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THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.

Mr. James Smith,[42] of Liverpool--hereinafter notorified--attributes the first announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of whom he gives the following account:

"In the year 1836, at which time Lacomme could neither read nor write, he had constructed a circular reservoir and wished to know the quant.i.ty of stone that would be required to pave the bottom, and for this purpose called on a professor of mathematics. On putting his question and giving the diameter, he was surprised at getting the following answer from the Professor: _'Qu'il lui etait impossible de le lui dire au juste, attendu que personne n'avait encore pu trouver d'une maniere exacte le rapport de la circonference au diametre.'_[43] From this he was led to attempt the solution of the problem. His first process was purely mechanical, and he was so far convinced he had made the discovery that he took to educating himself, and became an expert arithmetician, and then found that arithmetical results agreed with his mechanical experiments. He appears to have eked out a bare existence for many years by teaching arithmetic, all the time struggling to get a hearing from some of the learned societies, but without success. In the year 1855 he found his way to Paris, where, as if by accident, he made the acquaintance of a young gentleman, son of M.

Winter, a commissioner of police, and taught him his peculiar methods of calculation. The young man was so enchanted that he strongly recommended Lacomme to his father, and {47} subsequently through M. Winter he obtained an introduction to the President of the Society of Arts and Sciences of Paris. A committee of the society was appointed to examine and report upon his discovery, and the society at its _seance_ of March 17, 1856, awarded a silver medal of the first cla.s.s to M. Joseph Lacomme for his discovery of the true ratio of diameter to circ.u.mference in a circle. He subsequently received three other medals from other societies. While writing this I have his likeness before me, with his medals on his breast, which stands as a frontispiece to a short biography of this extraordinary man, for which I am indebted to the gentleman who did me the honor to publish a French translation of the pamphlet I distributed at the meeting of the British a.s.sociation for the Advancement of Science, at Oxford, in 1860."--_Correspondent_, May 3, 1866.

My inquiries show that the story of the medals is not incredible. There are at Paris little private societies which have not so much claim to be exponents of scientific opinion as our own Mechanics' Inst.i.tutes. Some of them were intended to give a false l.u.s.tre: as the "Inst.i.tut Historique,"

the members of which are "Membre de l'Inst.i.tut Historique." That M. Lacomme should have got four medals from societies of this cla.s.s is very possible: that he should have received one from any society at Paris which has the least claim to give one is as yet simply incredible.

NICOLAUS OF CUSA'S ATTEMPT.

Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.

The real t.i.tle is "Haec accurata recognitio trium voluminum operum clariss.

P. Nicolai Cusae ... proxime sequens pagina monstrat."[44] Cardinal Cusa, who died in 1464, is one of the earliest modern attempters. His quadrature is found in the second volume, and is now quite unreadable.

{48} In these early days every quadrator found a geometrical opponent, who finished him. Regimonta.n.u.s[45] did this office for the Cardinal.

HENRY CORNELIUS AGRIPPA.

De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons, 1550, 8vo.

De incert.i.tudine et vanitate scientiarum. By the same. Cologne, 1531, 8vo.

The first editions of these works were of 1530, as well as I can make out; but the first was in progress in 1510.[46] In the second work Agrippa repents of having wasted time on the magic of the first; but all those who actually deal with demons are destined to eternal fire with Jamnes and Mambres and Simon Magus. This means, as is the fact, that his occult philosophy did not actually enter upon _black_ magic, but confined itself to the power of the stars, of numbers, etc. The fourth book, which appeared after the death of Agrippa, and really concerns dealing with evil spirits, is undoubtedly spurious. It is very difficult to make out what Agrippa really believed on the subject. I have introduced his books as the most marked specimens of treatises on magic, a paradox of our day, though not far from orthodoxy in his; and here I should have ended my notice, if I had not casually found something more interesting to the reader of our day.

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WHICH LEADS TO WALTER SCOTT.

Walter Scott, it is well known, was curious on all matters connected with magic, and has used them very widely. But it is hardly known how much pains he has taken to be correct, and to give the real thing. The most decided detail of a magical process which is found in his writings is that of Dousterswivel in _The Antiquary_; and it is obvious, by his accuracy of process, that he does not intend the adept for a mere impostor, but for one who had a lurking belief in the efficacy of his own processes, coupled with intent to make a fraudulent use of them. The materials for the process are taken from Agrippa. I first quote Mr. Dousterswivel:

"... I take a silver plate when she [the moon] is in her fifteenth mansion, which mansion is in de head of _Libra_, and I engrave upon one side de worts _Schedbarschemoth Scharta_ch_an_ [_ch_ should be _t_]--dat is, de Intelligence of de Intelligence of de moon--and I make his picture like a flying serpent with a turkey-c.o.c.k's head--vary well--Then upon this side I make de table of de moon, which is a square of nine, multiplied into itself, with eighty-one numbers [nine] on every side and diameter nine...."

