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ON THE PROPERTIES OF THE NUMBER SEVEN.

JAWA Translation. n. ɑMA Jooks I know not whether any voice can sufficiently celebrate the nature of the hebdomad, white too excellent to be described by the power of words; yet it is not proper to be silent, though what is said about it is of the most wonderful nature; but we should endeavour, if we cannot relate all and its principal excellencies, to render manifest at least such of its properties as are accessible by our reasoning power. The hebdomad, then, is spoken of in a twofold respect; one, indeed, subsisting within the decad, which is seven times measured by the monad alone, and consists of seven monads; but the other is external to the decad, of which the principle is entirely the monad, according to double, or triple, or, in short, analo gous numbers; and such are the numbers,064 and 729: the former indeed increasing by a duplication from unity; but the other by a triplication. Each species, however, ought not to be negligently considered. The second species, indeed, has a most manifest prerogative. For the heb domad, which is compounded from double, or triple, or analogous numbors from the monad, is both a cube and a square, comprehending both species; viz. of the incorporeal and corporeal essence; the species of the incorporeal, indeed, according to the superficies, which is formed by squares; but of the corporeal, according to the other dimension, (depth) which is formed by cubes. But the credibility of what is said is most manifest in the above-mentioned numbers. For the hebdomad 64, which is immediately increased from unity in a duple ratio, is a square produced by the multiplication of 8 by 8, and it is also a cube, the side or root of which is 4. And again, the hebdomad, which is increased in a triple ratio from the monad, viz. 729, is a square, indeed, formed by the multiplication of 27 by itself, and is also a cube, the side of which is 9.* By always making, too, a hebdomad the principle, instead of the monad,

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Thus, 1X2X2×2×2×2×2=64; and 1x3x3x3x3x3x3=729.

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and increasing according to the sames. analogy, as far as to the hebdomad, you will always find that the increased number is both a square and a cube. The hebdomad therefore compounded in a duple ratio from 64, will be 4096, which is both a square and a cube; a square having for its side 64 but a cube, the side of which is 16.

Let us now pass to the other species hended in the decad, and which exof the hebdomad, which is compre hibits an admirable nature no less than the former hebdomad. This, therefore, is composed of one, two, and four, which possess two most harmonic ratios, the duple and the quadruple; the former of which forms the symphony diapason, and the latter the symphony desdiapason. This hebdomad also comprehends other divisions, consisting after a manner of certain conjugations.

For it is in the first

place divided into the monad and hexad, afterwards into the decad and pentad, and lastly into the triad and tetrad. But this analogy or proportion of numbers is also most musical. For 6 has to 1 a sextuple ratio, and the sextuple ratio produces the great est interval in tones, by which the most sharp is distant from the flattest sound, as we shall demonstrate when

we make a transition from numbers to harmonies. Again, the ratio of 5 to 2 exhibits the greatest power in harmony, nearly possessing an equal power with the diapason, as is most clearly exhibited in the harmonic canon. But the ratio of 4 to 3 forms the first harmony, the sesquitertian, which is diatessaron.

"Another beauty likewise of this hebdomad presents itself to the view, and which is to be considered as most sacred. For since it consists of the

triad and the tetrad, it exhibits that a direct line in things. And it must which is undiverging and naturally in be shown after what manner this is effected. The rectangular triangle, which is the principle of qualities,

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For 64×2×2×2×2×2×2=4096. And thus also the hebdomad compounded in a triple ratio from 64 will be 46656, which is both a square and a cube; for the square root of it is 216, and the cube root is 36.

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ON. THE PROPERTIES. OF THE NUMBER SEVEN.

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consists of the numbers 3, 4 and 5.*. But 3 and 4, which are the essence of. this hebdomad, form the right angle. For the obtuse and the acute exhibit the anomalous, the irregular, and the unequal; since they admit of the more and the less. But the right angle does not admit of comparison; nor is one right angle more right than another, but it remains in the similar, and never changes its proper nature. If, however, the right angled triangle is the principle of figures and qualities, and 3 and 4, the essence of the hebdomad, necessarily impart the right angle; this hebdomad may justly be considered as the fountain of every figure, and of every quality. To what has been said, it may be properly added, that 3 is the number of a plane figure, since a point is arranged according to the monad, but a line according to the decad, and a superficies according to the triad. But 4 is the number of a solid, by the addition of unity giving depth to superficies. Hence it is manifest, that the essence of the hebdomad is the principle of geometry and stenometry, and, in short, it is the principle of incorporeal and corporeal

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rectangular triangle, whose area is less than 6, will be incommensurable. Thus, if 5 is the area of a rectangular triangle, 2x5 2 Hence the two least sides will be either 2 and 5, or 1 and 10, and the hypothenuse will either be 29, or each of which is incommensurable. This also will be the case if the area is 4, or 3, or 2. And as the commensu rable is naturally prior to the incomImensurable, the rectangular triangle, whose sides are 3, 4, and 5, will be the principle of the rest. Hence, too, it is evident why 3 and 4 form the right angle.

