THE SQUARE OF THE CIRCLE
(x)
DEMONSTRATED FROM


THE CUBE, RATIONAL,
BY
EDWARD DINGLE.


PLYMOUTH:
GE1ORGE H. SELLICK, PRINTER AND PUBLISHER,
BEDFORD STREET.
189I.
Also to be had of the Author, at his residence, I9, King Street, Tavistock, Devon.
PRICE ONE SHILLING.








ADDENDA TO " THE BALANCE OF PHYSICS."
PREFACE.
SOME years since, I published the Work entitled as above, and it contained a
claim, with abundant evidence of the settlement, respecting the old difficulty concerning " The Square of the Circle " (pub. 1885). Hitherto I have seen no denial
of that evidence, until of late my attention has been directed to a paper on the subject, in a periodical, Vol. I., No. 2., called "The Monist," by HERM.AN SCHUBERT, which still seeks to maintain the rather modern idea, than belonged to many
earlier ages, that it was insoluble.* Whether he has or not seen my work I know
not. By this he reports, " It is impossible with ruler and compasses to construct a
square equal in area to a given circle. These are the words of a final determination
of a controversy which is as old as the history of the human mind. But the race of
circle-squarers, unmindful of the verdict of Mathematics, that most infallible of arbiters, will never die out, as long as ignorance and the thirst for glory shall be
united."
The learned Professor is very dictatorial here, but, unhappily for him, he has
not proved the circle is not itself found; and I shall show, in my examination of
his Paper, which is valuable as a history of the effort to discover the object named,
that in his expressions of contempt on those who have thought differently from him,
-so far as to make the attempt,-he includes some of the most illustrious mathematicians of ages past, amongst others, Archimedes, for one, who certainly secured,
as Schubert makes it appear, the nearest to that to be proved correct. Self-sufficiency is not all with those who hold it to be attainable.
Before I enter any further practical evidence, respecting the circle to the diameter, let us consider, with something of a fair and critical eye, the statements in
the learned Professor's history itself. As to matters of historic fact, it has its value,
and much to myself, as I knew that Archimedes used, as the best practically for x,
31-. But whether he had, to his satisfaction, demonstrated the reality of its perfect
value, or not, I had no information.  Herr Schubert gives proof he had not.
The words used as to the controversy I quote, " It is as old as the history of
the human mind," may be correct so far as uninspired writers go, which he traces
thus,-" In the oldest mathematical work we possess, we find a rule that tells us
how a square is equal to a given circle, and that this is a work no earlier than 2,000
and 1,700 B.C., which was composed on an earlier model, of King Raenmat, half a
thousand years older."
I It was kindly hinted me, in a notice by the American Editors.




4


PREFACE.


Suppose this to be all we have from such early sources; no book or record
can be cut out of entry, in respect to the point, that assumes to initiate all physical
Truth as by "weight to measure," or gives the statement that the whole universe
rests on that system which even the best mathematicians have to relapse to, for a
practical value in their calculations, and which all astronomers and chemists, electricians or other savants, find fully efficient to their demands, for securing practical
results by measure to measure. That Book has a statement older than King Raenmat's, given as the key to find it. It is much to be feared the further opposition
to 3} is resting on a desire, so many have undoubtedly shown of late years, i.e. to
ignore that divine volume, to the great injury of mankind (Isaiah xl. 12, Job xxviii.
25). By his history the Professor tells us of Arab, Greek, and Sicilian savants,
who all sought to find x as hopeful or rational.
Besides Archimedes, he tells us, France was rich in circle-squarers, and mentions some names of others, amongst them Gregory, Newton and Leibnitz, as stated
to have been seekers of its ratio as soluble, in hope. Thus, " Fruitful as the calculus of Newton and Leibnitz was for evaluation of x, the problem for converting a
circle into a square, having exactly the same area, was nowise advanced thereby."
How could it, if the base was uncertain?
Of the circle itself. The Hindu result he gives us to be 3, 1416, while x really
lies between 3,I41592 and 3,I41593, he says. I shall prove that the Hindu result
was really the nearest. Archimedes's ratio is stated as between 31- and 3+ —  With
such a host of men of science, who are also admitted to be men of first-class minds,
and whose heads it did not enter that they were seeking an ignis fatuus of hoplessness,-I do not see, with Professor Schubert, that he has a right to claim absolute
submission to an idea of more modern men,-that they have settled the point so infallibly that no man of sense may doubt the accuracy of their decisions, as it involves Law itself, is without, in mathematics, its requisite foundation. That is
that the decimal system is not fully competent to measure to a fraction, all true
geometrical forms, of which the radius is used by a pair of compasses to a numerical
scale, at units equal, but can be never found as to the circle value, it is the drawer
of and proceeds by, and the mass power to that of its squares= proportional.
The question is, perhaps (what these savants will be, no doubt, slow to admit),
that they have used a wrong system in their efforts to secure the point; but which
the decimal order, more simply examined, will itself give the answer to, and has;
and I trust, herein, to add other proofs to those already in the work quoted.
I might quote much more from the Professor's treatise, in evidence as to the
opposition of opinion between the great minds of earlier ages and the self-constituted
judges of modern days, whether of the French school he speaks of " who had
given up long since the idea of any further examimation of attempts of new men
to find x, or others."  But, there is one ground in particular, the Professor's
history is valuable to me by,-that referred to as to Archimedes's full success and
its general declaration of the same results by others. All failed in proof. It is
enough for me, from the known results of Kepler's third law, to be assured that
the circle to the distance is perfectly squared in natural fact, by a true circle 36o~.
For the squares of the times is, from a rule of strict observation, centre by centre,




