A Budget of Paradoxes Volume I Part 9

Gadbury, though his name descends only in astrology, was a well-informed astronomer.[222] D'Israeli[223] sets down Gadbury, Lilly, Wharton, Booker, etc., as rank rogues: I think him quite wrong. The easy belief in roguery and intentional imposture which prevails in educated society is, to my mind, a greater presumption against the honesty of mankind than all the roguery and imposture itself. Putting aside mere swindling for the sake of gain, and looking at speculation and paradox, I find very little reason to suspect wilful deceit.[224] My opinion of mankind is founded upon the {116} mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in, judging by experience. I do not say anything against Isaac D'Israeli for talking his time. We are all in the team, and we all go the road, but we do not all draw.

A FORERUNNER OF A WRITTEN ESPERANTO.

An essay towards a real character and a philosophical language. By John Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225] London, 1668, folio.

This work is celebrated, but little known. Its object gives it a right to a place among paradoxes. It proposes a language--if that be the proper name--in which _things_ and their relations shall be denoted by signs, not _words_: so that any person, whatever may be his mother tongue, may read it in his own words. This is an obvious possibility, and, I am afraid, an obvious impracticability. One man may construct such a system--Bishop Wilkins has done it--but where is the man who will learn it? The second tongue makes a language, as the second blow makes a fray. There has been very little curiosity about his performance, the work is scarce; and I do not know where to refer the reader for any account of its details, except, to the partial reprint of Wilkins presently mentioned under 1802, in which there is an unsatisfactory abstract. There is nothing in the _Biographia Britannica_, except discussion of Anthony Wood's statement that the hint was derived from Dalgarno's book, {117} _De Signis_, 1661.[226] Hamilton (_Discussions_, Art. 5, "Dalgarno") does not say a word on this point, beyond quoting Wood; and Hamilton, though he did now and then write about his countrymen with a rough-nibbed pen, knew perfectly well how to protect their priorities.

GREGOIRE DE ST. VINCENT.

Problema Austriac.u.m. Plus ultra Quadratura Circuli. Auctore P. Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.--Opus Geometric.u.m posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668, folio.[227]

The first book has more than 1200 pages, on all kinds of geometry. Gregory St. Vincent is the greatest of circle-squarers, and his investigations led him into many truths: he found the property of the area of the hyperbola[228] which led to Napier's logarithms being called _hyperbolic_.

Montucla says of him, with sly truth, that no one has ever squared the circle with so much genius, or, excepting his princ.i.p.al object, with so much success.[229] His reputation, and the many merits of his work, led to a sharp controversy on his quadrature, which ended in its complete exposure by Huyghens and others. He had a small school of followers, who defended him in print.

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RENE DE SLUSE.

Renati Francisci Slusii Mesolab.u.m. Leodii Eburonum [Liege], 1668, 4to.[230]

The Mesolab.u.m is the solution of the problem of finding two mean proportionals, which Euclid's geometry does not attain. Slusius is a true geometer, and uses the ellipse, etc.: but he is sometimes ranked with the trisecters, for which reason I place him here, with this explanation.

The finding of two mean proportionals is the preliminary to the famous old problem of the duplication of the cube, proposed by Apollo (not Apollonius) himself. D'Israeli speaks of the "six follies of science,"--the quadrature, the duplication, the perpetual motion, the philosopher's stone, magic, and astrology. He might as well have added the trisection, to make the mystic number seven: but had he done so, he would still have been very lenient; only seven follies in all science, from mathematics to chemistry! Science might have said to such a judge--as convicts used to say who got seven years, expecting it for life, "Thank you, my Lord, and may you sit there till they are over,"--may the Curiosities of Literature outlive the Follies of Science!

JAMES GREGORY.