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eminence with reference to all the numbers that are within the decad. For of these some beget, not being themselves begotten; but others are begotten, but do not beget; and others both beget and are begotten. The hebdomad, however, is alone beheld in no part of these, which may be confirmed by demonstration as follows. Unity, therefore, generates all the numbers that are posterior to it, but is by no means generated by any number. Eight is indeed generated by twice four, but generates no number within the decad. Again, 4 ranks among those natures that both beget and are begotten: for it generates 8 by being multiplied by 2, and is generated by twice two. But 7 alone, as I have said, is neither naturally" adapted to generate, nor to be generated. Hence other philosophers indeed assimilate this number to Victory, who is motherless and a virgin, and who is said to have sprung to light from the head of Jupiter. But the Pythagoreans assimilate it to the leader and ruler of all things. For that which neither generates, nor is generated, remains immoveable; for generation subsists in motion, since that also which is generated is not without motion. For that which generates is in motion, in order that it may generate, and also that which is generated, in order that it may be generated. But the most ancient principle and leader of things, of whom the hebdomad may appropri ately be said to be the image alone, neither moves nor is moved. Philolaus bears testimony to the truth of what I say in the following words: 'God (says he) is the leader and ruler of all things, being always one, stable, im moveable, himself similar to himself, and different from other things.' In intelligibles, therefore, the hebdomad exhibits the immoveable and the impassive; but in sensible it evinces a mighty and most connective power, by which, and by the periods of the moon, all terrestrial things are naturally adopted to be benefited. The manner, however, in which this is effected must be considered.

"The number 7 being added to unity, and the numbers that follow it generates 28, a perfect number, and

equal to its parts.

MAXIMA AND MINIMA. But the number

thus generated is apocatastatic of the moon; .e. has the power of restoring it to its pristine state, at the time in which the moon begins to receive a sensible increase of its figure, and to which, by decreasing, it returns. It increases, indeed, from the first lunar form illumination till it is bisected, during seven days: afterwards, in the same number of days it becomes full-orbed. And again, running back as it were from the goal through the same path, from being full-orbed, it becomes again bisected in seven days; and from this, in the same number of days, it acquires its first form, and thus gives completion to the number

28.

"The hebdomad also is called by those who employ names properly, telesphoros, or the perfector, because all things acquire perfection through this number. The truth of this, however, may be inferred from every organic body employing three intervals or dimensions, i. e. length, breadth, and depth, and four boundaries, a point, a line, a superficies, and a solid, from the composition of which the hebdomad is formed. It would, however, be impossible for bodies to be measured by the hebdomad, according to the composition of three dimensions and four boundaries, unless it happened that the ideas of the first numbers, viz. of one, two, three, and four, in which the decad is founded, comprehended the nature of the heb domad. For these numbers have indeed four boundaries; the first, the second, the third, and the fourth, but three intervals, the first interval being from 1 to 2, the second from 2 to 3, and the third from 3 to 4. Independent also of these things, the ages from infancy to old age most clearly exhibit the perfective power of the hebdomad, since they are measured by it. In the first seven years, therefore, the teeth shoot forth. In the second is the time of puberty. In the third, there is an increase of the beard. And in the fourth, there is an accession of strength. The season of marriage is in the fifth. But in the sixth, is the acme of intelligence. In

† For 1+2+3+4+5+6+7=28.