PREFACE.                                  5
taken by the orbits, as of a distance to 360~ absolute, to find the diameters by
times, on the proportionating cubes.  The value of that fact against the especial
modern idea of irrationality, appears never to have struck the attention of those
savants as against them.  I place these points, in advance, before my readers, to
show the miserable effects, as to further investigation, that these so satisfied
mathematical savants have necessarily produced, in leading careless examiners to
believe it insoluble, and so to lead them to follow the said French school, as to
be prejudiced against reading further.  In this effort to get attention, I have often
met with this:-"! the square of the circle has been proved impossible to be
found."  It satisfies the lazy as well as the bigots. Nothing but confidence in
"The Force ol Truth " could have induced me to publish a success, or hope to get
a sensible audience.  To prove the Bible (so slandered of late as to its scientific
inductions) was true, was my path of duty and sustaining hope. By this, too,
the teaching of dark-minded men, only increased the difficulty in present times.
But, I think light is dawning, and that the sceptics feel it is so; and, I quite agree
with the German writer, " That in.lMathemiatics, a conviction is only justlfied by
incontestible proof."




INTRODUCTION.
BEFORE I attend to the especial points of the further proofs for x, I desire to make a
few remarks on the principles of the circle. The straight line by which alone it can
be drawn has the first place in principles of Geometry over all Nature. But why?
Because it speaks to the demand of a straight immutable act of righteousness
in the drawer.  It is not a form in itself, but aids to correctness in all forms, as a law
rational. Thus the circle requires, and can be drawn as an unerring test of truth,
subject to it. Then, the circle speaks as the mother of all forms, to perfection
in life and truth. Euclid so begins, and by these incontestible primal points, all the
problems depend on, all forms so originate.  So Euclid is a geometrical witness to
the demand on eternal righteousness; and, whether seen, or not so to be a sound book
on law derivable. Also, the radii from the centre of any circle speak of life and
liberty, to extensions infinite-a joy and a rest. It is quite right in the grammar of
Mineralogy to make the cube the standard; but it, and all crystal modifications, were
first fluid globules in witness of life. The cube,-as capable of being built to most
solid resistance for breaking up into life, and has the root for the mass,-inertial in resistance-represents death —collapse-so all other crystals associate.  If, then, the
base has no power to develope in the circle the irational, the same deficiency must be
on the line, and disorder must be of an universal result. So Nature and Euclid are
made at variance as to calculating results of the problems, all of life or death. Now
the whole universe is a correct timekeeper to the hand of its M\aker; but, if the
ir-rationalistic savants are right, how then are the times so correct? That which
starts under all properties of law subject to error, we know, always increases it
toward ruin at once, and falsification.  Yet, out of this system of universal error,
some men of science-many, are teaching that from " the beginning, Man, the focus
of Nature's results, has progressed, and will, to find a perfect man "  Error everywhere in Nature, their apparent maker of man; yet man without Incarnation or
revelation improving.  Man and Nature, physically, from the first not fit to work
together, the perfect




THE ROOTS FOR "RATIONALITY."
IN one paper of "The Balance of Physics," I used the Table of
Numbers for Spherical Trigonometry, and proved, by working round
the whole Canon thereof, that the square of the circle is to be completed, notwithstanding the inaccuracies of the table, enforced on the
calculator by the circumscribed degree of a settled allowance of numbers he must use. No proof could be greater, as the circle gave all the
compensations finally.
But, it cannot be expected here that I should go through all the
abundant evidence in that work again for those who have not seen it,
whether Herr Schubert, or others.
I can, however, and in fact need for their sakes, to present "Law"
from the integers themselves of the Arithmetical Canon, as it was shewn
in the paper titled " The Square of the Circle by Simple Arithmetic,"
for on it my base is secured under infallible voices divinely presented
in the first chapter of Genesis. The decimal order thus, I, 2, 3, 4, 5,
6, I    - added=222, and 5-, 8, 9, the same, 22-.  This gives, of the
whole 45, the centre of gravity for unit, normal values in weight, (typal
of globules material) in the body of 7, while, when the cipher (nil for
a start) is generated by a multiplier fraction by reaction, there is the
numeral value by Io, central in 5, to be harmonized with on circuits.
Hence, between the two orders, all chemists find the variations made
between chemical cohesion and gravitational associations by weight to
weight only, and are to be found under this divinely given system of the
Genesis, as of measure to measure, divisible of equal sizes, on variations of
different densities and chemical sympathies, as the measure to measure
in the two classes by legal association demand. The one for more or
less rest; the other, so laid as to carry different degrees of breaking-up
power into action, whether, as to simple rotation, or designs to designs
organised by elective positions to law for order, by electrical sympathies
over changes. Then, as weight to weight is a law primal over all variations of all properties for the reaction, decimal in submission, action
got up by a necessary feeder, or multiplying agent to all the system,
("Let light be") so between the central rights of 7 in simple gravitational claim, and 5 for vitalizing use against it for chemical changes,
&c., &c., heat to gravitation goes to work, but amongst all chemical
changes, units of equality, aggregated, have to submit to 7 for the circle
of reactions, or, by weight to weight, to rule by measure. So, setting out
as tables of numbers do by a unit, and extension of the new figure for




