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ON THE PROPERTIES OF THE NUMBER SEVEN. 187 JAT:18 Translation. CHA Jooss and increasing according to the same u know not whether any voice can analogy, as far as to the hebdomad, sufficiently celebrate the nature of the you will always find that the increased hebdomad, which is too excellent to

number is both a square and a cube. be described by the power of words;

The hebdomad therefore compounded yet it is not proper to be silent, though

in a duple ratio from 64, will be what is said about it is of the most 4096," which is both a square and a wonderful nature; but we should en

cube; a square having for its side 647 deavour, if we cannot relate all and

but a cube, the side of which is 16.!oq ita principal excellencies, to render

Let us now pass to the other species manifest at least such of its properties hended in the decad, and which exa

of the hebdomad, which is compresi as are accessible by our reasoning hibits an admirable nature no less power. The hebdomad, then, is spoken of in a twofold respect; one therefore, is composed of one, two, and

than the former hebdomad. This, indeed, subsisting within the decad, which is seven times measured by the

four, which possess two most harmonic

ratios, the duple and the quadruple; monadalone, and consists of seven monads; but the other is external to the former of which forms the symthe decad, of which the principle is..phony diapason, and the latter the symentirely the monad, according to

phony desdiapason. This hebdomad double, or triple, or, short, analon also comprehends other divisions, congous numbers; and such are the

sisting after a manner of certain conLumbers, 64 and 729. the former jugations. For it is in the first indeed increasing by a . duplication

place divided into the monad and from unity, but the other by a tripli hexad, afterwards into the decad and cation. Each species, however, ought pentad, and lastly into the triad and

tetrad. But this analogy or propornet to be negligently considered. The

tion of numbers is also most musical. second species, indeed, has a most

For 6 has to 1 a sextuple ratio, and manifest prerogative. For the heb domad, which is compounded from

the sextuple ratio produces the greats double, or triple, or analogous num

est interval in tones, by which the Hors from the monad, is both a cube

most sharp is distant from the flattest and a square, comprehending both sound, as we shall demonstrate when

we make a transition from numbers species; viz. of the incorporeal and

to harmonies. Again, the ratio of corporeal essence; the species of the

5 to 2 exhibits the greatest power in incorporeal, indeed, according to the superficies, which is formed by harmony, nearly possessing an equal

power

with the diapason, as is most squares; but of the corporeal, as cording to the other dimension, clearly exhibited in the harmonic

canon. But the ratio of 4 to 3 forms (depth) which is formed by cubes. But the credibility of what is said

is

the first harmony, the sesquitertian,

which is diatessaron. most manifest in the above-mentioned numbers. For the hebdomad. 64, hebdomad presents itself to the view,

“ Another beauty likewise of this which is immediately increased from

and which is to be considered as most unity in a duple ratio, is a square

sacred. For since it consists of the produced by the multiplication of 8 by 8, and it is also a cube, the side triad and the tetrad, it exhibits that or root of which is 4. And again, direct live in things. And it must

which is undiverging and naturally in the hebdomad, which is increased in

be shown after what manner this is a triple ratio from the monad, viz.

effected. The rectangular triangle, 729, is a square, indeed, formed by

which is the principle of qualities, the multiplication of 27 by itself, and is also a cube, the side of which is 9.* By always making, too, a hebdomad For 64 x2x2x2x2x2x2=4096. the principle, instead of the monad, And thus also the hebdomad compounded

in a triple ratio from 64 will be 46656, Thux, 1x2x2x2x2x2x2=64; he shalar bebet he 200 meter he coule and 1 X3X3X3X3X3X3=729.

root is 36.

