Edict of the King of Prussia " (1773), already described; the fictitious supplement to the Boston Chronicle, printed on his private press at Passy in 1782, and containing a letter with an invoice of eight packs of 954 cured, dried, hooped and painted scalps of rebels, men, women and children, taken by Indians in the British employ; and another fictitious Letter from the Count de Schaumberg to the Baron Hohendorf commanding the Hessian Troops in America (1777) - the count's only anxiety is that not enough men will be killed to bring him in moneys he needs, and he urges his officer in command in America " to prolong the war.

00The French army, similarly arrayed, but with a few battalions attached to the cavalry wings, was more heterogeneous than the German, being composed of French, Hessian, German mercenaries, and Liegeois.

00In 1846 he was appointed professor at Marburg, and though this small university offered little scope for his activities as a teacher, a seat in the Hessian Landtag gave him his first experience of political affairs.

0023 (Hamburg, 1853), 226-327 (letters of Hessian deputies); Acta et scripta synodalia Dordracena ministrorum Remonstrantium, Hardervici, 1620 (valuable side-lights); A.

00Among other public places and buildings worthy of notice are the Roman Catholic church, with a splendid interior; the Kiinigs-platz, with a remarkable echo; the Karls-platz, with the statue of the landgrave Charles; and the Martins-platz, with a large church - St Martin's - with twin towers, containing the burial-vaults of the Hessian princes.

00There are also the Bose Museum, containing collections of pictures and antiquities of Hessian origin, museums of natural history and ethnography, an industrial exhibition hall, and an industrial art school.

00On the Hessian fly, Cecidomyia destructor, Say, the May brood of which produces swellings immediately above the joints of barley attacked by it, see Asa Fitch, The Hessian Fly (Albany, 1847), reprinted from Trans.

00The inhabitants are mainly of the Saxon stock and speak Low German dialects, except in the Upper Frankish district around Siegen, where the Hessian dialect is spoken.

00Among interesting landmarks are the Federal Inn (1763),(1763), in which President Washington was entertained in 1794, and which has been used as a banking house since 1814; the old county gaol (1770), used as such until 1848; and the site of the "Hessian Camp," where some of the prisoners captured during the War of Independence were confined.

00(1760-1785), who had become a Roman Catholic, 22,000 Hessian troops were hired by England for about X 3,191,000, to assist in the war against the North American colonies.

00In 1821 a small mediate principality was formed out of the old lordship of Ratibor and certain ecclesiastical domains, and was conferred upon Victor Amadeus, landgrave of Hesse-Rotenburg, as compensation for some Hessian territory absorbed by Prussia.

00Outside this, though not in hostility to it, Hanover, Brunswick, Oldenburg and Schaumburg-Lippe formed a separate customs-union, (Steuerverein) by treaties signed on the 1st of May 1834 and the 7th of May 1836, and to this certain Prussian and Hessian enclaves were attached.

00Prussia, on the other hand, announced its determination to carry out the principles of the Union and to maintain the Hessian constitution.

00What this means is that the Hessian lines are managed by the Prussian department.

00Chief among these is the barracks, erected by the colony in 1758 to mitigate the evils of billeting, and occupied by British troops during the Seven Years' War, and at different times by British, Hessian and American troops during the War of Independence.

00The Hessian star catalogue was published in Lucius Barettus's Historia coelestis (Augsburg, 1668), and a number of other observations are to be found in Coeli et siderum in eo errantium observationes Hassiacae (Leiden, 1618), edited by Willebrord Snell.

00In the war between Austria and Prussia in 1866, HesseDarmstadt was upon the side of the Austrians; Prince Louis accompanied his troops to the front, and was duly appointed by the grand-duke to the command of the Hessian division.

00These fine Rio hessian yarns form an important branch of the Dundee trade, and in some weeks during 1906 as many as 1000 bales were despatched to Brazil, besides numerous quantities to other parts of the world.

00Amongst these may be mentioned the following: Hessian, bagging, tarpaulin, sacking, scrims, Brussels carpets, Wilton carpets, imitation Brussels, and several other types of carpets, rugs and matting, in addition to a large variety of fabrics of which jute forms a part.