In the _De Occulta Philosophia_, p. 290, we find that the fifteenth mansion of the moon _incipit capite Librae_, and is good _pro extrahendis thesauris_, the object being to discover hidden treasure. In p. 246, we learn that a _silver_ plate must be used with the moon. In p. 248, we have the words which denote the Intelligence, etc. But, owing to the falling of a number into a wrong line, or the misplacement of a line, one or other--which takes place in all the editions I have examined--Scott has, sad to say, got hold of the wrong words; he has written down the _demon of the demons_ of the moon. Instead of the gibberish above, it should have been _Malcha betarsisim hed beruah schenhakim_. In p. 253, we have the magic square of the moon, with eighty-one numbers, and the symbol for the Intelligence, which Scott likens to a flying {50} serpent with a turkey-c.o.c.k's head. He was obliged to say something; but I will stake my character--and so save a woodcut--on the scratches being more like a pair of legs, one shorter than the other, without a body, jumping over a six-barred gate placed side uppermost. Those who thought that Scott forged his own nonsense, will henceforth stand corrected. As to the spirit Peolphan, etc., no doubt Scott got it from the authors he elsewhere mentions, Nicolaus Remigius[47] and Petrus Thyracus; but this last word should be Thyraeus.

The tendency of Scott's mind towards prophecy is very marked, and it is always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed is the prince who barters justice for l.u.s.t; he shall die in the gate by the sword of the stranger." Tippoo was killed in a gateway at Seringapatam.[48]

FINAEUS ON CIRCLE SQUARING.

Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.

Orontius[49] squared the circle out of all comprehension; but he was killed by a feather from his own wing. His {51} former pupil, John Buteo,[50] the same who--I believe for the first time--calculated the question of Noah's ark, as to its power to hold all the animals and stores, unsquared him completely. Orontius was the author of very many works, and died in 1555.

Among the laudatory verses which, as was usual, precede this work, there is one of a rare character: a congratulatory ode to the wife of the author.

The French now call this writer Oronce Finee; but there is much difficulty about delatinization. Is this more correct than Oronce Fine, which the translator of De Thou uses? Or than Horonce Phine, which older writers give? I cannot understand why M. de Viette[51] should be called Viete, because his Latin name is Vieta. It is difficult to restore Buteo; for not only now is _butor_ a blockhead as well as a bird, but we really cannot know what kind of bird Buteo stood for. We may be sure that Madame Fine was Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade rejoice in the fame which Hubertus Sussannaeus has given her.

I ought to add that the quadrature of Orontius, and solutions of all the other difficulties, were first published in _De Rebus Mathematicis Hactenus Desideratis_,[52] of which I have not the date.

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d.u.c.h.eSNE, AND A DISQUISITION ON ETYMOLOGY.

Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomic.u.m, id est, nova doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.[53]

People choose the name of this astronomer for themselves: I take _Ursus_, because he _was_ a bear. This book gave the quadrature of Simon d.u.c.h.esne,[54] or a Quercu, which excited Peter Metius,[55] as presently noticed. It also gave that unintelligible reference to Justus Byrgius which has been used in the discussion about the invention of logarithms.[56]

The real name of d.u.c.h.esne is Van der Eycke. I have met with a tract in Dutch, _Letterkundige Aanteekeningen_, upon Van Eycke, Van Ceulen,[57]

etc., by J. J. Dodt van Flensburg,[58] which I make out to be since 1841 in date. I should {53} much like a translation of this tract to be printed, say in the _Phil. Mag._ Dutch would be clear English if it were properly spelt. For example, _learn-master_ would be seen at once to be _teacher_; but they will spell it _leermeester_. _Of these_ they write as _van deze_; _widow_ they make _weduwe_. All this is plain to me, who never saw a Dutch dictionary in my life; but many of their misspellings are quite unconquerable.

FALCO'S RARE TRACT.

Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli quadraturam invenit. Antwerp, 1589, 4to.[59]

The attempt is more than commonly worthless; but as Montucla and others have referred to the verses at the end, and as the tract is of the rarest, I will quote them:

_Circulus loquitur._ Vocabar ante circulus Eramque curvus undique Ut alta solis...o...b..ta Et arcus ille nubium.

Eram figura n.o.bilis Carensque sola origine Carensque sola termino.

Modo indecora prodeo Novisque foedor angulis.

Nec hoc peregit Archytas[60]

Neque Icari pater neque Tuus, Iapete, filius.

Quis ergo casus aut Deus Meam quadravit aream?

_Respondet auctor._ Ad alta Turiae ostia Lac.u.mque limpidissimum Sita est beata civitas {54} Parum Saguntus abfuit Abestque Sucro plusculum.

Hic est poeta quispiam Libenter astra consulens Sibique semper arrogans Negata doctioribus, Senex ubique cogitans Sui frequenter immemor Nec explicare circinum Nec exarare lineas Sciens ut ipse praedicat.

Hic ergo bellus artifex Tuam quadravit aream.[61]

Falco's verses are pretty, if the U-mysteries be correct; but of these things I have forgotten--what I knew. [One mistake has been pointed out to me: it is Arch[=y]tas].

As a specimen of the way in which history is written, I copy the account which Montucla--who is accurate when he writes about what he has seen--gives of these verses. He gives the date 1587; he places the verses at the beginning instead of the end; he says the circle thanks its quadrator affectionately; and he says the good and modest chevalier gives all the glory to the patron saint of his order. All of little consequence, as it happens; but writing at second-hand makes as complete mistakes about more important matters.

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