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158 ON. THE PROPERTIES OF THE NUMBER SEVEN. ! consists of the numbers 3, 4 and 5.* *. eminence with reference to all the But 3 and 4, which are the essence of . numbers that are within the decad. this hebdomad, form the right angle. For of these some beget, not being For the obtuse and the acute exhibit : themselves begotten; but others are the anomalous, the irregular, and the begotten, but do not beget; and others unequal; since they a imit of the both beget and are begotten. The more and the less. But the right hebdomad, however, is alone beheld angle does not admit of comparisors; in no part of these, which may be nor is one right angle more right than confirmed by demonstration as folanother, but it remains in the similar, lows. Unity, therefore, generates all and never changes its proper nature. the nunibers that are posterior to it, If, however, the right angled triangle but is by no means generated by any is the principle of figures and quali- number. Eight is indeed generated ties, and 3 and 4, the essence of the by twice four, but generates no numhebdomad, necessarily impart the ber within the decad. Again, 4 ranks right angle ; this hebdomad may among those natures that both beget justly be considered as the fountain and are begotten : for it generates of every figure, and of every quality. 8 by being multiplied by ž, and is To what has been said, it may be generated by twice two. But 7 alone,' properly added, that 3 is the number. as I have said, is neither naturally of a plane figure, since a point is ar adapted to generate, nor to be gene, ranged according to the monad, but a rated. Hence other philosophers inbine, according to the decad, and a deed assimilate this number to Victory, superficies according to the triad. who is motherless and a virgin, and But 4 is the number of a solid, by who is said to have sprung to light the addition of unity giving depth to from the head of Jupiter. But the superficies. Hence it is manifest, Pythagoreans assimilate it to the that the essence of the bebdomad is Teader, and ruler of all things. For the principle of geometry and steno that which neither generates, nor is metry, and, in short, it is the prin- generated, remains immoveable; for ciple of incorporeal and corporeal generation subsists in motion, since natures.

that also which is generated is not “There is also naturally so much without motion. For that which of what is adapted to sacred concerns generates is in motion, in order that in the hebdomad, that it has a pre it may generate, and also that which

is generated, in order that it may be

generated. Viz. The first rectangular triangle, principle and leader of things, of

But the most ancient whose sides are commensurable,

consist whom the hebdomad may appropriof the numbers 3, 4, and 5. for the

ately be said to be the imagóralone, area of such a triangle is 6, being equal to hall the product of the two sides 3

neither moves por is moved. Philolaas 3X4..

bears testimony to the truth of what and 4, i. e. But the sides of any 2

I say in the following words: ‘God rectangular triangle, whose area is less (says he) is the leader and ruler of all than 6, will be incommensurable. Thus, things, being always one, stable, im. if 5 is the area of a rectangular triangle, moveable, himself similar to himself,

2 x 5 1x 10, and different from other things. In it will be equal to

2
or to

2 intelligibles, therefore, the hebdomad Hence the two least sides will be either exhibits the immoveable and the im. 2 and 5, or 1 and 10, and the hypo- passive; but in sensible it evinces a thenuse will either be : V29, or v 101, mighty and most connective power,

ench of which is incommensurable. by which, and by the periods of the This also will be the case if the area is 4, or 3, or 2. And as the commensu•

moon, all terrestrial things are natarable is naturally prior to the incom

rally adopted to be benefited. The mensurable, the rectangular triangle,

manner, however, in which this whose sides are 3, 4, and 5, will be the

effected must be considered. * principle of the rest. Hence, too, it is “The number 7 being added to evident why 3 and 4 form the right unity, and the numbers that follow it angle,

generates 28, a perfeet number, and

MAXIMA AND MINIMA."

