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For the Literary Magazine.

the progress of geometry.

GEOMETRY, which, in its ori-
ginal, was no more than the art of
measuring the earth, has been very
rarely applied to that purpose, in
after times. Its votaries have been
busily engaged in measuring sur-
faces and figures, which can only
exist in the imagination, such as

circles, spheres, cones, and pyra-
mids, of which, whatever applica-
tions have been made to the men-
suration of empyreal spaces, or ce-
lestial bodies, there has seldom been
any practical use made, in ascer-
taining heights and distances upon
the surface of the earth.

Kingdoms, provinces, towns, and
farms have indeed been surveyed,
but geometry has lent but little as-
sistance on those occasions. The
compass and the line have been al-
most the only instruments employed,
and in the use of these the greatest
blunders and inaccuracies are com-
mitted without scruple or compunc-

We can hardly, indeed, fail of
observing how much slower the
mathematical arts, in general, have
advanced than the mathematical
sciences. Though the former were
the first to start in the progress of
improvement, they appear to have
fallen behind almost from the first.
The rude manner in which Archi-
medes measured the apparent dia-
meter of the sun is well known; and
while that great geometer was in-
vestigating the properties of the
sphere and cylinder with an acute-
ness and depth that have been the
admiration of all succeeding ages, he
was resolving one of the simplest
problems of practical astronomy, in
a more inaccurate manner than
would be suffered in an ordinary sea-
man of modern times. When the
great problem of measuring the cir-
cumference of the earth was first
thought of, the principle upon which
the solution was attempted was
perfectly scientific; but the execu-
tion, though in skilful hands, was
in the highest degree slovenly and
inaccurate. The sages of modern
Europe have traversed the globe,
from the equator to the polar circle,
in order to resolve this great prob-
lem, and are still labouring hard, to
give perfect accuracy to their con-
clusions. The academicians of
Greece and Egypt put themselves to
no such inconvenience. One of them,
when he engaged in the inquiry, ne-
ver quitted his observatory; but

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having measured the sun's solstitial
elevation at Alexandria, where he
lived, he took for granted, on report,
that on the same day the sun was in
the zenith of Syene, being seen there
from the bottom of a deep well. He
also maintained, on no better autho-
rity, the distance and bearing of the
two places, and, with such data, was
not ashamed to say he had comput-
ed the circumference of the earth.

At a much later period, Norwood
set about determining the circumfe-
rence of the earth, with an accura-
cy as much superior to that of the
Greek geometer as it was inferior
to recent attempts. Having deter-
mined the latitudes of London and
York, by observation, he travelled
from the one place to the other,
measuring along the high road with
a chain, and taking the bearings
with a compass. He was satisfied
with the accuracy of his work:
“When I measured not,” says he,
I paced, and I believe the experi-
ment has come within a scantling
of the truth.”

It is instructive to compare these
early essays of practical geometry
with the perfection to which its ope-
rations have now reached, and to con-
sider, that while the artist had made
so little progress, the theorist had
reached many of the sublimest
heights of mathematical speculation;
that the latter has found out the area
of the circle, and calculated its cir-
cumference to more than a hundred
places of decimals, when the former
could hardly divide an arch into mi-
nutes of a degree; and that many
treatises had appeared on the pro-
perties of curve lines, before a
straight one had ever been accu-
rately drawn or measured on the
surface of the earth.

The progress made in the grand
trigonometrical survey of England,
which was begun in 1784, is more
honourable to geometry, than any
practical application of its principles
which has been recorded. In no
long time, we may derive from geo-
metrical skill an exact delineation of
Great Britain, an achievement
which has been so long shamefully

neglected. While the most pro-
found capacities have been stretched
to the utmost in determining the
course, distance, and diameter of a
planet, some hundreds of millions of
miles distant, the real dimensions
of the smallest lake or island on the
surface of our own globe has been
unknown. Men have accurately
surveyed the path which the moon
takes through the aerial spaces,
while they have remained wholly
ignorant of the shortest way between
the two principal towns in their na-
tive country.

The true reason of this difference
in the progress of speculative and
practical geometry lies, perhaps, in
the greater facility with which the
operations of the former are attend-
ed. It may seem at first a little pa-
radoxical to affirm, that it is more
easy to ascertain the diameter of
Saturn, and the days, hours, mi-
nutes, and seconds which it requires
to pass from one point in the heavens
to another, than to determine the
exact distance which separates two
places within sight of each other,
but the truth is, that the instruments
and calculations by which the for-
mer is effected can be managed by
a solitary student in his closet, with
little expence of any thing but of
time, patience, and attention; where-
as much more of these qualities are
demanded to make two rods or
chains of the same precise length,
to place them in the same straight
line, and to make the beginning of
one coincide with end of another.