142 LAN 
•with a very valuable Appendix, containing Theorems for 
the Calculation of Fluents; which are more complete and 
extenfive than thofe which are to be found in any author 
before him. 
fn the years 1781, 1782, and 1783, Mr. Landen pub- 
lifbed three fmall tradts On the Summation of Converg¬ 
ing Series ; in which he explained and ffiowed the extent 
of fome theorems which had been given for that purpofe 
by De Moivre, Stirling, and his old friend Thomas Simp- 
fon, in anfwer to what he conceived to be written to the 
difparagement of thofe excellent mathematicians. • It was 
the opinion of fome, that Mr. Landen did not fliow lefs 
mathematical Ikill in explaining and illuflrating thefe the¬ 
orems than he had done in his writings on original fub- 
jefls; and that the authors of them were as little aware 
of the extent of their own theorems as the reft of the 
world were, before Mr. Landen’s ingenuity made it ob¬ 
vious to all. 
About the beginning of the year 1782, Mr. Landen 
had made fueh improvements in his theory of rotatory 
motion, as enabled him, he thought, to give a folution of 
the general problem mentioned above; but, finding the 
refult of it to differ very materially from the relult of the 
folution of it given by d’Alembert, and not being able to 
fee clearly where that gentleman, in his opinion, had er¬ 
red, he did not venture to make his own folution public 
at that time. During the courl'e of that year, having pro¬ 
cured the Memoirs of the Berlin Academy for 1757, 
which contain M. Euler’s folution of the problem, he 
found that it gave the fame refit It which had been de¬ 
duced by d’Alembert; but the perfpicuity of Euler’s man¬ 
ner of writing enabled him to difeover where he had dif¬ 
fered from himfelf, which the obfeurity of the other pre¬ 
vented him from doing. The agreement, however, of 
two writers of fuch eltablilhed reputation as Euler and 
d’Alembert, made him long dubious about the truth of 
his own folution, and induced him to revife the procefs 
again and again, with the utmoft circumfpeftion ; and, 
being every time more firmly convinced that his own fo¬ 
lution was right, and their’s wrong, he gave it to the pub¬ 
lic in the 75th volume of the Philofophical Tranfaftions. 
Owing to the extreme difficulty of the fubje6l, together 
with the concife manner in which Mr. Landen had been 
obliged to give his folution, that he might confine it 
within proper limits for the Tranfa&ions,it was too hard, 
or at lealt too laborious, a talk for moll mathematicians to 
read it; and this circumftance, joined to the eftabliffied 
reputation of Euler and d’Alembert, induced many to 
think that their folution was right, and Mr. Landen’s 
wrong. Among the attempts made to prove it, was a 
long and ingenious paper by the learned Mr. Wildbore, a 
gentleman of very diltinguilhed talents and experience in 
fuch kind of calculations; which is given in the 80th vo¬ 
lume of the Philofophical Tranfaftions, and is decidedly 
in favour of the foreign mathematicians. Upon this Mr. 
Landen determined to revife and extend his folution, in 
order to make it more generally underftood. About this 
time, alfo, he accidentally met with the late P. Frifi’s 
Cofmographise Phyficae et Mathematics ; in the fecond 
part of which there is a folution of this problem, agree¬ 
ing in the refult with thofe of Euler and d’Alembert. Not- 
•withftanding the agreement of the great mathematicians 
above-mentioned againft him, our author was (till per- 
fuaded of the truth of his own folution, and proceeded to 
defend and explain it more at large. He was the more 
anxious to do this without lofs of time, on account of the 
declining (late of his health. For feveral years he had 
been feverely affli< 5 led with the (tone in his bladder, and 
about this time frequently fullered from it to fuch a de¬ 
gree, as to be confined to his bed for more than a month 
together. Yet even this dreadful diforder did not extin- 
guilh his ardour for mathematical ftudies; for the fecond 
volume of his Memoirs was written and revifed during 
the intervals of his complaint. This volume contains his 
laft labours on the folution of the general problem con- 
• -3 
LAN 
earning rotatory motion. It alfo comprifes a refolutKW 
of the problem relating to the motion of a top ; together' 
with an inveftigation of the motion of the equinoxes, in 
which Mr. Landen has, firft of any one, pointed out the 
caufe of fir Ifaac Newton’s miftake in his folution of this 
celebrated problem ; and fome other papers of confider- 
able importance. He juft lived to fee this work finiHied, 
and received a copy of it on the day before his death, 
which took place on January the 15th, 1790, at Milton, 
near Peterborough, in the feventy-firll year of his age. 
