INDEX.

Pages denoted by numerals of this kind (_287_) refer to biographical notes, chiefly by the editor. Numerals like 426 refer to books discussed by De Morgan, or to leading topics in the text. Numerals like 126 indicate minor references.

Abbott, Justice, I, _181_. Abernethy, J., II, _219_. Aboriginal Britons, a poem, II, 270. Academy of Sciences, French, I, 163. Adair, J., I, _223_. Adam, M., I, _65_. Adams, J. C., I, _43_, 82, 385, 388; II, 131, 135, 140, 303. Ady, Joseph, II, 42, _42_. Agnew, H. C., I, 328. Agricola, J., I, 394. Agricultural Laborer's letter, II, 16. Agrippa, H. C., I, _48_, 48. Ainsworth, W. H., II, _132_. Airy, I, _85_, 88, 152, 242; II, 85, 140, 150, 303, 347. Alchemy, I, 125. Alfonso X (El Sabio), II, _269_. Alford, H., II, _221_. Alfred, King, Ballad of, II, 22. Algebra, I, 121. Algebraic symbols, I, 121. Almanac, I, 300; II, 147, 148, 207. (_See Easter._) Aloysius Lilius, I, 362. Alsted, J. H., II, _282_. Ameen Bey, II, 15. Amicable Society, I, 347. Ampere, I, 86. Amphisbaena serpent, I, 31. Anagrams, De Morgan, I, 138. Anaxagoras, II, _59_. Anghera, II, 60, _60_, 61, 279. Annuities, Fallacies of, I, 157. Antichrist, I, 130. Antimony, I, 125. Antinewtonism, I, 162. Antinomians, I, 394. Antiphon, II, _59_. Antonie, F., I, _126_, 126. Apollonius, I, 41, 107. Apparitions, II, 47. Arago, I, _243_, 390. Aratus, II, _167_. Arbuthnot, I, _133_, 134. Archer, H., II, 90. Archimedes, I, 5, 11, 42, 83, 107. Archytas, I, _53_. Argoli, I, _104_. Aristocrat, as a scientist, I, 131. Aristotle, I, 5, 331. Arnobius, II, _73_. Arson, P. J., II, _207_. Ashton, R., II, _99_. Astrology, I, 118, 127, 128, 350; II, 43. Astronomer's Drinking Song, I, 380. Astronomical Aphorisms, I, 398. Paradox, I, 394. Police Report, I, 390. Society. (_See Royal Astronomical Society._) Astronomy, Bailly's exaggerated view of, I, 166. Astunica, Didacas, I, 90. Athanasian Creed, I, 371. Atheists, Philosophical, I, 1. Atoms, II, 191. {376} Attraction, I, 136, 151, 155. Augustine, St., II, _23_. Aurora borealis, I, 134. Austen, Jane, I, 191. Auzout, A., II, _300_. Aviation, Early ideas of, II, 8.