8


THE ROOTS FOR " RATIONALITY.7


reactions, o, we had I,oooo000000000 7= I42857,I42857; for ever.
The current value of decimals will give the same result, when 3 for the
diameter is added; and, if we use 10,0oo0000  7= 1,42857I1 SO multiplying 7 by 3= 21 + 142857; we get our 22 its equal for 7: 22 =X, so
37; 3,1428577, or 7: 22 give the same quotients for any circle to its
diameter by a scale certainly true. Thus, the skill of Archimedes, by
other more complex modes, approached very closely to this most certain
settlement by the integers in claim over each other, and for actual facts
(stubborn things) he used it as best. Then, 7 x 3= 22. With a decimal
70 X 37- 220: 70 X 3.14285 7 -= 220. 7: 22  70: 220 incontrovertibly.
This is simple, rational, and demonstrative, so far as finding the true
circle is concerned.  If proof is not allowed, when evidence is at all
roots unique, how can it exist at all?  Those who have not seen the
other proofs in the earlier works, cannot need more than this.
By these values, in association (for the contrasts needed) in this brief
summary of the rule, I shall work only in this paper. The evidence,
again, by a new order taken under them, will be complete for the circle
to the diameters chosen, and by a right submitted to by all to see the
results by,
THE WORK IN DEMAND.
We will now proceed to our actual work by a set of successional
evidences, and start on a root from 22 to o, by its half as of fractions,
normal at use.
Io03= I33I000 X 37=4I83I427
X2       x8
2203=   Io648000,,,, 334651427
4403,,  85I84000,,, 26772II427
88o3,, 681472000,,,,21417691424
I760o,, 5451776000,,,, I7134I531427
5451776000o I331000-4096
4096 is a root we fall into, at this fifth succession of our action, from
other primitives (derivable from the first standard decimal) and which is
the twelfth in the direct succession of cubic roots from I X 2 onwards,for diameters are changed from x 2 to x 8 for masses of the table standard,
given in the IIoth page of "The Balance of Physics," under the title
"The Multiplying Power of the Cube."   But our point here is, that
over these roots to their mass values, as diameters of solid cubes, the
multiplier x, true. or 3  carries the same fractions exactly to the
decimal ratio 's, finding it, or I42, which of each, to added ciphers
would give the incorruptible result of I428577 for ever, proof positive x
is found. Then, what will be the results divisional over each other?
334651424 - 4183I426= 7,4I83 426
26772I142                 33465142 
2677211427  33465I42,, 7,334651426     final fractions
2I41769142   267721427,, 7,2677211427     al ea
6 7          7             7     all equal.
I7I34I53I427,2I41769I42,, 7,214I769142 
4I83I427X4096,, 171341531426 




THE ROOTS FOR; RATIONALITY." 


g


This, at least, must be held to be neat work to mass cubic orders in
proof that our x is not subject to the mental disease of non compos
mentis ascribed to it by so many grand philosophers of the modern day
against, at least, the hope of earlier ones respecting it; and which, by
their dictation, more modern enquirers must be fools not to follow suit
to, as well as the seekers past away of the same. Who are the presumtuous?
The decimal system is, by some very learned idealists on the question,
held to have been invented by the Arabians, but, somehow it is found
in the records of Moses, as belonging to an earlier state at use, and, as
Noah worked by it, and Abraham plainly pleaded by it-from 50, 40,
20, o1 to 5, it is difficult to believe that it was unknown until his young
son Ishmael got so far as to have such a clever inventive family. But,
heads sometimes run under minds of peculiar currents on history. Now,
one thing, so far, appears clearly; that, if 3 is proved to carry the palm,
as duly derived from Law over the decimal order of the school-integers,
then not only is 3,I416 too low to 3,1428577, the right resultant to its
equal, i.e., 7: 22, but, also that the preferred value of 3,1415923 or
other lesser, one is further off than ever.
Also, the man who can think amidst too common modern ideals of
the human first estate, or at any time that anyone (but He who alone
could condense all moral obligations into the few words of the ten
commandments) could give the ist of Genesis as a son of nature's
evolutionary human primogenitor, must have a strange idea of what
logic is. Both revelations of law convey the evidence of the Divine in
their perfections, by even their condensed ratio of words. The one
agrees with admitted morals; the other, geology and equals astronomy,
&c., &c. I propose now to test the difference in fractional results by
the use of the savant's favourite practical ratio of 3 1416, for it is a
curious fact that, although refusing to allow that any definite sum could
be held attributable to get the circle by, from the diameter, they had to
manufacture one to go to work by at all. Could Nature, then, be at work
on the unknown to get up Kepler's Third Law for instance so certain,
or 360~ for the astronomical judge in test of all claims.
I must, for our new object, of necessity lend my sword 7 ths., while
I test their crooked, as still uncertain club, as well as the same roots
derived from 22, for mass values certain for diameters, as by their system
no such roots are possible to be found at true right in law at all.
II03
I331000 x3,14I6=4I81469,6000       +7=597352,8000
x8
Io648000,,,,33451756,8000,,,4778822,4000
8584000,,,, 267614054,4000,,,38230579,2000
681472000,,,, 2140912435,2000,,305844633,6000
5451776000,,,7127299481,6000,,,2446757068,8000
43614208000,, 1I37018395852,8000,,,,I9574056550,4000
Here, as the same multiplier is used and divisor, it follows that as the
masses work by 8 for a multiplier to each, according to the law for




