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418 Mr. Taylor on Relative Nothing in Mathematics. (June 1, But when they saw him hence a pris'ner With guilty horror he review'd the past, borne,

And thus the wretched Prelate breath'd his Their sorrowing hearts their benefactor mourn, last. With strecn ng eyes towards Heav'n their hands they spread,

MR. EDITOR, And loud implor'd its blessings on his head.* YOUR correspondent Philomath, in But louder still their indignation rose, your last Magazine, by representing me While imprecating curses on his foes.

as saying what I did not, and ornitting to Pursue him hence to Leicester's sacred mention what I did say, has acted the

shrine, His forfeit life just ready to resign ;

part of a reviewer, rather than that of a Worn down with age, with sickness and mathematician: for he says, “ that I

maintain, that nothing divided by a nunie despair, To his attendant hear him thus declare : ber, will produce a quotient of some “ Mark, good Sir William,t what I say to value.” This was never asserted by me thee,

of that which is absolute nothing, as “ Ambition shun, its false allurements flee; must be obvious to any of the readers of “) ye who bask in Fortune's sunny ray,

your Magazine. But what I did say, “ Who woo her smiles, her smiles as false and which he has omitted to notice, is as as gay,

follows:-/" Philomath is doubtless well " See where the wreck of her caprice I lie, acquainted with the distinction made by “ Cut off from grace and royal clemency. Dr. Cheyne in his Philosophical Prin“ Oh! had I serv'd my God with half the ciples of Religion, between relative and zeal

absolute nothing; that as the Dr. says, “ I've manifested for my sov'reign's weal,

in p. 8, of the second part of that work, “ He had not left me in this drear estate :

relative nothing is an infinitely little Ah! vain regret, 'tis now for e'er too late! “Then had my hoary hairs form'd Virtue's quantity;" and " that unity divided by

an infinite number of unities, makes the Nor to the grave disgracefully gone down. quotient relative nothing." Now, Sir, “ The die is cast, grim Death asserts his claim,

as 1 divided by 1+1+1+1, &c. ad infi“And life hut flickers with a dying flame.

uitum, gives 1 1 for the quotient, 1—1, “ Slaves of ambition ! here approach and read according to Dr. Cheyne, is an infinitely “ Your fate, and in my end behold your small quantity. Hence, though absolute meed;

nothing divided by a number will not “ For know to mortal man it ne'er was giv'n produce a quotient of some value, yet “To lord jt o'er his race in spite of Heav'n. relative nothing will. “ Even angels from their spheres ambition This distinction, however, between rethrew,

lative and absolute nothing is not only “ And after them eternal vengeance drew; adopted by Dr. Cheyne, but also by Dil" Shall man, frail man, that puny worm of ton and Emerson. For the former, in

earth, “ Presumptuous dare what blasted heav'nly to enter here into the dark algorithm of

the Preface to his Fluxions says, “ Not “ He whose frail life hangs on a slender . nothings, and infinitely less than nothread,

things, 'tis simply impossible that the "A breeze can snap, and join him to the quotient of real quantity, divided by real dead."

quantity, should ever be nothing in a ma

thematical sense. Such a quotient may * " But to tell you the truth, there were possibly be infinitely smali, and so be noalso many of the people of the country ase thing in a physical sense, or nothing in a sembled at the sate, lamenting his depar. cumparative sense, and with respect to ture, in number above 3000, who, after opening the gate that they had a sighte, be purum nihil, or strictly and ab

some other quantity; but that it should your Grace! God save your Grace! the foule solutely nothing, is, I think, strictly and evil take them that have taken you from us;

absolutely false." And Emerson, in his wee praye God that vengeance may light Algebra, p. 209, says" that o in a naupon them; and thus they ran after him thematical sense never signifies absolute through the towne of Cawood, for he was nothing ; but always nothing in relation there very well beloved both of riche and to the object under consideration."— In poore."

consequence of this, in Cor. 4, he says, The preceding notes were extracted from " that if o be divided by o, the quotient an old scarce book, entitled, Negociations of is a fiuite quantity of some sort." Thomas Holsey, the great cardinal ly his in Cor. 2.'" that if o multiply an infgentleman usher. + Sir William Kingston.

