Augustus De Morgan

“ I shall observe of this egregious astronomer, that there is in this work, so much artless narrative, and at the same time so much palpable imposture, that it is difficult to know when he is speaking what he really believes to be the truth. ”

“ If I may say what is in my mind, without imputation of disrespect, I suspect some actuaries have a bias: they would rather have Petty the greater for their Coryphæus than Graunt the less. [219]
Pepys is an ordinary gossip: but Burnet's account has an animus which is of a worse kind. He talks of "one Graunt, a Papist, under whose name Sir William Petty [220] published his observations on the bills of mortality." ”

“ L'Algebre est la science curieuse des Sçavans et specialement d'un General d'Armée ou Capitaine, pour promptement ranger une Armée en bataille, et nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle, outre les figures de l'Arithmetique. ”

“ Craig imitated Newton's title, and evidently thought he was making a step in advance: but it is not every one who can plough with Samson's heifer.
It is likely enough that Craig took a hint, directly or indirectly, from Mohammedan writers, who make a reply to the argument that the Koran has not the evidence derived from miracles. They say that, as evidence of Christian miracles is daily becoming weaker, a time must at last arrive when it will fail of affording assurance that they were miracles at all: whence would arise the necessity of another prophet and other miracles. ”

“ 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 Hyperbolæ Quadratura, [231] held himself to have proved that the geometrical quadrature of the circle is impossible. ”

“ It is enough for me that Graunt, whose honesty was never impeached, uses the plainest incidental professions of authorship throughout; that he was elected into the Royal Society because he was the author; that Petty refers to him as author in scores of places, and published an edition, as editor, after Graunt's death, with Graunt's name of course. The note on Graunt in the Biographia Britannica may be consulted; it seems to me decisive. Mr. C. B. Hodge, an able actuary, has done the best that can be done on the other side in the Assurance Magazine, viii. ”

“ Together with a modest enquiry into this present comet, London, 1681, 4to. A satirical tract against the cometic prophecy:
"This present comet (it's true) is of a menacing aspect, but if the new parliament (for whose convention so many good men pray) continue long to sit, I fear not but the star will lose its virulence and malignancy, or at least its portent be averted from this our nation; which being the humble request to God of all good men, makes me thus entitle it, a Petitioning-Comet." ”

“ Quære, 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. ”

“ 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. ”

“ Montucla says of him, with sly truth, that no one has ever squared the circle with so much genius, or, excepting his principal 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.
RENE DE SLUSE. Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège] , 1668, 4to. [230] The Mesolabum is the solution of the problem of finding two mean proportionals, which Euclid's geometry does not attain. ”

“ He is wronged by being coupled with Joseph Scaliger, as the two great instances of men of letters who have come into geometry to help the mathematicians out of their difficulty. I have never seen Scaliger's quadrature, [201] except in the answers of Adrianus Romanus, [202] Vieta and Clavius, and in the extracts of Kastner. [203] Scaliger had no right to such strong opponents: Erasmus or Bentley might just as well have tried the problem, and either would have done much better in any twenty minutes of his life. ”

“ 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. ”

“ Accordingly, the College of Physicians has a right to abandon its motto, which is Ars longa, vita brevis, meaning Practice is long, so life is short.
HOBBES AS A MATHEMATICIAN. Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. London, 1666, 4to. In six dialogues: the sixth contains a quadrature of the circle. [197] But there is another edition of this work, without place or date on the title-page, in which the quadrature is omitted. ”

“ P means plus in commerce and pikemen in the army; M means minus, and musketeer in the art of war;... R signifies root in the measurement of a cube, and rank in the army; Q means square (French quarè, as then spelled) in both cases; C means cube in mensuration, and cavalry in arranging batallions and squadrons. ”

“ And here are the words, on the independent testimonies of Clavius and Kastner:
"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum, tanto plus poterit ambitus polygoni quam ambitus circuli." [210]
There is much resemblance between Joseph Scaliger and William Hamilton, [211] in a certain impetuousity of character, and inaptitude to think of quantity. Scaliger maintained that the arc of a circle is less than its chord in arithmetic, though greater in geometry ”

“ This seems to be connected with the publication of another quadrature, without date, but about 1670, as may be judged from its professing to answer a tract of Wallis, printed in 1669. [198] The title is "Quadratura circuli, cubatio sphæræ, duplicatio cubi," 4to. [199] Hobbes, who began in 1655, was very wrong in his quadrature; but, though not a Gregory St. Vincent, [200] he was not the ignoramus in geometry that he is sometimes supposed. His writings, erroneous as they are in many things, contain acute remarks on points of principle. ”

“ And the more sides a polygon to be inscribed in a circle successively has, so much the greater will the perimeter of the polygon be than the perimeter of the circle."
211 ↑ De Morgan took, perhaps, the more delight in speaking thus of Sir William Hamilton (1788-1856) because of a spirited controversy that they had in 1847 over the theory of logic. Possibly, too, Sir William's low opinion of mathematics had its influence. ”

“ This is a celebrated speculation, and has been reprinted abroad, and seriously answered. Craig is known in the early history of fluxions, and was a good mathematician. He professed to calculate, on the hypothesis that the suspicions against historical evidence increase with the square of the time, how long it will take the evidence of Christianity to die out. ”

“ 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 ”

“ Vieta, the first man of his time, who answered him, had such regard for his opponent as made him conceal Scaliger's name. Not that he is very respectful in his manner of proceeding: the following dry quiz on his opponent's logic must have been very cutting, being true. "In grammaticis, dare navibus Austros, et dare naves Austris, sunt æque significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora triginta sex segmenta BCDF. Illa adsumptiuncula vera est, hæc falsa." ”

“ And now one of many instances in which literature gives to literature character in science. Anthony Teissier, [213] the learned annotator of De Thou's biographies, says of Finæus, "Il se vanta sans raison avoir trouvé la quadrature du cercle; la gloire de cette admirable découverte était réservée à Joseph Scalinger, comme l'a écrit Scévole de St. Marthe." [214]
JOHN GRAUNT AS A PARADOXER. Natural and Political Observations ... upon the Bills of Mortality. By John Graunt, citizen of London. London, 1662, 4to. [215] This is a celebrated book, the first great work upon mortality. ”

“ Although he left a manuscript on alchemy, and wrote a book entitled Delights for Ladies to adorne their Persons (1607) , he was knighted for some serious work on the chemistry of agriculture, fertilizing, brewing, and the preserving of foods, published in The Jewell House of Art and Nature (1594) .
262 ↑ "Those who wish to call a man a liar and deceiver speak of him a writer of almanacs; but those who (would call him) a scoundrel and an imposter (speak of him as) a chemist."
263 ↑ "Trust your barque to the winds but not your body to a chemist; any breeze is safer than the faith of a chemist." ”