Encyclopaedia Britannica, or, a Dictionary of arts, sciences, and miscellaneous literature : enlarged and improved. Illustrated with nearly six hundred engravings > Volume 13, MAT-MIC

14
MATHEMATICS.
Hts theory
of analyti¬
cal func¬
tions.
Labours of
La Place.
* Tom. 6.7.
Works of
Coufin, La¬
croix, Bof-
fut, and
Legendre.
Agnefi’s
analytical
inftitutions.
17S4.
Mafcheroni
on the
circle.
fmall, occafioncd by the variation of one or more of the
terms which exprefs it. This calculus is as much fu-
perior to the integral calculus, as the integral calculus
is above the common algebra. It is the only means
by which we can refolve an immenfe number of prob¬
lems dc maximis et minimis, and is neceffary for the fo-
lution of the moft interefting problems in mechanics.
His theory of analytical functions is one of the moft
brilliant fpecimens of human genius. In the Memoirs
of Berlin for 1772 he had touched upon this intereft-
ing fubjeft, but the theory was completely developed
in 1797 in his work entitled Theorie des fonEtions ana-
hjtiques, contenant les principes du calcul differentiei,
degagees de toute conjideration d'itfniments petits, ou
evanouifj'ements, ou des limites, ou des fluxions ; et re-
duit a I'anahjfe algebrique des quantiles flmes. In a great
number of memoirs which are to be found in the Me¬
moirs of the Academy of Paris, in thofe of the Acade¬
my of Berlin, and in thofe of the French Academy, La¬
grange has thrown light on every branch both of the
common algebra and the new analyfis.
93. The new geometry has likewife been much indebt¬
ed to the celebrated Laplace. His various papers in the
Memoires des Spavans Etrangers *, and the Memoirs of
the French Academy, have added greatly to the higher
calculi, while his application of analyfis to the celefti'al
phenomena, as exhibited in the Mechanique Celefle, and
his various difeoveries in phyfical aftronomy, entitle him
to a high rank among the promoters of fcience.
94. Among the celebrated French mathematicians of
the laft and prefent century, we cannot omit the names
of Coufin, Lacroix, and Boffut} all of whom have writ¬
ten large works on the differential and integral calculi,
and illuftrated the new analyfis by their difeoveries.
The Elemens de Geometric by Legendre is one of the
beft and moft original works upon elementary geometry,
and his papers in the Memoirs of the Academy contain
feveral improvements upon the new analyfis.
95. In Italy the mathematical fciences were deftined
to be improved and explained by a celebrated female.
Donna Maria Gaetana Agnefi was profeffor of mathe¬
matics in the univerfity of Bologna, and publilhed a
learned work entitled Analytical Inflitutions, contain¬
ing tire common analyfis, and the differential and in¬
tegral calculi. It has been tranflated into Englifh by
Profeffor Colfon, and was publiihed at the expence of
Baron Maferes. A few years ago feveral curious pro¬
perties of the circle have been difeovered by Mafche¬
roni, another Italian mathematician, who has publiihed
them in his interefting work fur le Geometric du Cam¬
pus.
96. In England the mathematical fciences have beenEnglifli
fuccefsfully cultivated by Emerfon, Baron Maferes, Dr matiioma.
M. Young, Dr Hutton, Profeffor Vince, and Profeffor UciaijS‘
Robertfon of Oxford. The Doctrine of Fluxions by -merfon.
Emerfon, and his Method of Increments, are good in¬
troductions to the higher geometry. The Scriptures
Logarithmici of Baron Maferes } his TraBs on the Re- Baron M*«
folution of Equations ; his Principles of Life Annuities, fews.
and his other mathematical papers, do the higheft ho¬
nour to his talents as a mathematician 5 while his zeal
for the promotion of the mathematical fciences, and his
generous attention to thofe who cultivate them, entitle
him to the noble appellation of the friend and patron of
genius. Dr Matthew Young, bilhop of Clonfert, has Dr M.
given a fynthetical demonftration of Newton’s rule for Young,
the quadrature of fimple curves j and has written on
the extraction of cubic and other roots. Dr Hutton Dr Huttost
and Dr Vince have each publifhed feveral elementary an[l Dr
treatifes on mathematics, and have invented ingeni-Vince’
ous methods for the fummation of feries. Mr Robert- Mr Robert,
fon of Oxford is the author of an excellent treatife onlou-
conic feCtions.
97. The ancient geometry was afliduoufly cultivated Scottifii
in Scotland by Dr Robert Simpfon and Dr Matthew
Stewart. Dr Simpfon’s edition of Euclid and his treatife
on conic feCtions have been much admired. The 2V’cC?.r Pr SimP-
Phyfical and Mathematical of Dr Matthew Stewart,lon‘
and his Propofltiones Geometricce more veterum demon-
flratce, contain fine fpecimens of mathematical genius. In Dr M.
the prefent day the names of Profeffor Playfair and Pro- Stewart,
feffor Leflie of the univerfity of Edinburgh, Mr Wal¬
lace and Mr Ivory now of the Royal Military College
at Great Marlow, are well known to mathematicians.
Mr Playfair’s Elements of Geometry, and his papers on Mr Play-
the Arithmetic of Impoflible Quantities and on Porfms, are tUr‘
proofs of his great talents as a mathematician and a phi-
lofopher. Mr Leflie, well known for his great difeo- Mr Leflie,
veries on heat, has found a very fimple principle, capable
of extenfive application, by which the complicated ex-
preflions in the folution of indeterminate problems may
be eafily refolved. Mr Wallace’s papers on GeometricalMr Wal-
Porifms in the 4th vol. of the Edinburgh TranfaCtions,,ace-
difplay much genius 5 and Mr Ivory’s Treatifes in the Mr Ivory,
laft vol. of Baron Maferes’s Scriptures Logarithmici, and
his paper on A New Series for the ReBiflcation of the
Ellipfls, Edin. Tranf. vol. 4th. entitle him to a high
rank among modern mathematicians.
I Mathema¬
tical,
Matiock.
mat
MATHEMATICAL, any thing belonging to the
fcience of mathematics.
MATHEMATICAL Inflruments, fuch inftruments as
are ufually employed by mathematicians, as compaffes,
feales, quadrants, &c.
Machine for dividing MATHEMAT1CAL Inflruments.
See R a v s den’s Machine.
MATLOCK, a town or village of Derbylhire, near
%
MAT
Wickfwmrth, fituated on the very edge of the Der- Matlock,
•went 5 noted for its bath, the water of which is milk--y—
warm } and remarkable for the huge rocks in its envi¬
rons, particularly thofe called the Torr, which is 140
yards liigh. It is an extenfive ftraggling village, built
in a very romantic ftyle, on the fteep fide of a moun¬
tain, and containing, in 18cI, above 2000 inhabitants.
Near the bath are feveral fmall houfes, whofe fituation