00But if the given curve has a node, then not only the Hessian passes through the node, but it has there a node the two branches at which touch respectively the two branches of the curve; and the node thus counts as six intersections; so if the curve has a cusp, then the Hessian not only passes through the cusp, but it has there a cusp through which it again passes, that is, there is a cuspidal branch touching the cuspidal branch of the curve, and besides a simple branch passing through the cusp, and hence the cusp counts as eight intersections.

00xxviii., 1844); in the latter of these the points of inflection are obtained as the intersections of the curve u = o with the Hessian, or curve A = o, where A is the determinant formed with the second derived functions of u.

00We have in the Hessian the first instance of a covariant of a ternary form.

00The Hessian A has just been spoken of as a covariant of the form u; the notion of invariants and covariants belongs rather to the form u than to the curve u=o represented by means of this form; and the theory may be very briefly referred to.

00Intellectual interests of a high order have always characterized, Leipzig, and what Karl von Holtei once said of it is true to-day: "There is only one city in Germany that represents Germany; only a single city where one can forget that he is a Hessian, a Bavarian, a Swabian, a Prussian or a Saxon; only one city where, amid the opulence of the commercial world with which science is so gloriously allied, even the man who possesses nothing but his personality is honoured and esteemed; only one city, in which, despite a few narrownesses, all the advantages of a great, I may say a world-metropolis, are conspicuous !

00The church also contains the tombs of numerous Hessian landgraves and knights of the Teutonic Order.

00In Germany, Ips and Passau on the Danube, and Gross Almerode in Hesse, are the best known localities producing fireclay goods, the crucibles from the last-mentioned place, known as Hessian crucibles, going all over the world.

00As children they played by the Hessian bales of asbestos at the nearby railhead and played on the open tips around Harridge mill.

00Two ladies (Mrs Burgess and Mrs Hall) were employed to sew up and mend the hessian sacks - quite a messy job.

00Billy snuggled deeper in his hessian blanket and dreamed of rabbits fighting pirates on the high seas.

00denominator factors, that the complete system of the quadratic is composed of the form itself of degree order I, 2 shown by az 2, and of the Hessian of degree order 2, o shown by a2.

01Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.

01In other directions also the expansion has been rapid; the village of Bornheim was incorporated in Frankfort in 1877, the former Hessian town of Bockenheim in 1895, and the suburbs of Niederrad, Oberrad and Seckbach in 1900.

01A third of the leading brigade (British) was killed and wounded in the vain attempt to break through the strong defences of the village, and some French squadrons charged upon it as it retired; a colour was captured in the melee, but a Hessian brigade in second line drove back the cavalry and retook the colour.

01In 1846 he was appointed professor at Marburg, and though this small university offered little scope for his activities as a teacher, a seat in the Hessian Landtag gave him his first experience of political affairs.

0123 (Hamburg, 1853), 226-327 (letters of Hessian deputies); Acta et scripta synodalia Dordracena ministrorum Remonstrantium, Hardervici, 1620 (valuable side-lights); A.

01Among other public places and buildings worthy of notice are the Roman Catholic church, with a splendid interior; the Kiinigs-platz, with a remarkable echo; the Karls-platz, with the statue of the landgrave Charles; and the Martins-platz, with a large church - St Martin's - with twin towers, containing the burial-vaults of the Hessian princes.

01There are also the Bose Museum, containing collections of pictures and antiquities of Hessian origin, museums of natural history and ethnography, an industrial exhibition hall, and an industrial art school.

01On the Hessian fly, Cecidomyia destructor, Say, the May brood of which produces swellings immediately above the joints of barley attacked by it, see Asa Fitch, The Hessian Fly (Albany, 1847), reprinted from Trans.

01The inhabitants are mainly of the Saxon stock and speak Low German dialects, except in the Upper Frankish district around Siegen, where the Hessian dialect is spoken.

01Among interesting landmarks are the Federal Inn (1763),(1763), in which President Washington was entertained in 1794, and which has been used as a banking house since 1814; the old county gaol (1770), used as such until 1848; and the site of the "Hessian Camp," where some of the prisoners captured during the War of Independence were confined.

