A Budget of Paradoxes Volume I Part 38

[122] While Newton does not tell the story, he refers in the _Principia_ (1714 edition, p. 293) to the accident caused by his cat.

[123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared at Rome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. and _Apollonius redivivus_ at Venice in 1607. He was a n.o.bleman and was amba.s.sador from Venice to Rome.

[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was an engineer and a soldier, and his _La Disme_ (1585) was the first separate treatise on the decimal fraction. The contribution referred to above is probably that on the center of gravity of three bodies (1586).

[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion to Catholicism. He became a Jesuit, and was professor of mathematics at Vienna and later at Gratz. In his _Centrobaryca seu de centro gravitatis trium specierum quant.i.tatis continuae_ (1635), of the edition of 1641, appears the Pappus rule for the volume of a solid formed by the revolution of a plane figure about an axis, often spoken of as Guldin's Theorem.

[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died at London in 1615. He was a fellow of Caius College, Cambridge, and in his work ent.i.tled _The correction of certain errors in Navigation_ (1599) he gives the principle of Mercator's projection. He translated the _Portuum investigandorum ratio_ of Stevin in 1599.

[127] De Morgan never wrote a more suggestive sentence. Its message is not for his generation alone.

[128] The eminent French physicist, Jean Baptiste Biot (1779-1862), professor in the College de France. His work _Sur les observatoires meteorologiques_ appeared in 1855.

[129] George Biddell Airy (1801-1892), professor of astronomy and physics at Cambridge, and afterwards director of the Observatory at Greenwich.

[130] De Morgan would have rejoiced in the role played by Intuition in the mathematics of to-day, notably among the followers of Professor Klein.

[131] Colburn was the best known of the calculating boys produced in America. He was born at Cabot, Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown remarkable skill in numbers as early as 1810, he was taken to London in 1812, whence he toured through Great Britain and to Paris. The Earl of Bristol placed him in Westminster School (1816-1819). On his return to America he became a preacher, and later a teacher of languages.

[132] The history of calculating boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine, could extract cube roots at sight at the age of eight. Tom Fuller, a Virginian slave of the eighteenth century, although illiterate, gave the number of seconds in 7 years 17 days 12 hours after only a minute and a half of thought. Jedediah Buxton, an Englishman of the eighteenth century, was studied by the Royal Society because of his remarkable powers. Ampere, the physicist, made long calculations with pebbles at the age of four. Gauss, one of the few infant prodigies to become an adult prodigy, corrected his father's payroll at the age of three. One of the most remarkable of the French calculating boys was Henri Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for the Academie des Sciences, and a report was written by Cauchy. His specialty was the solution of algebraic problems mentally. He seems to have calculated squares and cubes by a binomial formula of his own invention. He died in obscurity, but was the subject of a _Biographie_ by Jacoby (1846).

George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an arithmetical prodigy at the age of ten, and did not attend school until he was twelve. Of the recent cases two deserve special mention, Inaudi and Diamandi. Jacques Inaudi (born in 1867) was investigated for the Academie in 1892 by a commission including Poincare, Charcot, and Binet. (See the _Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of the Sorbonne). He has frequently exhibited his remarkable powers in America.

Pericles Diamandi was investigated by the same commission in 1893. See Alfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_, Paris, 1894.

[133] John Flamsteed's (1646-1719) "old white house" was the first Greenwich observatory. He was the Astronomer Royal and first head of this observatory.

[134] It seems a pity that De Morgan should not have lived to lash those of our time who are demanding only the immediately practical in mathematics.

His satire would have been worth the reading against those who seek to stifle the science they pretend to foster.

[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in 1694. He was well known as an astronomer, mathematician, and jurist. He lived with De Thou at Paris, and accompanied him to Holland. He traveled extensively, and was versed in the astronomical work of the Persians and Arabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) that he attacked Kepler's laws. His tables were shown to be erroneous by the fact that the solar eclipse did not take place as predicted by him in 1645.

[136] As it did, until 1892, when Airy had reached the ripe age of ninety-one.

[137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584.

[138] "The false Pythagorean doctrine, absolutely opposed to the Holy Scriptures, concerning the mobility of the earth and the immobility of the sun."

[139] Paolo Antonio Foscarini (1580-1616), who taught theology and philosophy at Naples and Messina, was one of the first to champion the theories of Copernicus. This was in his _Lettera sopra l'opinione de'

Pittagorici e del Copernico, della mobilita della Terra e stabilita del Sole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. The condemnation of the Congregation was published in the following spring, and in the year of Foscarini's death at the early age of thirty-six.

[140] "To be wholly prohibited and condemned," because "it seeks to show that the aforesaid doctrine is consonant with truth and is not opposed to the Holy Scriptures."

[141] "As repugnant to the Holy Scriptures and to its true and Catholic interpretation (which in a Christian man cannot be tolerated in the least), he does not hesitate to treat (of his subject) '_by hypothesis_', but he even adds '_as most true_'!"

[142] "To the places in which he discusses not by hypothesis but by making a.s.sertions concerning the position and motion of the earth."