159 equal to its parts. But the number the seventh, there is an amelioration ? thus generated is apocatastatic of the and an increase both of intelleet and moon; 1. e. has the power of restoring reason. But in the eighth, perfection it to its pristine state, at the time in in each. In the ninth there is equity which the moon begins to receive a and mildness, the passions for the sensible increase of its figare, and to most part becoming gentle. And in" which, by decreasing, it retums. It the tenth age, is the desirable end of increases, indeed, from the first lunar life, the organic parts being still form illumination till it is bisected, eñtíre; for extreme old age is want to during seven days: afterwards, in supplant and afflict. Solon also the the same number of days it becomes Athenian legislator, enumerates In full-orbed. And again, running back man life by the above-mentioned heb as it were from the goal through tře domads. But Hippocrates, the physame path, from being full-orbed, it , sician, says, there are seven ages; viz. becomes again bisected in seven days; of the infant, the child, the lad, the and from this, in the same number of

yotmg man, the man, the elderly man, days, it acquires its first form, and and the old man, and these are mcathus gives completion to themumber sured by hebdomads, but do not ex28.

tend beyond seven. His words are "The hebdomad also is called by as follow: 'In the nature of man those who employ names properly, there are seven seasons, which they telesphoros, or the perfector, because call ages, the infant, the child, the all things acquire perfection through lad, &c. And infancy, indeed, conthis number. The truth of this, how tinues to the shedding of the teeth, eyer, may be inferred from every or but the child to the generation of the ganic body employing three intervals seed, which extends to twice seven or dimensions, i.e. length, breadth, years. The lad continues till the and depth, and four boundaries, a beard becomes rough with hairs; but point, a line, a superficies, and a solid, the young man, as far as to the infrom the composition of which the crease of the whole body, which exhebdomad is formed. It would, how tends to four times seven years. The ever, be impossible for bodies to be man continues as far as to fifty years measured by the hebdomad, accord- wanting one, i.e. to seven times seven ing to the composition of three dimen- years; but the elderly man, as far as sions and four boundaries, unless it to fifty-six years, i. e. to seven times bappened that the ideas of the first eight years. · And all the years that numbers, riz, of one, two, three, and follow this pertain to the old man.” four, in which the decad is founded,

(To be continued.) comprehended the nature of the bebé domad. For these numbers have indeed four boundaries; the first, the

MAXIMA AND MINIMA. second, the third, and the fourth, but three intervals, the first interval being Sir,-I am exceedingly obliged to from 1 to 2, the socond from 2 to 3, your correspondent, G. S., for his able and the third from 3 to 4. Inde communication in No. 322; but I pendent also of these things, the ages regret to say, that he has quite misfrom infancy to old age most clearly

taken the drift of my enquiry. exhibit the perfective power of the I was perfectly aware that some hebdomad, since they are measured quantities admit of no maximum, and by it. In the first seven years, there others of no minimum; and I by no fore, the teeth shoot forth. In the means intended to dispute the corsecond is the time of puberty. In the rectness of making the fuxion of a third, there is an increase of the . maximum or minimum = 0, but the beard. And in the fourth, there is an sole point upon which I asked for eluaccession of strength. The season of cidation was this whether in an immarriage is in the fifth. But in the possible question, such as the one' I sixth, is the acme of intelligence. In proposed, the impossibility could be

deduced from the fusionary expres# For 1+2+3+4+5+6+1=28. sion of it? And I illustrated my

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ALINOR CORRESPONDENCE-INTERIM Notices. meaning by referring to the case of flife, in two instances, in consequence of swa.

lowing a wasp, the following remedy, if made an indeterminate problem in algebra,

public through your much read Magazine, may whose impossibility becomes apparent, in similar cases prove effectual.

I am, Sir, yours, by applying the common rules for

A. E. R. solving an equation. Now, as it is plain that, whether a question be Swallowing a Wasp.--As soon as possible, dis

solve salt in the mouth, swallow the saliva ; repossible or not, it can always be cast

peat it while there is a tendency to inflammation into the form of an algebraic equa or swelling. tion, does not the same hold good

For the Sting of a Wasp, or Bee.-Moisten with regard to fluxions? And as its salt with a little water, and instantly rub the impossibility can be clearly deduced part affected with it. from the simple form of its algebraical Rifle Match.-Mr. Editor, Should any of your

numerous readers have been as much interested expression, can it likewise be deduced

as I was by the perusal of the Essay on Rifles from its fluxionary one?