nite quantity, the product' is a finite quantity."

birth ;

And

nam

1

1

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1815.] On the Production of Something out of Nothing. 419

According to Dr. Wallis, likewise, and relative nothing, I certainly had some Neiwentiit, 1-1,1–2+1, and such like symptoms of a species of TAIASPSON EIA expressions, are infinitely small quanti- about me, when I opined that the learnties. For the former, in his Arithmetica ed mathematician might be the erudite Infinitorum, p. 151, has the following Platonist; for said I to myself, who remarkable words :-“ Dum vero diffe- knows but this deep scholar may try to rentiam infinite parvum pro nulla haben- make something out of nothing; and, dam dicimus, caute hoc accipiendum est, having once proved the necessary exneque enim id ubique, sed aliquando lap- istence of relative noting, may thience sui occasionem prabet. Cum enim infi- infer, that this relative nothing must nite purvum infinities multiplicatur, as exist eternally, that nothing is immaterial surgit nonnunquam quantitassatis magna, and something material, and therefore nempe illa ipsa cujus illa fuit alin that matter is eternal, avd that it is quota pars utut infinite parva : no matter if there is nothing ! 60+ = 1 et A+ SA” Here

But, sir, t! is th alog about nothing the doctor evidently acknowledges that has made me forget something that I

had to

say,

which 5,5, that after exhaust&c. 1+1+1+1+ ad infinitum, and ing all our stores or learning, we shall

only find ourselves, in this dark state of 1+2+3+4+5 &c. ad infinitum, are infi- mortality, playing a game of blindman's nitely small quantities. But the former buff; and so, sir, I proceed to notice a of these is equ i to 1—1, and the latter question put by the learned Philomath to 1---2+1. ' And he also admits, that in your preceding number, when he asks, the former, multiplied by 1+1+1+1 “ What mathematician would engage in &c.ad infin. and the latter by 1+2+3+4 argument with a person who maintains &c. ad infin. produces 1.

that 1—1, -3, &c. are infinitely Nejwent it too, in his Analysis Infinito- small quantities; and that nothing dirum, p. 3, asserts that if m denote an infi- vided by a number, will produce a quonite quantity, and d any finite one, then tient of some value ?"

To answer Philomath's question is is the infinitesimal of a.

above my powers; I know not what maYours, &c. Tros. TAYLOR.

thematician would do all this; and inManor-place, Walworth, May 1, 1815.

deed I can only reply in the words of a prudent Frenchman, who, when required

to sign his name with his opinion on MP.. EDITOR,

the question, “ Shall Napoleon BuonaI HAVE been much amused of late parte be Consul for life?” very cautiwith the controversy between Messrs. ously wrote, “ I cannot tell !" But, sir, Taylor and Philomath, in some of your I can tell Philomath something which recent numbers; and which, like most he may think even more strange, which other disputes, was about nothing. is, that unity may be produced out of Now, Sir, though I have no fear for no- nothing, by the multiplication and divithing absolutely, as some unlearned phi- sion used in the Algebraic calculations of Jologers express themselves, yet I must infinite lines. confess I was rather alarmned at the idea If Piilomath has any remembrance of of nothing relatively, because I reasoned his school hours, be may perhaps recolthus :-to say that there can be absolute lect a puzzling question which appeared nothing, is equal to saying that absolute some years ago in a Mathematical Diary, nothing can erist whilst nothing has ex- published, I think, in the north of Engistence; in short, if we attempt to speak Jaod :of absolute nothing, we can only do so “ With three cyphers make a sum, by an absolute contradiction of te: ms, Which shall be a maximum.” asserting that a thing can be which has The solution of which is simply thus:no existence; perhaps, however, since

oto Des Cartes has taken thought as the proof of eristence (cogito, ergo sum) per After saying so much about nothing, I haps, sir, some of those learned gentle- ani afraid, Mr. Editor, that some of your folks who make such a fuss about no readers, applying the old rule of is we thing, can think about it as well as they three,” &c., may perhaps set me down as · can write.

one ofthe 3 cy: », nay, as the maximum, So far, sir, it may be said that I had and therefore nothing shall prevent me, got hold of something since I had thus from signing inyself your's mathemati• clearly proved the non-existence of abso- caily, for the present, QIAOTAIANP. lute nolling; but then, with respect to Greek-street, Nay 1.