1668. In this year James Gregory, in his _Vera Circuli et Hyperbolae Quadratura_,[231] held himself to have proved that {119} the _geometrical_ quadrature of the circle is impossible. Few mathematicians read this very abstruse speculation, and opinion is somewhat divided. The regular circle-squarers attempt the _arithmetical_ quadrature, which has long been proved to be impossible. Very few attempt the geometrical quadrature. One of the last is Malacarne, an Italian, who published his _Solution Geometrique_, at Paris, in 1825. His method would make the circ.u.mference less than three times the diameter.

BEAULIEU'S QUADRATURE.

La Geometrie Francoise, ou la Pratique aisee.... La quadracture du cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe du Roi ...

Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died in 1674].[232]

If this book had been a fair specimen, I might have pointed to it in connection with contemporary English works, and made a scornful comparison.

But it is not a fair specimen. Beaulieu was attached to the Royal Household, and throughout the century it may be suspected that the household forced a royal road to geometry. Fifty years before, Beaugrand, the king's secretary, made a fool of himself, and [so?] contrived to pa.s.s for a geometer. He had interest enough to get Desargues, the most powerful geometer of his time,[233] the teacher and friend of Pascal, prohibited from {120} lecturing. See some letters on the History of Perspective, which I wrote in the _Athenaeum_, in October and November, 1861. Montucla, who does not seem to know the true secret of Beaugrand's greatness, describes him as "un certain M. de Beaugrand, mathematicien, fort mal traite par Descartes, et a ce qu'il paroit avec justice."[234]

Beaulieu's quadrature amounts to a geometrical construction[235] which gives [pi] = [root]10. His depth may be ascertained from the following extracts. First on Copernicus:

"Copernic, Allemand, ne s'est pas moins rendu ill.u.s.tre par ses doctes ecrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la force de ses Problemes, si sa trop grande presomption ne l'avoit porte a avancer en cette Science une proposition aussi absurde, qu'elle est contre la Foy et raison, en faisant la circonference d'un Cercle fixe, immobile, et le centre mobile, sur lequel principe Geometrique, il a avance en son Traitte Astrologique le Soleil fixe, et la Terre mobile."[236]

I digress here to point out that though our quadrators, etc., very often, and our historians sometimes, a.s.sert that men of the character of Copernicus, etc., were treated with contempt and abuse until their day of ascendancy came, nothing can be more incorrect. From Tycho Brahe[237] to Beaulieu, there is but one expression of admiration for the genius of Copernicus. There is an exception, which, I {121} believe, has been quite misunderstood. Maurolycus,[238] in his _De Sphaera_, written many years before its posthumous publication in 1575, and which it is not certain he would have published, speaking of the safety with which various authors may be read after his cautions, says, "Toleratur et Nicolaus Copernicus qui Solem fixum et Terram _in girum circ.u.mverti_ posuit: et scutica potius, aut flagello, quam reprehensione dignus est."[239] Maurolycus was a mild and somewhat contemptuous satirist, when expressing disapproval: as we should now say, he pooh-poohed his opponents; but, unless the above be an instance, he was never savage nor impetuous. I am fully satisfied that the meaning of the sentence is, that Copernicus, who turned the earth like a boy's top, ought rather to have a whip given him wherewith to keep up his plaything than a serious refutation. To speak of _tolerating_ a person _as being_ more worthy of a flogging than an argument, is almost a contradiction.

I will now extract Beaulieu's treatise on algebra, entire.

"L'Algebre est la science curieuse des Scavans et specialement d'un General d'Armee ou Capitaine, pour promptement ranger une Armee en bataille, et nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a 5 figures particulieres en cette sorte. P signifie _plus_ au commerce, et a l'Armee _Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons.

[It is quite true that P and M were used for _plus_ and _minus_ in a great many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armee _rang_. Q signifie _quare_ en l'un et l'autre usage. C signifie _cube_ en la mesure, et _Cavallerie_ en la composition des bataillons et escadrons.

