Weekly national intelligencer., 1850-11-09

himself counsel and because the high character ability,
and general fairness your journal do not allow 70 doubt
that my petition will be granted.
charged with saying that there is but one kind OF
quantity in geometry whereas all geomeers heretofore have
said that there three kinds am charged with saying
that ssevery mathematical right line is rectangk whose
breadth Is " whereas all geomeers heretofore have al
ssd that line has breadth. And these aser-
,ons are pronounced hereses" Why Not because they
have examined and found to be untrue for their truth is
abundany demonstrated by the cearest and puest demon
srsos but because they opposed 10 the received OPT
OF geometers and mahematicians for two thousand
years past which opinions but opinions not supported BY
demonstrations.
Poor old Galileo great hereto in his day. He stouty
declared earth round the sum- when the learn
ed world for thousands Of years. had been of different
opinion II however turned in the end that the hereto was
right and the learned world was wrong Their opinions
could not Withstand the force Of his deonsaons so they
concluded last to allow the earth to revove about the SUM-
and the world made great step forward in the science Of
tonomy So, hereto am, venture TO predict that these
opinions Of geomeers and mahematcians though venerable
with the age of thousands OF years. and though they may
possibly weigh my demonstrations down for time venture
predict that opinions will at last yield to demonstrations.
and that the world will make great step forward in the sci
eDce of geometry and mathematics
"Tiuth crushed to earth will rise again,
For Gods eternal years are hers;
While error, wounded, writhes in pain
And dies amid her worshippers"
Lord Bacon enumerates, among the mpedimens to the
progress of human knowledge, TOO great and
kind of alteration of the mind and understanding of man,
and dstrst that any thing should be be found
which the world should have missed and passed long
time" This +" dstrus' came costing Calico his life
but the days Of monkh nqusions over and therefore,
perhaps my poor humble neck may be sae At any rate,
neck neck, if may be allowed brief space your
columns, shall not hesitate declare my heretca
lions in the face of the world and will endeavor give
reason for the faith that il Is in
The old definitions Of geometers that line is length
without breadth" and "suface is length and breadth
have lWavs beer a in
the science, and the Of rejecting minds has
always revoed against them Geometers themselves have
always felt embarrassed any attempts to explain hem As
for bringing them to any test OF demonstration, they
did, and could The explanations Of these definitions
by the distinguished Professor Smson Of Glasgow, the
elaborate Of any which have seen and have generally
been deemed the most satisfactory and adopted by succeed
ing geomeer But the entire aacy Of those explanations,
am bold say perfectly shown in the second section
my "New Elements"
Now the perfect and science of geometry should
have no mystery about it and IN truth has none When
Its laws and principles understood every thing about
plain the road to mill. Geometry very
sbe and practical science She does not begin her work
with distractions. She attempts to sJmeng
with nothing whatever vain magnatons bave been indnged
hitherto by her voaries. Her magic wand by which she
performs many wonderful works. an ideal line with
out BREADTH but postiue magnitude: by which
magnitude having extension every direction from
That magnitude always simple cube, and nothing else
The cube her unit and she but unit in all her
measurements. If you ask her to simply line
length, say the length Of your parlor she will inquire by
what standard shall be measured, what shall be the un
If you tell her FOOT she takes her cubic foot in her hand
and applies it's length or linear edge along the distance
qred and tells you how many times the length Of her unit
must be repeated make the length Of your parlo Again;
you ask her TO measure extension in two directions length
and breadth the Of your parlor aoO and to return
the account in feet she takes her unit the cubic foot and
applies its length and breadth, face, sufficient
ber of the foo and tells you how many
feet contains If you ask her how much space exten-
sion there is in the whole oom she then applies the ,oho
unit and fills the room with cubic feet and tells you how
many holds And thus she every lhRg always
with that simple square block.
Now geometry is very particular never to make bunde
I'll be bound you sha'n catch her in mistake you watch
her your whole life long. And the is, because che
always this plain square block cubic block in every
thing she does, and then she knows what she about
With these cubic units she always makes and all
her dsmers her her circumference her sodities
and her surfaces And all the units in operation being
Of one form and size they always together like
cockwork When YOU require her do any work for you,
she will always allow you to select unit of any size you
please. 1t may small as the particle which
your Imagination conceive, you only get hold Of
and put into her hands, il may be large
tain the great planet Jupiter it is all the to her
she gives you full swing throughout all space But when
you have selected your unit then she says hands off 1t il
not TO be varied in form the mionth part of the finest
ha during the you require her make.
After geometry revealed the great that all he
measurements made by cubes, and nothing else
w hdt OF operation were very lew
and exceedingly simple soon discovered that she had bu
one simple law for The and comparison Of da
meters areas and crcumferences Of all plane figures what
soever and that her diameter Of extension in all plane figure
the diameter Of inscribed circle Then the universe
law which applies to all plane figures this viz four time
the area divided BY the diameter always equals the crcum
For instance inch for the unit and max
circle four inches in diameter. Then you NAV draw aroun
the circle any ectnea figure you please and the area
that figure shall contain exactly material enough 10 make
line inch ,oid and length jus, equal permee
Of the figure. You may vary the figure 10 thousand differ
-ent FORMS and The result will always be the same
To make circumference Of any plane figure peometr
applies line Of the cubic units around the figure outside
H. but touching and takes four cubic units thus
40 round one cubic and enclose area The law in plan
figures already stated always briggs point Of eouait
at four Four times the Of any plane figure divided
its diameter equals its circumference, and four times Ii
area divided by the circumference always equals the diane
ter diameter being the diameter Of inscribed circle.
Tue same or a similar universal law applies To the con
ssrson Of dismeter soidty, and surface OF all solid figure
Bot in solids the point of equality 10 sx, because the cu
unit~hss faces and order to make surface TO u
cubic unit, geometry obliged To apply SIX more cudt uni
each face and then she has surface entirely encos
the whole H. and every where touching H. And she
taken make this sursce such thst she
always give you exact nunt OF it and compare acc
rately with diameter sres soidty, any thing y
choo-e ask her. And then she applies her beautiful 81
pie, sublime Law s Solids masking her diameter Of ext
and the diameter Of inscribed sphere
isneter is oue sodiy equals onesI'h Of the surface.
diameter NIX, s0dy and surface equal For assans