Mr. Landen was not only diftinguiffied by his eminent 
talents as a mathematician, but by the excellence of his 
moral character. The ft rift integrity of his conduft, his 
great humanity, and his readinefs to ferve every perlon to 
the utmoft of his abilities, juftly procured him the refpect 
and efteem of all who knew him, and filled them with 
deep regret for his lofs. Gent. Mag..March 1790. 
LAN'DEN, a town of France, in the department of the 
Dyle, fituated on the river Becke, where a bloody battle 
was fought on the 29th of July, 1693, between the army 
of the allies, under the command of William III. king of 
England and the eleftor of Bavaria, and the French un¬ 
der the duke of Luxemburg. The French army amount¬ 
ed to 80,000 men, and the allies to little more than half 
that number. The French were repulfed two or three: 
times, and loft a great many officers and men; but, re¬ 
turning to the charge, they gained a victory, which, how-, 
ever, coft them dear, having 15,000 men killed, and be¬ 
tween 9 and 10,600 wounded. The confederates loft 
fixty pieces of cannon, nine mortars, a great number of 
ftandards and colours, with about 8000 men killed and 
wounded. It is fixteen miles fouth-eaft of Louvain, and 
feventeen weft-fouth-weft of Liege. 
LAN'DENDORFF, a town of Auftria: nine miles 
fouth of Laab. 
LANDERNEAU', a town of France, and principal’ 
place of a dillrift, in the department of the Finifterre : 
two and a half polls north-eaft of Bred, and fixty-feveri 
and a quarter weft of Paris. Lat.48.27.N- Ion. 4. 10. W. 
LANDERO'N, a town of SwifTerland, in Neufchatel, 
fituated at the fouth-weft extremity of the lake of Bienne, 
built in the year 1324, by Rodolph V. count of Neuf¬ 
chatel. The inhabitants are papilts. In the year 1707, 
this town refufed to acknowledge the king of Pruffia for 
fovereign, and was reduced by force of arms. It is feven 
milesnorth-eaftofNeufchale!,and nine fouth-weft ofBienne. 
LAN'DES, a department of France, bounded on the 
north by the department of the Gironde, on the eaft by 
the departments of the Lot and Garonne, and Gers, on the 
fouth by the Lower Pyrennees, and on the weft by the 
fea; about fixty miles from north to fouth, and nearly as 
much from eaft to weft. It is in general a fandy unfruit¬ 
ful country, covered with heaths, and thinly cultivated, 
except towards the fouth-eaft, where it contains fome 
good land, and feveral towns. The principal rivers are 
the Douze and Adour. Mont de Marfan is the capital. 
LAN'DESHUT, a town of Silelia, in the principality 
of Schweidnitz, on the Bober. In this town is a Roman- 
catholic church, with a Lutheran gnadenkircke, or permif- 
five church, and a Latin fchool. This toleration of the 
Lutheran church and fchool was purchafed by a loan of 
80,000 florins to the emperor, befides a prefent of 12,000. 
The town itfelf was founded in 1292. In 1638, the great- 
eft part of it was deilroyed by fire ; and in the following- 
year it was pillaged and demolilhed with fo much barba¬ 
rity, that only two perfons remained there. It enjoys 
now, however, a flourifhing linen-trade. It is eighteen 
miles weft-fouth-weft of Schweidnitz, and eight fouth- 
fouth-weft of Jauer. Lat. 50.30. E. Ion. 15. 55. E. 
LANDEVAN', a town of France, in the department of 
the Morbihan : eight miles north-well of Auray, and eight 
fouth-eaft of Hennebon. 
LANDEVIL'LE, a town of France, in the department 
of the 3 /endee : eight miles north of Sables d’Glonne, and’ 
fifteen weft of Roche fur Yon. 
LAN'DGRABEN, 