IO


THE ROOTS FOR " RATIONALITY.7'


cube to cube, so the other quotients follow, but the results by this fixed
value used is but to settle the reaction by 7 into death, under 8 - 2 = 4,
onward to ultimate values. By our own ratio for x, a fraction is always at
hand to carry the work on by into life. So breach of the Sabbath law was
death. But. even here, 7 is proved to be the true arranger, and judge
of the evidence from absolute bases, the cubic masses, for life.  But, if
the circle itself is claimed to be for ever irrational, i.e., uncertain in
value; how could any squares as cubes for such roots be gotten at all?
We have for the favourite value from Professor Schubert, 3,141593
to 3,141592. From another, I have 3,1415926.* Let us see what the
first two will produce; though which is best, who is to decide?


I331000X 3,14I593  = 4I8I460,283000
I0648000,,,,33451682,264000
85184000,,,267613458,112000
681472000,,,, 2409076648,96000
5451776000,,,,I7I2726I3I9,I68000
43614208000,,,,137018090553,344000


- 7-=59735I,469000,,,4778811,752000,,, 38230494,016000,,, 305843952,128000,,,, 244675I617,024000
5,,19574012936,I92000


These all run into death, having no fraction to mingle with the surroundings.  Our test, each line of descent being a multiple of 8 to its
predecessor.
We will also try the lower estimate this mathematician gives, between
which and that previous x is said to run.


I331000 X 3,141592 
x 8.
10648000,,,,
85184000,,
681472000,,   1,
5451776000,,,
43614208000,,


4181458,952000. 7= 597351,2788577


3345I67,6600oo,,
267613372,928000,,
2 140906983,424000,
17127255867,39200,,
137018046939,136000,,, 477881o,2308577, 3823048I8,468577,,305843854,7748577,,2446750838,I988577,,19574006705,5908577


Here we have a terminal, finally running under the ruling 7, to a
direct set, 857; of our witnesses, in proof that our x is right, although
unlike to that of the first result, they do not begin with the I427 of the
primal right.  So far, however, it corroborates the true decimals to affix
to 3, the Index, 857; must finish here.  But whatever here appears to
get towards value in efficiency, is at once destroyed, as far as Professor
Schubert's estimates go, as the true is not here, but in some unknown
and unknowable computation between these two last.   This one has a
sort of sword, at least; but, it is destroyed by its needed mixture with
those of 3,141593 of death.  So, our sword of the Lord's gift, that is,
the Sabbatic value of life-powers all through nature, for design in the
settings of the nuclei, either of man for the hope of eternal life, natural
at first, or approximates in degrees through generative seeds, to a true
womb to keep up species, is even, in unwilling evidence from     the
enemies of the line of justice shewn out here.,*  lements of (Geometry, by A. 13-:.L., improved by SA.MSON  -I' PLAYFAIR.




THE ROOTS FOR " RATIONALITY."