and Rifle shooting, contained in one of your

recent Numbers, they will be glad to be informI will explain myself still more ed, that they will shortly have a fine opportunity familiarly, since I am really anxious of seeing the practical use of that deadly weapon

exemplified by two of our best riflemen, who for an answer to my query. Suppose have made a match to fire, at Chalk Farm, at I were to put the following question the distance of 100 and 200 yards. Any person

inquiring at the bar of the Chalk Farm taverns to an algebraist : Can I pay £10 in

within three weeks hence, will hear of the day. half guineas ?-A. It is impossible; fixed on. for 20 half guineas are too many, and

Your obedient servant, 19 too few.–Very true, I reply; but this is not the answer I desire: turn the question into an algebraic equa

INTERIM NOTICES. tion, and show its impossibility from that. This, of course, can be easily We have received a printed statement, signed done; and this is what I wish to

" William Culbard, 138, St. John-street, West

Smithfield,", in which the writer certifies that he know with respect to an impossible was favoured a few days ago with a ride in s question translated into a fuxionary

new steain-carriage, weighing less than one ton,

belonging to Sir James Anderson, Bart. and W. equation.

H. James, Esq., from Vauxhall-bridge to the I enquired, in conclusion, hot the

Swan at Clapham, a distance of ef miles, which

it accomplished in about 10 minutes, being at the question was to be solved when re rate of 15 miles an hour. Mr. Culbard does stricted to whole numbers, in which

not hesitate to add, “ that had this carriage

been on the Manchester and Liverpool Railroad case it becomes possible: G. S. has

(wbere the friction 'is ten times less than on a omitted to answer this. I have found common road), it would bave gone three or four

times faster than the fastest of the vebicles tried a method which gives a correct solu thereon!!" We shall be glad to receive some tion; but I should like to see whether further information respecting this prodigy of Those who understand the subject far

invention. 1 etter than I do would adopt the The manner in which our columns are occu. iame.

pied, will explain to Mr. Baddeley-Henry D

Mr. Walker-Mr. Harrison Mr. Davy S. P. I remain, sir, your much obliged,

W.--the author of “ Notes on Town," and so

veral other esteemed Correspondents, the cause D. C. of the delay in the insertion of their communi

cations.

We do not believe one word of Mega's stateMINOR CORRESPONDENCE.

ment; we know some parts of it to be wilfully

false. Sir, I have in my possession a plan that will completely consume the smoke arising from a steam-engine fire. It is particularly well adapt

the paper of “ Medicus" would better seie ed for locomotive steam-carriages, as it would

some of the medical journals. occupy little room, would not require any oxtra fues, and only add a few pounds to the weight

Communications received from Mr. Hopwood of the machine. The writer of this is willing to

-R. R.-Another Eye-witness-Mr. Reere communicate it toany gentleman of respectable

H. E. Y. E.--Ferro-R. W. F.-A Turner

K. c. lity; and if it does not answer in the manner stated above, no remuneration will be expected. The address of the writer may be obtained by applying at the office of the « Mechanics LONDON: Published for the Proprietor, by Magasine."

M. SALMON, at the Mechanics' Magazino Yours, &c.

Office, No. 115, Fleet Street; where Comiau. 2.

nications for the Editor (post paid) are reAntidote in case of Swallowing or being Sering

quested to be addressed. by Waspi.-Sir, Having lately heard of the loos M. SALMON. Printer. Fleet Street

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Mechanics' Magazine,

MUSEUM, REGISTER, JOURNAL, AND GAZETTE,

No. 323.)

SATURDAY, OCTOBER 31, 1829.

(Price 3d.

THE · SANS PAREIL," LOCOMOTIVE STEAM ENGINE OF $

MR. ACKWORTH, OF DARLINGTON.

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VOL. XII.

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