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TIONS.

DIONYSIUS AT CORINTH AND THE BOUR

BONS,

420

Extract from Chateaubriand on Rerolutions. (June 1, CHATEAUBRIAND'S Essay On Revolu- domineer orer children, from an babi

tual love of tyranny. Justinus, on the [We have the gratification to be enabled to

contrary, believes he only acted thus iu

order that the Corinthians might not take submit to our readers a chapter taken at random from this forthcoming work of the any umbrage at bim. Was it not rather above-mentioned admired writer, which we despair which reduced the King of Syhave announced as being in its progress racuse to such grovelling conduct? By through the press.)

insulting a person, you pay at last rerider him worthy of insult. When a wretch feels that his character is gone, and that

even the pity of mankind is withdrawn, ON the arrival of Dionysius at Co he plunges entirely into disgrace as into a rinth, all crowded to obtain the gra. species of death. tifying sight of a monarch in adversi In site of the mask of insensibility, ty. We do not so much love liber which ihe monarch of Sicily wore upon ty as we hate the great; because we his face, I doubt whether the corner of cannot endure the happiness of others, the public square, which served for his and imagine that the great are happy.- bed during the night, and which he peras kings appear to be of a species dis. haps shared with some beggar of Corinth, tinct from the rest of the human race, was not moistened with tears. Sereral they do not obtain a tear of pily in the expressions which escaped ibis prince, day of affliction. “ That is the man,” justify my conjecture. says every one to himself, “ who com Diogenes, meeting him one day, said, inanded other men, and who could in a “Thou hast not deserved such a face." moment have deprived me of liberty or Dionysius, mistaking the motive of this life.” Always mean in our propensities, remark, and astonished at finding conwe crouch at the feet of princes when in passion among mankind, could pot retheir glory, and Aly in their faces when strain an emotion of sensibility. He rethey are tallen.

plied, “ Thou dost pity me then? I What should Dionysius have done in thank thee.” The simplicity of this exhis' distress ? He should have known, pression, which might have subdued eren that the tiger of the desart is less to be the soul of Diogenes, only irritated the feared by the wretched than society.

ferocious cynic.

« Pity thee!" ex: He should have retired into some wild claimed he; “ thou deceivest thyself, place to lament his past errors, and above slave. I am in lignant at seeing the ia all, to conceal his tears.

a city, where thou canst still enjoy some The Prince of Syracuse afforded an degree of happiness.”. God forbid that important lesson to the Corinthians, and such philosophy as this should ever be strangers came in great numbers to be- mine! hold the extraordinary sight. The mi On another occasion the same prince, serable king was tatters, and passed being inportuned by a man who ophis time in the public squares, or at the pressed him with indecent familiarities

, doors of taverns, where he received, from tranquilly said, “ Happy they who have the compassionate, remains of wine and learned to suffer!" broken victuals. The populace assem Sometimes he knew how to repel a bled round him, and Dionysius degraded gross insult by a severe retort. A Cohimself so far as to amuse them with rinthian, who was suspected of being a jokes. He afterwards repaired to the pickpocket, shook his tunic as he apa shops of perfumers, or visited the female proached, to shew that he did not consingers, heard them rehearse the parts ceal a poniard, which was the custom they had to perform, and argued with when approaching the tyrants. “ Do them on the rules of music, Ere long that as you go away," said Dionysius to he was obliged, for the purpose of avoid- him. ing death from hanger, to teach gram Fortune, however, mixed some sweet mar in the suburbs to the children of ingredients in his bitter cup, but this was people in low circumstances, and even only to renderthe draught more nauseous, ihis was not the lowest degradation to Dionysius obtained permission to travel

, which fortune reduced him.

and Pbilip received him in his kingdom Such unworthy conduct has led man. with all the honours due to its rapk. kind to examine the causes of it. Cicero He had been a pedagogue at Corinth, inakes a cruel remark on the subject, king again at the royal table of Macedowhen he says, that Dionysius wished to ' nia, and was once more reduced to po

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1815.1
Chateaubriand's Essay on Revolutions.