II


Before we proceed further, I may note this important point. If the
diameter from a given scale of units equal (which is the law thereof),
be used to find a circle, as of it the radius, I ask what right have you to
present it as a true base at all. Only because you must have one.
Certainly, if the circle when proved on its accepted nearest ideal ratio
is not certain, then on the principle that where multiplication is not
sure (at any value), the subtractive right to be so is gone. Iid this never
strike the savants for the claim over the first problem of Euclid, and,
hence for all Euclidean demonstrations whatever. For, therein the absoluteness of the straight line, and the circle is the root of every problem set.
Hence there must be a root absolute for x, or Euclid is all uncertain
rubbish; which I, at least, am not prepared to condemn it to, or from
arithmetical results perfect. Have I not as much a right to claim, that
any number as a straight line by a scale, moved round a centre to make
the circle, is to be the base to find the diameter, as the other, that his
diameter by the same scale is a true one to law, and give, a circle value at
once? That the sum which cannot be claimed certain forward by multiplication, cannot be held true by the divisor backward, is but common
sense, and of arithmetic or geometry.
Hitherto, we have taken our cube roots from 22 to be worked under
7, which, amongst the integers of the line, holds the sheer mechanical
or weight centre for reactions. We shall now use those of the true
table of root successions, from I + I = 2 as the first double, and on by the
same ratio, 4, 8, i6, 32, &c., from the table.  The third of the cube,
for its multiplying power,* thus:-taking it at its direct progress derivately from roots and cubic masses, in circle lines. Again, Professor
Schubert carries his right for his line of the circle with vast values, as
from globe to globe; so, we start this point here on high definite roots,
real, starting at the seventh from 23 inclusive, i.e., 128 diameter.f
I283=    2097152 X 3= 659IO49;
X2         x8
2563,,  I6777216,,,, 527283937
5123,, 134217728,,,, 421827145~
IO243,, I073741824,,,  33746171617
20483,, 8589934592,,,, 269969392897
So far, we get a constant return of the one life-giving ratio for an
eternal carrier thereof. That first, for 31. For 7, as divisor over either
123456789,00 added for ever, or the reversed order of the integers, is
the only one that will not run out to death, i.e., have a carrying fraction.
I23456789* 7 = 17636684,I428571 by the cipher addings 6; and so, for
ever, also 98765432IOo0000  7 = 141093471,4285713
2097152 X 3,416 =      65884127232   7 =941206176, death again
I677726,,,,      5270730T,7856.. 
134217728,,,,    42658414,2848,,,, 
1073741824,,, 3373267314,2784,,,,,, 
8589934592,,,, 269861385I4,2272,,,,,,
" See Balance of Physics," PARiRID( E &  CO., Publishers, London, or the Author himself.
See " Balance of Physics," pages 78 and 79.




12


THE ROOTS FOR " RATIONALITY."


Here from this table of abstract rights for diameters and their masses,
we have no semblance of harmony in the fractions thrown off; and
the less the value added to 3,-the index,-worse it must go.
But, we can further prove the perfect rule of 7 by using successional
values from either of our cubes above of the table, thus:

I293= 246689    7 = 3066697
~,,,,,    X 37,, 67467366
3I3,, 2248091   7,, 32II556
3, X 37, 3922576,,,        x 37,, 39225717


I303= 2197000  7 =313857;
2197000 X 36= 9048577
1323= 229968. 7 = 3285666
2299968 X 3= 7229470o


Hence, we found at our own scale a true instant return in 7 from the
use of the masses of these standard cubes for the range of the circle
as the diameters. When no internal fraction exists, or any organical
body, which can carry on life with the aid of the surrounding feeding
elements, death must follow. We can have a corresponding test in the
following, as our fraction runs between 142857 and 142858.


I293
21466891I42857=    I5,3834  dif, 142858,,   I5,389 
1303
2197000,,,,, 15,54130 ),, 142857,, 15,54145 J
1313
2248091,,,,, 15,105236 ),, 142858,, 15,11522I i
1323
2299967,,,,, 5,67098,,  142857,, 15,67113 
1333
2352637,,,, 6,66925    diff,,,, I4258,, 16,66909 J the.15 x 4=60. i6, changing by
triplet 3 in I333


But, go on as these changes may, any of the masses taken from the
successors of the multiplying ratio of the table starting from the normal
cube 23=8, it will be found to give the same fraction,;. So 83-= 52 X
3;= 2609, hence it will be needless to go further in this course. Even in
the choice of a cube for a nucleus to work on, we see the need of
elective decision under mental attributes required, as we find in efforts
to all inventions. Election by just selection is a law universal to all
practice for free working associations, as in all our inventions forced
upon the organizers thereof. Designed they must be by mind over
matter, as for our factors to factors for a coinage to work by, also values
in metals, under commerce, or get out a rotating machine, otherwise
nature works only to the boil of equal hemispheres with no motion out
of the first place held of the whole, no united rotation.
Certainly the mathematicians cannot deny me the just right to dictate
a circle by a scale and to find its true proportioning value from a cube,
any more than they can claim to dictate a diameter by a scale to find a




THE ROOTS FOR " RATIONALITY.'