Quant a l'operation de cette science, c'est {122} d'additionner un _plus_ d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait le moindre du _plus_, et la reste est la somme requise ou nombre trouve. Je dis seulement cecy en pa.s.sant pour ceux qui n'en scavent rien du tout."[240]

This is the algebra of the Royal Household, seventy-three years after the death of Vieta. Quaere, is it possible that the fame of Vieta, who himself held very high stations in the household all his life, could have given people the notion that when such an officer chose to declare himself an algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu, and all the _beaux_. Beaugrand--not only secretary to the king, but "mathematician" to the Duke of Orleans--I wonder what his "fool" could have been like, if indeed he kept the offices separate,--would have been in my list if I had possessed his _Geostatique_, published about 1638.[241] He makes bodies diminish in weight as they approach the earth, because the effect of a weight on a lever is less as it approaches the fulcrum.

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SIR MATTHEW HALE.

Remarks upon two late ingenious discourses.... By Dr. Henry More.[242]

London, 1676, 8vo.

In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two tracts, an "Essay touching Gravitation," and "Difficiles Nugae" on the Torricellian experiment. Here are the answers by the learned and voluminous Henry More. The whole would be useful to any one engaged in research about ante-Newtonian notions of gravitation.

Observations touching the principles of natural motions; and especially touching rarefaction and condensation.... By the author of _Difficiles Nugae_. London, 1677, 8vo.

This is another tract of Chief Justice Hale, published the year after his death. The reader will remember that _motion_, in old philosophy, meant any change from state to state: what we now describe as _motion_ was _local motion_. This is a very philosophical book, about _flux_ and _materia prima_, _virtus activa_ and _essentialis_, and other fundamentals. I think Stephen Hales, the author of the "Vegetable Statics," has the writings of the Chief Justice sometimes attributed to him, which is very puny justice indeed.[244] Matthew Hale died in 1676, and from his devotion to science it probably arose that his famous _Pleas of the Crown_[245] and other law works did not appear until after his death. One of his {124} contemporaries was the astronomer Thomas Street, whose _Caroline Tables_[246] were several times printed: another contemporary was his brother judge, Sir Thomas Street.[247] But of the astronomer absolutely nothing is known: it is very unlikely that he and the judge were the same person, but there is not a bit of positive evidence either for or against, so far as can be ascertained.

Halley[248]--no less a person--published two editions of the _Caroline Tables_, no doubt after the death of the author: strange indeed that neither Halley nor any one else should leave evidence that Street was born or died.

Matthew Hale gave rise to an instance of the lengths a lawyer will go when before a jury who cannot detect him. Sir Samuel Shepherd,[249] the Attorney General, in opening Hone's[250] first trial, calls him "one who was the most learned man that ever adorned the Bench, the most even man that ever blessed domestic life, the _most eminent man that ever advanced the progress of science_, and one of the [very moderate] best and most purely religious men that ever lived."

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ON THE DISCOVERY OF ANTIMONY.

Basil Valentine his triumphant Chariot of Antimony, with annotations of Theodore Kirkringius, M.D. With the true book of the learned Synesius, a Greek abbot, taken out of the Emperour's library, concerning the Philosopher's Stone. London, 1678, 8vo.[251]

There are said to be three Hamburg editions of the collected works of Valentine, who discovered the common antimony, and is said to have given the name _antimoine_, in a curious way. Finding that the pigs of his convent throve upon it, he gave it to his brethren, who died of it.[252]

The impulse given to chemistry by R. Boyle[253] seems to have brought out a vast number of translations, as in the following tract:

ON ALCHEMY.

_Collectanea Chymica_: A collection of ten several treatises in chymistry, concerning the liquor Alkehest, the Mercury of Philosophers, and other curiosities worthy the perusal. Written by Eir.

Philaletha,[254] Anonymus, J. B. Van-Helmont,[255] Dr. Fr. {126} Antonie,[256] Bernhard Earl of Trevisan,[257] Sir Geo. Ripley,[258]

Rog. Bacon,[259] Geo. Starkie,[260] Sir Hugh Platt,[261] and the Tomb of Semiramis. See more in the contents. London, 1684, 8vo.