421 verts. These strange vicissitudes might narchs will be as unfortunate as Diowell teach the Prince of Sicily the folly nysius. of life, and the vanity of the characters From the first ages of the world to the which he had played. The father of period from which the Bourbons were Alexander, nevertheless, did himself ho- expelled from France, history supplies a nour by respecting the unfortunate; great number of fugitive princes, who though he could not refrain from saying were a prey to that grief which is the to his guest, at first sight of him, with a common lot of man. In ancient times, degree of warmth, “ Low could you lose we particularly observe the blind moan empire which your father so long narch who traversed Greece, leaning on knew how to preserve?"--" I inherited Antigonus; Theseus, the legislator and his power," replied Dionysius, “ but not defender of his country, who was bahis fortune." This observation explains 'nished by an ungrateful people; Orestes the history of the human race. One accompanied by a single friend; Idomenight, when the two tyrants were fa neus driven from Crete; Demaratus, miliarly engaged in bacchanalian orgies, king of Sparta, who retired to the court that of Greece asked that of Sicily, how of Darius ; Hippias, who died at the long his father, Dionysius the elder, was battle of Marathon while trying to recoemployed in composing so great a num ver his crown; Pausanias II. king of ber of poems? “As long as you and I Sparta, condemned to death, and saved have employed ourselves in drinking,” by flight; Dionysius at Corinth; Darius answered the dethroned king gaily. Aying alone from Alexander, and assas

Fate chose at last to terminate this sinated by his courtiers; Cleomenes, the great drama of the school of kings, by a worthy successor of Agis, crucified in de nonement not less extraordinary than Egypt, to which he had retired; Antioits other scenes. Dionysius, reduced to chus Hierax, who took refuge at the the lowest degree of misery, or having court of Ptolemy, and was cast by him lost his senses through chagrin, joined a into a dungeon: Antiochus X. wanderbody of priests in the service of Cybele, ing among the Parthians and in Cilicia; and a monarch of Syracuse was seen, Mithridates seeking in vain for an asywith his lotty stature and half-closed lum at the court of Tigranes, his son-ineyes, passing through the cities and law, and reduced so far as to poison towns of Greece, dancing and skipping himself; Tarquin driven from Rome by while he struck the tabor, and then holds Brutus, and in vain raising all Italy in ing out his hand to those around, for the his behalf; with a crowd of monarchs in purpose of receiving their pititful alms. ibe two empires, whom it would be too

If I have seemed to dwell long upon tedious to enumerate. Among the mothe misfortunes of Dionysius, the reason dera nations, we observe in Africa Geliis obvious. Besides the great lesson mer,* dethroned by the Vandals, and rewhich they supply, Europe has before ber duced to cultivaie a field will lois own eyes at the inoment I write this, a strik hands; in Italy, Lamberg, the first fugiing example, not of the same vices, but tive prince of modern Europe; Pietro almost of the same adversity. The legi de Medici, who, but for Philip de Cutimate sovereign of France is now wan inines, could not have effected bis redering through Europe at the mercy of treat to Venice ; the Einperor Henry IV. mankind.

fiying from his son; the Count of Flanders Though a fourishing kingdom, a nu- pursued by Artavelle; Charles V. of merous people, and illustrious birth, France, deprived of his rank hy the faccombine to increase the bitterness of the This history is atteering, and exhibits fate experienced by Louis, still be need one of the most extravrdinary sports of tornot fear that he will, like the kings of an- tune. On the day after Gelimer secretly detiquity, be redaced to the lowest degree parted from Car hage, Belisarius dined in the of indigence. This difference is caused palace of this prince of the Vandals, and was by the relative state of constitutions. waited upon by that unfortunate monarth's Among the ancients, a fugitive prince slaves, feasting upon plate and the same met with nothing but republics, the inha- viands which has been prepared for his rebitants of wbich exulted in his distress ; fallen into the hands of the Roman Genie

past. The fugitive king, having afterwards whereas, in the modern world, he will ut least find princes to supply hiin with the

ral, was conducted to Constantinople, where necessaries of life. Should the day ar

he prostrare i linself before Justinian, and

had a small portion of land given to him in rive when Europe is converted into a de

a comer ut the empire.- Procop: de Beb. Diocracy, the last of the dethroned mo

l'anul. lii. 1, 1, 21, New MONTHLY Mac.--Vo. 17.

