Weekly national intelligencer., 1851-11-15
NATIONAL INTELLIGENCER.
ANALYTICAL GEOMETRY.

ANALYTICAL GEOMETRY.
Among the numerous popular alaciesis the notion ha
mathematics are dry. Amy study will Of be dry when
no, understood Thus nothing less interesting than poetry
TO wholly unpoec mind. Now, if any person finds mahe
mates dry he may be he does not understand them In
this fed to resp where have not quite impossible
Nor can the wit of lay railroad through it,
able one, by sitting still, to go ahead
So much apropos to q few remarks Analytical Geome-
uy branch Of mathematics uniting the graces Of geometry
TO power and subey Of analysis Dsscares was truly
great man. Though his head full Of vorces right honest
vorces, and mint juap barsloP whPoos 10 cere-
bral If be much addicted TO oraeiug on
apples of his neghbo. his intellectual orchard bore
enough Of the best ut pay ample reprisals The finest
product OF DESCRIBES mind analytical geometry, which,
in oil its great principles essentially his work De
veoped and perfected s the whole Of mathe
ruacs furnishes nothing attractive or ntrnscay beau
tu While elementary geometry unimPorant things
in such solemn way that grow seemingly wise quite
too soon calculus " the ghosts Of departed quanes
with kind of ranscendentsl which, Car
lyle says "grnds the true product under with
out other effort part than steady turning Of the
handle The is evident, the other to, difficult and
mysterious Descriptive geometry also has much Of beauty
but meager in principles and tsdousy opeose in its
methods Being in its origin that Monge, the lu
ous founder Of the Polytechnic School, shape and
system there is doubtless very much remaining to be done
ere capacities fully developed. When is mature,
and the books made less clumsy, will be the natural
and fitting ves,ibule of analytical geometry The clear
geomecal conceptions which would then give should pre-
cede the analysis Of lines and surfaces Without this pre-
paraion there danger Of analytical geometry degenerang
into mere ageb and thus becoming nearly barren of inter-
ard value No person is fit dscuss the general equa
n Lne-- .t~ic.r l~~-
NOT keep the geometry Of the analysis clearly mind is
fault Of of analytical researches that their geOmet
cal Interpretation 10 much left out OF eight that they
sa 1eess distractions 10 whose abstracng and
concreng powers fall below those Of Lapace Poissan,
Cauchy.
Analytical Geometry is that branch of mathematics in
which lines and surfaces discussed by The aid of agebac
symbols In treating plane curves two sKes are assumed
the coordnaies of any point of the paIe the lines
from point the drawn parallel to the axes The
length these coordnaes for the different points Of
called varabs and represented by andy The
aon these vasbles for any plane expressed
by equation In other WORDS the coodinates of all the
Ioins any particular curve, circle, paraboa,
cycod, b. aud particular relation to each other
which relation would be proposition in common language
but in equation. BY discussing this equaton
all the eres Of particular may be determined in
rigorous and beautiful manner singulary in contrast with
the verboseness and ndectness Of pure geometry BY using
three and coordnaes curves OF double curvature like
the helix and all geometica surfaces like the sphere the
epsoid the hecol be discussed Tie method abb
soute general for all lines and surfaces of regular
tica character though is not customary in elementary
introduce those whose equations involve logahms
sines taDgen &C. The of comic sections, and the
surfaces generated by revolving comic sections around their
form the staple Of these eaises The reason OF thsis
that any other surface must give equation above
the secod degree conaning functions
either of which makes knorty subject for common
Students and needs the skeleton keys of calculus Any
comparing the facility certainty, and concseness OF ana
yica geometry with the wordy ungeneazed and fouitous
fhnl~
Descaes and pronounce this Of stage coach
railroad The English have reason to know this for their
adhesion the geomec method under the spell Of Newions
guidance KEEP, them long sadly the dark, until by a
turn better reason they again able TO read the works
of their French and German neighbors.
In fine, we would say that any young man who wishes to
saHs % 6sc s
midnight oil to master analytical geometry Elementary
geometry, algebrs, and plane gonometry somewhat tho
roughly studied will with assduty resolution, and faculty.
enable him to proceed without difficulty through Davies
Church. Biol For beginner the best of these will quite
surely be Prof. Churchs recent work. If he has not made
the best English textbook this subject be not done his
duty The clerness and appropriate character OF his in
struction TO fourteen successive classes the u s. Military
Academy show that it his duty to improve his pre-
dscessors. We think he has done to such extent
much to facilitate the study Of this subject The
given the preface justify placing the parabola before the
epse and hyperboa though strictly speaking should
between The parade of enunciaon is wisely dispensed
and timely intelligence given that the comic sections
cut from cone. II 10 sad Inversion 70 leave tbs as part
ing word when bidding crooked friends
As would be convenient have all the principal equations
and expressions Of analytical geometry collected venture
the suggestion that in edition, which must soon be re-
quired such collection be supplied 30, touchiog hat
10 Descartes, Biol, Davies, and Church, retire not
though without expressing hope that too boasu Amerc,
may in due time produce something above textbook ii
mathematics, well bevy Of those wht
could understand il when produced. ER.H
sElenent. of An.lxtc.l Ceome,rv by Albert E. Church
A. NJ, Professor Mathematics U. s. Military Academy
New York George Putnam 15s Broadway, 1884, pp 2e7