Vermont phÅ“nix. [volume] (Brattleboro, Vt.) 1834-1955, 1843-03-24
THREATENED REVOLUTION
ea@s IN SCIENC


which, in my estimation, may be of some i'm
portance to science in some of its departments
and which il is my purpose TO publish as soor
as circumstances will admit, have thought i
not inappropriate to advertise or suggest my
purposes TO the world and therein to intimate
the nature of some of the leading topics o
which have treated.
propose as the tite-page to my humble
work the following, viz: Ratio in Unity, o,
Unity IF Purpose; being an inquiry into the
philosophy of numbers in respect TO their adap-
tation to geometric quantities and their adj
measurement, and to the investigation of the
laws Of nature, and especially those which OPP
crate in controlling the motions and in produ.
cling the consequent phenomena in the plaueta-
~ world; to which is appended such theoreti-
cal suggestions and hypothetic correlatives as
analogy might seem to deduce from a train OF
demonstrated facts or propositions.
The work will commence with treatise
upon the quadrature Of The circle; thus disre-
garding, otherwise than with sovereign scorn
and contempt, all such low ridicule of the at
tempts to solve that important problem as may
be found in such works as Montuclo's History
Of Mathematics and Reefs Cycopedia.
In reference to the quadrature of the circle
cannot but apprehend that have treated the
subject in manner somewhat different from
the methods heretofore pursued, as il is quite
result, and that, too, by the various methods
which have applied for ascertaining the ratio
between the diameter and the circumference;
and whether the result which | have arrived at,
and the method or methods adopted for obtain
ing such result, amounts to actual demonstra-
ton of the long sought for problem shall most
cheeriully submit to The judgment.
have never supposed, nor have proceeded
upon the principle, that solution of the quad
mil n n
stract demonstration, not preceded by an en-
quiry into the laws and economy of numbers
in their application to the admeasurement Of
geometric figures, by reason Of, or in conse-
quence OF, their ratios, powers, and roots, pre-
paratory to their peculiar applicability to the
admeasurement of the circle also; whereby the
remote as well as the approximate steps tend
ing towards the result sought, were as well
marked or defined by an inductive course and
mode OF reasoning as plain to be traced, and as
obvious in their progress and conclusion, as
those which lead to any demonstration what
ever.
In all my researches in reference to the quad
nature | have always endeavoTed to act upon
the principle of wise legislation, by keeping
constantly in view "the old law, the mischief
and the remedy;" and although, for many
years, have been satisfied as to the result of
my researches in reference to this one PROPOSE
t'Sh VI PiOu'Shj 10 ooHlC puuisHtu UlUtS VIII
show, yet have been unwilling to present the
same to the world unconnected and unsupport-
ed by correative matter of equal Importance to
science of that Of the quadrature itself
am aware that it has been imagined by ma
ny, and even by the learned, that demonstra-
fton of the quadrature could serve but little
purpose otherwise than to CRAFTY the curiosity
OF mathematlcians, inaSmuch as the methods
by approximation now extant are supposed to
civ al Of N.
Teal purposes; but cannot see WHY the same
mode of reasoning would not have equally ap-
piled to demonstration Of the 47th problem of
Euclid, the demonstration OF which settled an
inhnlty OF questions which otherwise must con-
stantly arise without an arbter TO settle them
So il must be in the case of the circe-that
figure in geometry, of all others the most use
lul, whose arcs are the measures of all angles
logarlthms are the measures of all ratios a
demonstration OF the ratios of the measures of
which, unhestatingly declare will develop
,ae,c principles in respect TO the law, the phi
losophy, the economy of numbers, in their per-
feet applicability to the laws ofnature and their
development, and to the eternal fitness of
things.
II it were certain that the present method of
arriving at the measures of the circle was ba-
sed on correct principles, the approximation
would necessarily be sufficiently exact for all
practical purposes; but if the principles upon
which they proceed are not knolrn TO be cor
rect, surely it must require demonstration not
only TO detect the error in principle, but also
the amount Of error in fact; and that the error,
both in principle and in fact, is great, do not
hesitate To declare; and ! have yet to learn
that the methods proposed by Lord Brounker
and Mr. Wallis, which have been esteemed,
perhaps, the best, have any tendency whatever
IN developing the true quadrature of the circle,
or that the method is in any wise based upon
the principle of the DETECTION of planet from
tangent to its orbit
And do not hesitate to declare that by such
process they do not make their circle round
one, but that 1t is longer than il is broad; that
they do not thereby obtain the true ratio be-
tween the diameter and the circumference; and
what is a remarkable fact as any one will dis
cover, they have not been able by such process
to revolve over the horns of the octants, (if +
may so speak;) they have made no progress
towards Just or true result, after passing the
crcumscrbed octagon of the circle.
Again: the form, or rather measures, of the
circle now extant do not comport or agree with
the famous law OF Kepler, that great chronom-
eter oil the Universe, which has not only stood
the test of observation from his time to the
present, but has been the base of all astronom-
icaI calculation, and which, long ere this,
should not only have squared OF quadraed the
Circle, OUT should nave discovered to mankind
the law OF gravity, or the laws of force and
motion, and thereby have saved astronomers
from continual exploration for equations depen-
ding upon Fictitious circumstances, in order TO
bring facts and observed phenomena to cores
pond or square with what has been promuga-
ted as the general law of gravity.
Assuming boldness from having thus ventu-
red TO break through scholastic bars and bolts
which have long been accommodating, with a
view to personal examination of the premises,
conceived the enterprise of attacking the or
acle itself, and of laying open and bringing to
light It's inmost recesses, with view to aScer-