I3


circle; and, I am the more consistent in claiming to get a proportion by my
three equal values, 3;, 3,142857I or 7  22, they being from gravitation,
as a mass, additively to heat —the subtractive principle as we call it,
so to be of a true value for the circle to that diameter. So, I take the
liberty to fly on high ground, whether of a set of microbes as
Professor Schubert likes to call his equal measures, or, as I should,
equalized globules of matter for a straight line to be brought into a
circle. So, taking a length equal to 88463564o0906337 I find that all
reactions run in a centre by enumerative rights only.
22 7:: 88463564o090633: 281,474,976,710,656, which having the
cube root found for it, gives ~/65536 absolute.
So again, 281474976710656 x 3,142857;=8846364o090633,142857;,
or I, a true x. Alter these values, three, the least fraction, and no
such returns could exist by a circle to a scale to find a proportional
cube, nor could this exist if the demand of Herr Schubert was not
settled for this hereby (or other savants), be they as illustrious amongst
men as they may for mathematical inventions. The simple old one is
the best. It is by their aid I had from the modernly so despised
inspired Biblical record, given by Him who made the worlds to be
rational, and to work on the scale of weight to measure, power to
power, of the decimal orders, that I succeeded; and I fear as to
objectors, it often has been hinc il/ce lachritime, it has been so coldly
received before this. If it had helped the evolutionists, what echoes
laudative would have followed.
If we take the actual cube of the root 65536, the sixteenth in succession from 23 inclusive of this first, and multiply it by only one, the least of
their favourite approaches to the square of the circle, we shall have the
difference in 88427935034393,204352 and no witness to the true decimal
affix to 3, the index appear terminally. No wonder the savants with such
aids found nothing. They were looking for the needle in a bundle of straw
-the needle being in its true sheath after all. They are thrown out of any
cube root by reaction at all on the right I claim to demand this
diameter=28i,474,976,7io,656, to be reduced to a circle as readily as
any other to a straight line, or vice versi, by a proportional cubic map.
Also, I have attended to the generally admitted right for 360~ the horizontal claim, to be a real x. If it is true that x is irralional, this claim
is so; and so for reductions to minutes and seconds, &c., &c., by 6oths.
Could these savants not see this?  Let us put the sum 360~ at work.
360~ X 60o   2600' X 60 =- I296000ooo"X 22-28512000-7 =407342
and the ciphers, if further added, will go on to give the successive 8577
Reduce it, as a sphere to a diameter from the seconds, and we have
22: 7:: 1296000": 412363,80. Add ciphers, and we get the constant
action to reaction of a pure elliptic in 6,3,6,3 for ever in the quotient, by
140 to 80 in the constant remainders. This fact, put before any right
minded man, is a demonstration for x, found alone. I do not think
but that Archimedes, or the Christian Sage, Sir Isaac Newton, would
have at once admitted it, and been pleased it was found and provable
in such a simple manner.




14


THE ROOTS FOR i RATIONALITY."


The further point for the circle to be reduced to its own square, must
remain as a question of the transfiguration of solids holding equal
measures, in different forms, by equal enclosures, as any circle divided
by 4 will, to give the outlines of such square will show.
I will re-introduce here a table from the "Balance of Physics," in one
of many proofs the circle to the diameter was there demonstrated by,
page 190.
No one can doubt that 360~ is of a pure circle to geometry, as of a
line to time and distance.  I reduce it to seconds.
70~
2/1296000": 3,I428577:: 25200:61111,144000
648000:,,,,,,:1222224,144000
324000:,,,,   244444,144000
162000:,,,,,,  488888,144000 ^
Now, first it will be asked, what right have I to introduce 7 degrees
as a divisor, normal in right, over 360~ the horizon. For this I must
trouble the algebraists, let their idea be what it may, to a mere sum of
figures, intact in a degree, with
25200" )2206000000000( 5,142857,3600 again, so that to go on
126000           again with the tables' catechism  of
3600           ciphers added for more numbers, we
shall have an eternal return of the same fraction. As I stated, this
table was a clear proof of the decimal value in the square of the circle.*
The index here is that of the other centre to law, i.e, to numerative
right by  0. 2= 5. We will test one of the favourites of the savants'
algebraic:1296000: 3,141593::25200":61086,687600     disorder in the
64800":,,.,,     22173,39600      fractions.
Then, testing this again by 129600o0  60= 21600'
21600': 3,I42857: 25200": 3666666,14400 as before, to order.
But,,: 3, 141593:,,:3665I9I,I8000 lost.
It is useless to test the other, which holds by 3,141592 or the unknown quantity between, speculative for ever, of the savants. They
really cannot be allowed, however, to reduce the work of Nature,
designed to be ruled and measured by man, on time between cause and
effect, to a mere non comipos imentis. That is to their own works and
inventions, not Jehovah's.
I scarcely suppose any mathematician, whether Professor Schubert or
other, would on reflection respecting the tale astronomy tells, by which
alone the nautical almanack and others are alone possible to be either
made correct, or, if in error detected thereby, as by a certain judge over
it, would deny that there are, beside 360~, two others, which form certain
mean values of decision for all such calculations.
In the Table itself, there was the misfortune of me of the eights being left out in printing, but the cause was
evident by the rate for the successions.




THE ROOTS FOR " RATIONALITY."


The one is the diurnal rate of twenty-four hours, and the circle of the
earth's ecliptic 23~ 27' mean value. But if all circles of value in orbital
fact are but uncertain, because no circle exists as known ralional, but
all remaining hopeless to reduce to evidence for the accurate in value
with certainty. Has this again escaped their observation, that those
also must remain so? How, then, can they be the judges over all
astronomical operations?  The idea of irrationzal is a direct inconsistency here, and belongs to the assertors of it only. Here I will
place the evidence also in full and sufficient record:
360~
I296000 X 2  2592000 and 86400   X 3 = 259200 a decimal less.
86400,, 6,, 518400 and 1296000,, 4,, 5184000,, 9,, 77760 and,,,, 6,,7770000
I296000o  x       60,, 7776000,,             I15,,  86400"= 24 hours
What a union of perfectly, well-known, and beautiful standards to the
horizontal circle, as ever their demand for designs to fit the earth to work
to it, is here, of which, as far as I know, astronomers themselves have no
acquaintance! But we will now test these by their associations under
the pure square of the circle; for here the earth's time diurnal is proved
equal to run on exactly a decimal less than that of the horizontal line
it turns to-a most important fact as to her being made the first for a
standard to all globes or other figures organized to commence with her
day to night mean:Add more cyphers, and the
24 hours = 86400 x 3 =27I542   j currentvalue 85 7 runs on for
24 hours = 864100 x 3= "27I5427                7..   -7 2  864the finalities of reactions in
22    7: 86400,00     2749090,2 law.
Action to reaction equal in constantly recurring two remainders23~ 27 
7: 22:: 84420": 265320",-or by the ecliptic angle.
84420 x 37= 265320",, 3, I42857 =265320,000000
The latter multiplier will apply with 7: 22 over all-comers. But we
will test the Ecliptic angle with the fellowship demand on it, and then
the same forces at work as produce the decimal motion also works the
annual.
22: 7:: 84420,00: 26860909 or 09 for ever to 2 and 20 again in
direct recurring remainders claimable for ever, exactly the same as
we have for the earth's diurnal motion by time. So the tracing for the
earth's ecliptic angle under 9go to 84420":: o,1428577 is here, as in the
little work on this Ecliptic Angle, especially verified as to making the
earth to be in danger as the standard for all, as the order is therein attested
further by the addition of the Index 3.




