Augustus De Morgan

“ If the northern hemisphere were land, and all the southern hemisphere water, ought we to call the northern hemisphere an island, or the southern hemisphere a lake? Both the questions would be good exercises for paradoxers who must be kept employed, like Michael Scott's [17] devils. The wizard knew nothing about squaring the circle, etc., so he set them to make ropes out of sea sand, which puzzled them. Stupid devils; much of our glass is sea sand, and it makes beautiful thread. Had Michael set them to square the circle or to find a perpetual motion, he would have done his work much better. ”

“ THIS LEADS TO THE CHURCH QUESTION. The Satanic doctrine that a church may employ force in aid of its dogma is supposed to be obsolete in England, except as an individual paradox; but this is difficult to settle. Opinions are much divided as to what the Roman Church would do in England, if she could: any one who doubts that she claims the right does not deserve an answer. ”

“ In this place doth a poet dwell, Who oft the stars will closely scan, And always for himself doth claim What is denied to wiser men;— An old man musing here and there And oft forgetful of himself, Not knowing how to rightly place The compasses, nor draw a line, As he doth of himself relate. ”

“ 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.
BUNGUS ON THE MYSTERY OF NUMBER. Petri Bungi Bergomatis Numerorum mysteria. ”

“ An ass is equally pressed by hunger and by thirst; a bundle of hay is on one side, a pail of water on the other. Surely, you will say, he will not be ass enough to die for want of food or drink; he will then make a choice—that is, will choose between alternatives of equal force. The problem became famous in the schools; some allowed the poor donkey to die of indecision; some denied the possibility of the balance, which was no answer at all.
MICHAEL SCOTT'S DEVILS. The following question is more difficult, and involves free-will to all who answer—"Which you please." ”

“ 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. ”

“ The writer informs his friend (whom he wished to convince that even a Lutheran would have burnt Bruno) that all Rome would tell him that Bruno died for Lutheranism; but this is because the Italians do not know the difference between one heresy and another, in which simplicity (says the writer) may God preserve them. That is to say, they knew the difference between a live heretic and a roasted one by actual inspection, but had no idea of the difference between a Lutheran and a Calvinist. ”

“ BOVILLUS ON THE QUADRATURE PROBLEM. In hoc opere contenta Epitome.... Liber de quadratura Circuli.... Paris, 1503, folio. The quadrator is Charles Bovillus, [35] who adopted the views of Cardinal Cusa, [36] presently mentioned. Montucla is hard on his compatriot, who, he says, was only saved from the laughter of geometers by his obscurity. Persons must guard against most historians of mathematics in one point: they frequently attribute to his own age the obscurity which a writer has in their own time. ”

“ The queer paradoxes of that tract leave us in doubt as to everything but this, that the church (man) is not bound to give his whole counsel in all things, and not bound to say what the things are in which he does not give it. ”

“ Montucla, or his source, ought not to have made this mistake. He had been at the Greek to correct Philo Gadetanus, as he had often been called, and he had brought away and quoted ἀπὸ Γάδαρων. Had he read two sentences further, he would have found the mistake.
We here detect a person quite unnoticed hitherto by the moderns, Magnus the arithmetician. The phrase is ironical; it is as if we should say, "To do this a man must be deep in Cocker." [24] Accordingly, Magnus, Baveme, [25] and Cocker, are three personifications of arithmetic; and there may be more. ”

“ The world shall stand six thousand years, and then it shall be consumed by fire: two thousand yeares voide or without lawe, two thousand yeares under the law, and two thousand yeares shall be the daies of the Messias.... ”

“ I am told that the Ritualists give short and practical sermons; if so, they may do good in the end. The English Establishment has always contained those who want an excitement; the New Testament, in its plain meaning, can do little for them. ”

“ His Histoire des Sciences Mathématiques appeared at Paris in 1838, the entire first edition of volume I, save some half dozen that he had carried home, being burned on the day that the printing was completed. He was a great collector of early printed works on mathematics, and was accused of having stolen large numbers of them from other libraries. This accusation took him to London, where he bitterly attacked his accusers. There were two auction sales of his library, and a number of his books found their way into De Morgan's collection. ”

“ 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. ”

“ Lyons, 1550, 8vo. De incertitudine 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 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 lust; 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. ”

“ He wrote numerous works, chiefly on astronomy. He is also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germanus de Regiomonte, etc.
46 ↑ Henry Cornelius Agrippa was born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble in 1535. He was professor of theology at Cologne and also at Turin. After the publication of his De Occulta Philosophia he was imprisoned for sorcery. Both works appeared at Antwerp in 1530, and each passed through a large number of editions. A French translation appeared in Paris in 1582, and an English one in London in 1651. ”

“ He was born at Lyons in 1640, and died at Paris in 1703. He published several arithmetics, dedicating them to his patron, Colbert. One of the best known of his works is L'arithmétique, ou le livre facile pour apprendre l'arithmétique soi-mème, 1677. The French word barême or barrême, a ready-reckoner, is derived from his name.
26 ↑ Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom Cato or Tully could have acknowledged for their countryman." His works on arithmetic, music, and geometry were classics in the medieval schools. ”

“ It also appeared at Paris in editions of 1499, 1513, and 1518, and at Oxford in 1637.
14 ↑ Jean Buridan was born at Béthune about 1298, and died at Paris about 1358. He was professor of philosophy at the University of Paris and several times held the office of Rector. As a philosopher he was classed among the nominalists. ”

“ He was made professor of mathematics in the Collège Royal (later called the Collège de France) in 1532. He wrote extensively on astronomy and geometry, but was by no means a great scholar. He was a pretentious man, and his works went through several editions. His Protomathesis appeared at Paris in 1530-32. The work referred to by De Morgan is the Quadratura circuli tandem inventa & clarissime demonstrata ... ”

“ Rumpat et serpens iter institutum, [19] —a line of Horace, which the demons interpret as a direction to come athwart the proceedings of the Institute by a sly trick. Until we saw this, we were suspicious of M. Libri, [20] the unvarying blunders of the correspondence look like knowledge. To be always out of the road requires a map: genuine ignorance occasionally lapses into truth. ”

“ This is reasonable sagacity, and very likely the correct account; but I am quite sure that, in the fit of elephant-worship under which the story was first told, it was told as I have first stated it.]
GIORDANO BRUNO AND HIS PARADOXES. [Jordani Bruni Nolani de Monade, Numero et Figura ... item de Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo. [65] I cannot imagine how I came to omit a writer whom I have known so many years, unless the following story will explain it. The officer reproved the boatswain for perpetual swearing ”