[143] "_Copernicus._ If by chance there shall be vain talkers who, although ignorant of all mathematics, yet taking it upon themselves to sit in judgment upon the subject on account of a certain pa.s.sage of Scripture badly distorted for their purposes, shall have dared to criticize and censure this teaching of mine, I pay no attention to them, even to the extent of despising their judgment as rash. For it is not unknown that Lactantius, a writer of prominence in other lines although but little versed in mathematics, spoke very childishly about the form of the earth when he ridiculed those who declared that it was spherical. Hence it should not seem strange to the learned if some shall look upon us in the same way.

Mathematics is written for mathematicians, to whom these labors of ours will seem, if I mistake not, to add something even to the republic of the Church.... _Emend._ Here strike out everything from 'if by chance' to the words 'these labors of ours,' and adapt it thus: 'But these labors of ours.'"

[144] "_Copernicus._ However if we consider the matter more carefully it will be seen that the investigation is not yet completed, and therefore ought by no means to be condemned. _Emend._ However, if we consider the matter more carefully it is of no consequence whether we regard the earth as existing in the center of the universe or outside of the center, so far as the solution of the phenomena of celestial movements is concerned."

[145] "The whole of this chapter may be cut out, since it avowedly treats of the earth's motion, while it refutes the reasons of the ancients proving its immobility. Nevertheless, since it seems to speak problematically, in order that it may satisfy the learned and keep intact the sequence and unity of the book let it be emended as below."

[146] "_Copernicus._ Therefore why do we still hesitate to concede to it motion which is by nature consistent with its form, the more so because the whole universe is moving, whose end is not and cannot be known, and not confess that there is in the sky an appearance of daily revolution, while on the earth there is the truth of it? And in like manner these things are as if Virgil's aeneas should say, 'We are borne from the harbor' ...

_Emend._ Hence I cannot concede motion to this form, the more so because the universe would fall, whose end is not and cannot be known, and what appears in the heavens is just as if ..."

[147] "_Copernicus_. I also add that it would seem very absurd that motion should be ascribed to that which contains and locates, and not rather to that which is contained and located, that is the earth. _Emend._ I also add that it is not more difficult to ascribe motion to the contained and located, which is the earth, than to that which contains it."

[148] "_Copernicus._ You see, therefore, that from all these things the motion of the earth is more probable than its immobility, especially in the daily revolution which is as it were a particular property of it. _Emend._ Omit from 'You see' to the end of the chapter."

[149] "_Copernicus._ Therefore, since there is nothing to hinder the motion of the earth, it seems to me that we should consider whether it has several motions, to the end that it may be looked upon as one of the moving stars.

_Emend._ Therefore, since I have a.s.sumed that the earth moves, it seems to me that we should consider whether it has several motions."

[150] "_Copernicus._ We are not ashamed to acknowledge ... that this is preferably verified in the motion of the earth. _Emend._ We are not ashamed to a.s.sume ... that this is consequently verified in the motion."

[151] "_Copernicus._ So divine is surely this work of the Best and Greatest. _Emend._ Strike out these last words."

[152] This should be Cap. 11, lib. i, p. 10.

[153] "_Copernicus._ Demonstration of the threefold motion of the earth.

_Emend._ On the hypothesis of the threefold motion of the earth and its demonstration."

[154] This should be Cap. 20, lib. iv, p. 122.

[155] "_Copernicus._ Concerning the size of these three stars, the sun, the moon and the earth. _Emend._ Strike out the words 'these three stars,'

because the earth is not a star as Copernicus would make it."

[156] He seems to speak problematically in order to satisfy the learned.

[157] One of the Church Fathers, born about 250 A.D., and died about 330, probably at Treves. He wrote _Divinarum Inst.i.tutionum Libri VII._ and other controversial and didactic works against the learning and philosophy of the Greeks.

[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology at Parma and Bologna, and was later professor of astronomy. His _Almagestum novum_ appeared in 1651, and his _Argomento fisico-matematico contro il moto diurno della terra_ in 1668.

[159] He was a native of Arlington, Suss.e.x, and a pensioner of Christ's College, Cambridge. In 1603 he became a master of arts at Oxford.

[160] Straying, i.e., from the right way.

[161] "Private subjects may, in the presence of danger, defend themselves or their families against a monarch as against any malefactor, if the monarch a.s.saults them like a bandit or a ravisher, and provided they are unable to summon the usual protection and cannot in any way escape the danger."

[162] Daniel Neal (1678-1743), an independent minister, wrote a _History of the Puritans_ that appeared in 1732. The account may be found in the New York edition of 1843-44, vol. I, p. 271.

[163] Anthony Wood (1632-1695), whose _Historia et Antiquitates Universitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are among the cla.s.sics on Oxford.

[164] Part of the t.i.tle, not here quoted, shows the nature of the work more clearly: "liber unicus, in quo decretum S. Congregationis S. R. E.

Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."

[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman who did so much for legislative and educational reform in India. His father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.

[166] The article referred to is about thirty years old; since it appeared another has been given (_Dubl. Rev._, Sept. 1865) which is of much greater depth. In it will also be found the Roman view of Bishop Virgil (_ante_, p.