THE ROOTS FOR " RATIONALITY. 


The beauty of the two following operations in test to our claim, can
best be seen in what, I suppose, the algebraists most despise-that is,
full sums of figures.
0,1428577                    3,1428577
86400                        86400
o,57142800                   1257142800
8837142                     18857142
II42856                    25,142856
123427                       1,2342 7
I23,42857,1427               2715,42857,142 
The most attentive repeats of the decimals of the square of the circle
throughout the both. To resist the evidence is only a bigotry like
insanity. In each case add the decimals needed, and they appear for
ever six in return. This is decisive evidence, not only as to x not
being irrational, but of the perfect beauty in the earth's design, to be
worked by new light solar gasses of electrical support for all her work
rotative, and the ecliptic angle in the revolution, which so comes in
by the latter also, under 360~, the astronomer's test ratio.
And now a word respecting Professor Schubert's last demand to prove
x is found in full only by reduction of the circle to a square. I have
used the map of a square to find the line for a true base as diameter.
To take the map of a sphere so large demands the rule for the transfiguration of solids, of course. It is a question for the engineers in
common.
But in testing what a circle is, we have nothing to do really with
microbes or globules, as they both have length with breadth and depth,
except as they are used for changes to carry it by their arithmetized
centres. A pure circle, to its lines, is to be dealt with on the same root
mathematicians demand for a pure straight line, i.e., it has neither
depth or breadth, but only length, and invisible. In our arithmetic the
size of the figures affects not the reaction. The only way it is brought
into practice in material life is by the work of Jehovah in the unchanging value of the earth's diurnal action reckoned by time, or by the orbit.
Then the working action rests on the decimal changes of all the
properties of matter over the centre, also invisible, and there it is
worked out. But we can enumerate its value by decimal deductions to
its signs and lines; but in all cases a map of equalized, equally ideal
units are held to be subject to fall from one form to another under a
rule of law to proof granted.
So, as a cube has equal. lines over the centre right angular to
each other, and a sphere at all lines around the centre, I hold
that it follows that if the circle's dimensions are held subject to be
reduced to those equal circles, all for a square, which is done by a
division by 4, the true square is found for its map and area, as any pure




THIF ROOTS FOR " RATIONAIITY."


I7


sphere may be held to fall to that form by three lines of recession from
points over the centre necessary for it. I do not think any practical
engineer, as to equal contents or area, would differ from me; but
whether this is to be accepted as a pure mathematical demonstration or
not, one thing is certain, that unless the actual value for x to find the
absolute sphere to act on, as of true circles round, is first decided, it
can be of no use whatever to try. What can be done to get its
dependant square?
The first point I have settled for anyone who wishes to attest, as he
thinks best, the other point. As to the prejudice against examining
any new effort, it looks like the old one of pride and bigotry. " Have
any rulers believed in him?"  Who sets them   up?   Themselves,
Galileo, Copernicus, Newton, and many others have had it to deal
with, and held it worthless up to the time of the first inventor of power
by steam, or the commanding genius that found the canal passage to
India feasible, although he failed in that of Panama, to be ruled by
prejudice.
Let us have our time to settle one thing at a time, at least; and the
base here for the other is what is wanted first. In connection, I can
only say if another starts up who succeeds in anything further, I shall
be most happy to hear of it. My object is simply to prove the Bible
to be an aid. In all my labours I have had nothing to keep me much
interested in this from other easier studies but that which first led me
into action, i.e,, to prove the libels thrown by modern scientists on the
Bible false; and it is all I care about particularly, although in the
course of it I found much pleasure in the new facts I had reached after
and found. The main point I have succeeded in. I belong to no
college of the learned, who would have some associated minds to
uphold them. I have fought, wisely or not, alone and unaided, except
as I accepted facts proved by others in print, which I always acknowledged. I hold in contempt all plagiarisms or jealousy of others, but as
an English gentleman, and especially as a Christian, to maintain the
infallibility of the Bible, and help all men to see its value. I work
against all enemies of my race, and seek the Truth on all points therefrom in honour of God the giver, and by the aid of His spirit only.
I may note this point in final conclusion on this subject. It is
admitted that facts are stubborn things to object to; I suppose the
algebraists fully thought so.
New views are drawn direct from the decimal fountain, back to which
(let other evidence be of thirteen pages or eight of algebra) there must
be a demand to give their conclusion direct to figures, however pretty
and complete to others of their class such studies in detail may appear.
But even Professor Schubert admits that many of his history (where
their note of it is recorded) say they found 31 practically best. Thus"It is further worthy of remark that the earlier of these Hindu
mathematicians does not mention either the value of 37 of Archimedes,
or the value of 37,0' of Ptolemy, but that the latter knows of both
values, and especially recommends that of Archimedes as the most