01(1760-1785), who had become a Roman Catholic, 22,000 Hessian troops were hired by England for about X 3,191,000, to assist in the war against the North American colonies.

01In 1821 a small mediate principality was formed out of the old lordship of Ratibor and certain ecclesiastical domains, and was conferred upon Victor Amadeus, landgrave of Hesse-Rotenburg, as compensation for some Hessian territory absorbed by Prussia.

01Outside this, though not in hostility to it, Hanover, Brunswick, Oldenburg and Schaumburg-Lippe formed a separate customs-union, (Steuerverein) by treaties signed on the 1st of May 1834 and the 7th of May 1836, and to this certain Prussian and Hessian enclaves were attached.

01The Hessian star catalogue was published in Lucius Barettus's Historia coelestis (Augsburg, 1668), and a number of other observations are to be found in Coeli et siderum in eo errantium observationes Hassiacae (Leiden, 1618), edited by Willebrord Snell.

01In the war between Austria and Prussia in 1866, HesseDarmstadt was upon the side of the Austrians; Prince Louis accompanied his troops to the front, and was duly appointed by the grand-duke to the command of the Hessian division.

01The demand for this class of bagging, which is made from fine hessian yarns, is still great.

01These fine Rio hessian yarns form an important branch of the Dundee trade, and in some weeks during 1906 as many as 1000 bales were despatched to Brazil, besides numerous quantities to other parts of the world.

01Amongst these may be mentioned the following: Hessian, bagging, tarpaulin, sacking, scrims, Brussels carpets, Wilton carpets, imitation Brussels, and several other types of carpets, rugs and matting, in addition to a large variety of fabrics of which jute forms a part.

01Secondly, as to the inflections, the process is a similar one; it can be shown that the inflections are the intersections of the curve by a derivative curve called (after Ludwig Otto Hesse who first considered it) the Hessian, defined geometrically as the locus of a point such that its conic polar (§ 8 below) in regard to the curve breaks up into a pair of lines, and which has an equation H = o, where H is the determinant formed with the second differential coefficients of u in regard to the variables (x, y, z); H= o is thus a curve of the order 3 (m - 2), and the number of inflections is =3m(m-2).

01xxviii., 1844); in the latter of these the points of inflection are obtained as the intersections of the curve u = o with the Hessian, or curve A = o, where A is the determinant formed with the second derived functions of u.

01We have in the Hessian the first instance of a covariant of a ternary form.

01The Hessian A has just been spoken of as a covariant of the form u; the notion of invariants and covariants belongs rather to the form u than to the curve u=o represented by means of this form; and the theory may be very briefly referred to.

01The church also contains the tombs of numerous Hessian landgraves and knights of the Teutonic Order.

01In Germany, Ips and Passau on the Danube, and Gross Almerode in Hesse, are the best known localities producing fireclay goods, the crucibles from the last-mentioned place, known as Hessian crucibles, going all over the world.

01The demand for this class of bagging, which is made from fine hessian yarns, is still great.

01Secondly, as to the inflections, the process is a similar one; it can be shown that the inflections are the intersections of the curve by a derivative curve called (after Ludwig Otto Hesse who first considered it) the Hessian, defined geometrically as the locus of a point such that its conic polar (§ 8 below) in regard to the curve breaks up into a pair of lines, and which has an equation H = o, where H is the determinant formed with the second differential coefficients of u in regard to the variables (x, y, z); H= o is thus a curve of the order 3 (m - 2), and the number of inflections is =3m(m-2).

01He had just finished dressing for his ride, and wore a blue uniform, opening in front over a white waistcoat so long that it covered his rotund stomach, white leather breeches tightly fitting the fat thighs of his short legs, and Hessian boots.

01Men in military uniforms and Hessian boots could be seen through the windows, laughing and walking through the rooms.

01He wore a woman's loose gown of frieze, blue trousers, and large torn Hessian boots.

01Jauntily shifting the position of his legs in their tight riding breeches, diffusing an odor of perfume, and admiring his partner, himself, and the fine outlines of his legs in their well-fitting Hessian boots, Nicholas told the blonde lady that he wished to run away with a certain lady here in Voronezh.

01we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +ï¿½(g x) 3 and immediately solved.

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