Vowlin,

SK

422

Chateaubriand's Essay on Revolutions, (June 1, tion of Charles of Navarre ; Charles upon any certain datum as to the nature VII. confined to his city of Orleans; of misfortune. It is probable that it acts lienry VI. of England, dethroned, re upon us by secret causes which bear restored, and dethroned again; Edward serence to our habits and prejudices, and IV, wandering in the Low Countries, de- by the situation in which we find ourprived of all support; Ilenry IV. of selves with relation to surrounding obFrance pursued by the league; Charles jects. Dionysius, who was so coniempII. of England obliged to sleep in an oak tible at Corinth, would perhaps lave in his own states, while his family on the been a very great man in the hands of continent were obliged to remain in bed his subjects at Syracuse. for want of fire; Gustavus Vasa buried Let us, however, investigate the subin the mines; Stanislaus, king of Poland, ject further. Having considered mistorescaping in disguise from his palace; tune in itself, let us examine it as to its James II. finding refuge in France, but exterior relations. whose descendants had not a place The sight of distress causes different on which they could rest their heads ; sensations in different persons. The great, Maria carrying her son through the that is to say, the rich, cannot behold i ranks of the Hungarians; and, finally, without extreme disgust. Nothing can the Bourbons terminating the list of il- be expected of them but insoleni pity, lustrious sufferers. In this catalogue of presents, and a sort of politeness ten nuisery, every one may satisfy the incli- times worse than insult. nation of his heart : envy inay contem The merchant, if you enter his counplate kings, pity the unfortunate, and phi- Ling-house, will suddenly gather up the losophy mankind.

money which happens to be upon his Thrice happy you, who look as from the desk. This mean procecding confounds shore,

the unfortunate as much as the dishonest, And have no venture in the wreck you see ! As to nations, they treat you accordIle who repeated these two lines was not ing to their national heat. In Germany a favourite of prosperity. It was the the unfortunate man meets with real hosunfortunate King Richard II., who on pitality; in Italy, with degradation, but the very morning that he was assassi- in some instances with delicate sensibinated, cast his eye over the plain which lity; in Spain, with disgraceful haughtiadjoined his prison, and envied the shep- ness, but sometimes with noble synupahierd won he saw quietly seated in the thy, The French nation, in spite ot its valley with his flock,

barbarity when assembled en masse, is There has been much disputation on the most charitable of all, and the most the subject of misfortune as or every sensible of a fellow-creature's distress, other. I subjoin a few reflections, which because it is beyond contradiction the I believe to be new.

least fond of gold. Disinterestedness is How does misfortune act on mankind ? a quality which my countryinen einiDoes it increase the energy of soul, or nently possess above all the other padiminish it? If the former, why was tions of Europe. Money is of no value Dionysius so dastardly? If the latter, to them, provided they have enough to why did the Queen of Trance display so live upon. In Holland, the unfortunate much fortitude ?

man experiences nothing but brutality; Does it assume the character of the in England he is held in sovereign convictim ? If so, why did Louis, who was tempt; but though the individuals who so timid in the days of happiness, appear constitute that nation are greedy of su courageous when adversity overtook wealth, still they are equally generous, him? And why did James II., who was considered as a body. In fact, I do not so brave in prosperity, fly on the banks know two nations inore completely opof the Boyne when he had nothing more posed to cach other in genius, manners, to lose?

virtues, and vices, than the English and Does misfortune, then, transform inan- French*; with this difference, that the hind? Are we strong because we were English generously acknowledge the weak, and weak because we were strong? French to possess several good qualities,

Against this position it may be stated, whereas the latter deny merit to any but that the pusillanimous Roman einperor themselves. who concealed himself in a private cor Let us now examine whether we may ner of his palace at the moment of his not deduce from these observations some death, had always been the same; and rules as to conduct in misfortune. I the Briton, Caractacus was as noble in know three of these. the capital of the world as in his forests. An unhappy inan is an object of cur

It appears, then, it possible to reason osity. We examine him; we like

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