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the seventh, there is an amelioration? and an increase both of intellect and reason. But in the eighth, perfection in each. In the ninth there is equity and mildness, the passions for the most part becoming gentle. And in the tenth age, is the desirable end of life, the organic parts being still entire; for extreme old age is wont to supplant and afflict. Solon also the Athenian legislator, enumerates human life by the above-mentioned heb-1 domads. But Hippocrates, the physician, says, there are seven ages; viz. of the infant, the child, the lad, the young man, the man, the elderly man, and the old man, and these are measured by hebdomads, but do not extend beyond seven. His words are as follow: In the nature of man there are seven seasons, which they call ages, the infant, the child, the lad, &c. And infancy, indeed, con tinues to the shedding of the teeth, but the child to the generation of the seed, which extends to twice seven' years. The lad continues till the beard becomes rough with hairs; but the young man, as far as to the increase of the whole body, which extends to four times seven years. The man continues as far as to fifty years' wanting one, i. e. to seven times seven years; but the elderly man, as far as to fifty-six years, i. e. to seven times eight years. And all the years that follow this pertain to the old man." (To be continued.)

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MAXIMA AND MINIMA.

Sir, I am exceedingly obliged to your correspondent, G. S., for his able communication in No. 322; but I regret to say, that he has quite mistaken the drift of my enquiry.

I was perfectly aware that some quantities admit of no maximum, and others of no minimum; and I by no means intended to dispute the correctness of making the fluxion of a maximum or minimum 0, but the sole point upon which I asked for elucidation was this-whether in an im possible question, such as the one I proposed, the impossibility could be deduced from the fluxionary expression of it? And I illustrated my

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peat it while there is a tendency to inflammation or swelling.

For the Sting of a Wasp, or Bee.-Moisten salt with a little water, and instantly rub the part affected with it.

Rifle Match.-Mr. Editor, Should any of your numerous readers have been as much interested. as I was by the perusal of the Essay on Rifles" and Rifle-shooting, contained in one of your

ed, that they will shortly have a fine opportunity of seeing the practical use of that deadly weapon exemplified by two of our best riflemen, who have made a match to fire, at Chalk Farm, at the distance of 100 and 200 yards. Any person inquiring at the bar of the Chalk Farm tavern within three weeks hence, will hear of the day

fixed on. Your obedient servant,

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I will explain myself still more recent Numbers, they will be glad to be inform familiarly, since I am really anxious for an answer to my query. Suppose I were to put the following question to an algebraist: Can I pay £10 in half guineas?-A. It is impossible; for 20 half guineas are too many, and 19 too few.-Very true, I reply; but this is not the answer I desire: turn the question into an algebraic equa tion, and show its impossibility from that. This, of course, can be easily done; and this is what I wish to know with respect to an impossible question translated into a fluxionary equation.

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I enquired, in conclusion, how the question was to be solved when restricted to whole numbers, in which case it becomes possible: G. S. has omitted to answer this. I have found a method which gives a correct solution; but I should like to see whether those who understand the subject far letter than I do would adopt the

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INTERIM NOTICES.

We have received a printed statement, sighed "William Culbard, 138, St. John-street, West Smithfield," in which the writer certifies that he was favoured a few days ago with a ride in a new steain-carriage, weighing less than one ton, belonging to Sir James Anderson, Bart. and W. H. James, Esq., from Vauxhall-bridge to the Swan at Clapham, a distance of 24 miles, which it accomplished in about 10 minutes, being at the rate of 15 miles an hour. Mr. Culbard does not hesitate to add, "that had this carriage been on the Manchester and Liverpool Railroad (where the friction is ten times less than on a common road), it would have gone three or four times faster than the fastest of the vehicles tried thereon!!" We shall be glad to receive some further information respecting this prodigy of invention.

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MINOR CORRESPONDENCE. 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 ed for locomotive steam-carriages, as it would Occupy little room, would not require any extra flues, and only add a few pounds to the weight of the machine. The writer of this is willing to communicate it toany gentleman of respectability; 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 1 "Mechanics applying at the office of the Magasine."

Yours, &c.

Z.

Antidote in case of Swallowing or being Stung by Wasps.-Sir, Having lately heard of the loss

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Communications received from Mr, Hopwood -R. R.-Another Eye-witness-Mr. Reere H. E. Y. E.-Ferro-R. W. F.-A Turner K. C.

LONDON Published for the Proprietor, by M. SALMON, at the Mechanics Magazine Office, No. 115, Fleet Street; where Communications for the Editor (post paid) are requested to be addressed.

M. SALMON, Printer, Fleet Street.

Mechanics' Magazine,

MUSEUM, REGISTER, JOURNAL, AND GAZETTE.

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SATURDAY, OCTOBER 31, 1829.

[Price 3d.

SANS PAREIL," LOCOMOTIVE STEAM ENGINE OF
MR. ACKWORTH, OF DARLINGTON.

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