i8


THE ROOTS FOR "' RATIONALITY."


useful one for practical application." Again, "With regard to the
mathematicians of Greece that follow Archimedes, all refer to and
employ the approximate value of 3;, without however contributing
anything new or additional to the problem of the quadrature of the
cyclometre."  Why did Archimedes use 37? Yet, against all fact in
practice, the author of the paper in "The Monist" seeks to maintain
the presumption of those who at least thought and attempt to find the
possible absolute. What, then, have algebraists done to contribute to the
problem of cyclometres? By their own showing nothing; for even if
it lay between 3,141593 and 3,141592 as he asserts, who could say it
was indefinite somewhere between them. And 3,1416 is admittedly a
needed judge till a better be found. Archimedes must have thought
that for practice 37 was better than anything like 3,1416 or its neighbours. I have no doubt algebra has its use, but it certainly does not
always, as in this case, shorten the line of demonstration, and can
do nothing against pure decimal decisions, the final test of all such
workings for facts, and it can be shown it is not equal to find it. It
must be revealed to man in a key divine.
I add a new witness to elliptical powers by 3T over decimal action to
another given in "The Balance of Physics." That was derived from
22: 7:: 98765432I: 3142536742 x 9 = 2828282828 x by the integers
in succession, and then by 37, all quotients set into a column as this is.
We will now show the reflex result lby 22: 7:: 123456789:
3928I705 3 x 9 = 353535350 7
9 being a correct reactor, is thus seen to work with 3I, its coadjutor
therein to ellipsis entire between them.
35353553507 x 2=707070700o4 x 3= 2222222201,,,, 3,, IO606o6056050,, 3333333302,,,,      4,, r14414I40I,,,, 4444444403,  5,, I76767675I12,,, 5555555504,,,, 6,, 2I212120II,,,  6666666666605,,   7,, 24747474525,,,,777777776,,, 8,, 2828282802 2,,,8888888807,,, 9,, 3 I81818152,,,  99999999908,, I,, 353535350322,,, IIIIIIII09
This beautiful result proves the co-efficient value for the circle of 37
to 9, as was shown in the earlier instance by the use of the major line;
and be it remembered that in that first 314253674 not only strikes into
the 3,14 start of the decimal x 3,142857, but also that the earth's orbit
in time does the same, to show her a designed standard vessel, but with
concessions set in to meet the working with her sun, which provides her
gases of support and power, and to carry her moon. Earth's orbital
time, 3I4720I4-".  The first reaction by x io here, to start by the unit
again, is not upset by the use of 3; for the other squares of the circle
-the left hand columns running down by the integers of succession.
At the right hand, and all the belly by 23456789 to the reaction of
the ruling father of all, the unit one. No man of judgment could doubt




THE ROOTS FOR 4 RATIONALITY." 


I9


the evidence complete for x true to be here, and the other case referred
to. There will be carrying fractions for life in each, but I have not
thought it requisite to enter them.
I now leave this question for Herr Schubert and others to determine,
and not doubting his sincerity of opinion or purpose, by his own
words in test. He says:
" But what kind of people are these circle-squarers when examined
by the light? Almost always they will be found to be imperfectly.educated persons whose mathematical knowledge does not exceed that
of a modern college freshman," &c. Has such education been infallible
always, by his own account? Again, "Similarity in the case of all
other attempted solutions of the problem, either logical fallacies or
violations of elementary arithmetical, or geometrical truths, may be
pointed out."
How, then, in this latter respect, for one who found not out that the
value of his straight line for any base was undermined by the idea
irrational for the circle from it,-that it affected all the problems of
Euclid with the palsy.
That subtraction must reduce its opponent multiplication to have
equal results in irrationalit'y or rationaiity on bases as well as products,
or that the square could not be found before the circle itself. Then
truly he says, "The quadrature of the circle for it stands or falls with the
problem of rectification."  True; but if this is true, I have by the aid
of the Mosaic institution of law in respect of rotation turning on a
settled root by the forces doing it, whether of chemical powers set or not,
by perfectly formed rectification for all parts together as a body, so as
to get the whole mass to rotate, instead of half and half in a boil, I thus
placed it in the body of the figure 7. I leave this for those not bound
to human presumption for the infallible to consider; but by its value as
directly derived from the Bible, and the decimal order to its parts as I
found it. No doubt to find Archimedes was the best mathematician
will be galling to the moderns.