Babbage, C., I, _207_, 290, 291; II, 181. Bachet, de Meziriac, I, _161_. Bacon, F., I, 5, _75_, 75, 76, 79, 89, 145, 331. Bacon, R., I, 5, _126_, 126, 360; II, 94. Baconian controversy, I, 141. Baden Powell, II, _267_. Bailly, J. S., I, 166, _166_, 308. Baily, F., I, 308, _309_; II, 16, 143, 188. Baily, R., II, 16. Baker, T., II, _302_. Bakewell, F. C., II, 156, _156_. Banks, J., I, 28. Barberini, M., II, _267_. Barker, C., II, _262_. Baronius, I, 33, 35; II, _62_. Barreme, I, _42_. Barrett, G., II, _188_. Barrow, I., I, _160_; II, 302. Baruel, de, I, 165. Bassano, Duc de, II, 3, 339. Baxter, T., I, 146. Bayle, P., II, _73_. Beaufort, F., II, _267_. Beaugrand, I, 119, _121_. Beaulieu, I, _119_, 119, 121. Beaune, de, II, _59_. Becourt, R., II, 277. Bedford, Duke of, (6th), I, _182_. Behmen, I, _168_, 254; II, 317. Bellenden, W., I, _175_. Bentley, I, _110_. Berkeley, G., II, 346. Bernard, E., II, _297_, 300. Bernardus Trevisanus, I, _126_, 126. Bernoullis, I, 130, _150_, _335_, 336. Bertius, P., II, _300_. Bese, I, _66_. Bessel, I, _384_; II, 2. Bethune, I, _99_, 279, 291. Bettesworth, I, 19. Beza. (_See Bese._) Bickersteth, E. H., I, _238_. Bidder, I, _86_. Biden, J., II, 158, _160_. Bidle, (Biddle), I, 239. Biot, I, _85_. Birch, T., I, _108_; II, 304, 313. Birks, T. R., II, 158, _158_. Bishop, G., I, _386_. Bishops as Paradoxers, I, 226. Boccaccio, I, 38. Boethius, I, _42_, 45. Boehme. (_See Behmen._) Boncompagni, I, _298_. Boniface, St., I, 32. Bonnycastle, J., II, _16_. Booker, I, 115. Boole, G., I, _261_, 332; II, 75, 79. --A tribute to, II, 79. Borelli, G. A., II, _300_. Borello, I, _69_. Boreman, I, 113. Borron, Mrs., II, 7. Boscovich, I, _156_, 164. Bouguer, II, _301_. Bouillaud, I, _87_; II, 295. Bouvard, A., I, _327_. Bovillus, I, _44_; II, 324. --Epitome of, I, 44. Bowdler, H. M., I, _194_. Bowring, J., I, _352_; II, 256. Boyle, R., I, 24, _125_; II, 300. Bradley, I, 24. Bradwardine, I, _227_, 228, 229. Brahe. (_See Tycho B._) Brancker, I, 107; II, _300_. Brenan, J., I, 330, _330_. Brewster, D., I, 39, _137_, 140; II, 214, 288, 372. Briggs, I, _69_; II, 299, 302. Bright, J., II, _235_. Brinkley, J., I, _311_. Britannicus, D., II, 8. British Museum library, I, 151. Brothers, R., I, _315_; II, 97. Brougham, Henry, Lord, I, _191_. Brouncker (Brounker), I, _132_; II, 302. Brown, W., II, _168_. Browne, T., I, 31. Brucker, I, _61_. Brunet, I, _402_. Bruennow, I, _386_. Bruno, I, _59_, 59. Bryson, II, _59_. Buergi, I, 52. Buffon, I, _282_. Bulstrode, II, 84. Bungus, I, _55_, 55, 57. Buoncompagno, U., I, _362_. {377} Burgon, J. W., II, _30_. Buridan, I, _37_. --Questiones morales, I, 37. Buridan's Ass, I, 37. Burke, E., I, _173_. Burlesque, Frend's, I, 208. Burnet, G., I, _107_. Burney, Frances, I, _190_. Burton, Frances B., I, 374. Busby, R., II, _313_. Buteo, I, _51_. Butler, G., I, _199_. Butler, S., II, _218_. Buxton, J., I, _86_. Byrgius. (_See Buergi._) Byrne, O., I, _329_; II, 186, 190. Byron, I, 186; II, 270, 273.

Cabbala, I, 272. Calculating Boys, I, 86. Calculus, I, 129. Calendar. (_See Easter._) Cambridge Poets, II, 269. Campanus, I, 42, _43_. Canning, Geo., II, _145_. Carcavi, I, _106_. Cardanus, II, _59_. Carlile, R., I, _271_. Carlyle, T., II, _373_. Carnot, I, 107. Caroline tables, I, 124. Casaubon, I, _111_. Case, J., I, _128_, 128. Cassini, J., I, _172_. Castel, I, _148_, 148. Castiglioni, I, _139_. Castlereagh, I, 185, _186_. Cataldi, I, _69_, 69. Catcott, A., I, _237_. Causans, de, I, _298_. Cavalieri, I, _106_. Cavendish, C., I, _106_; II, 299, 312. Cavendish, W., I, _290_. Caxton, W., II, _281_. Cayley, A., II, _292_. Cecil, R. (1st Earl of Salisbury), II, _330_. Centrifugal force, II, 268. Ceulen. (_See Van Ceulen._) Challis, J., I, _390_; II, 141. Chalmers, I, _102_; II, 219. Chambers, E., II, _282_. Chambers, R., I, _344_, 344. Charles IX, II, 94. Charles X, II, 1. Chasles, I, _39_, 229. Chesterfield, Earl of (4th), II, _298_. Chiffinch, W., II, _50_. Ch'in Chiu-shang, II, 66. Chitty, J., II, _323_. Chiu-chang, Suan-shu, II, 67. Christian Evidence Society, I, 270. Christie, I, 27. Christmann, I, 272, _272_. Church question, I, 62. Church, The word, II, 30. Circle squarers. (_See Squaring the Circle._) Circulating media of mathematics, I, 107. Ciruelo. (_See Sanchez._) Clairaut, I, _219_, 382. Clarence, Duke of, I, 179. Clarke, R., I, _255_. Clavius, I, 11, _69_, 111, 112, 335, 362, 363, 372; II, 59. Clayton., Geo., II, _98_. Cluvier, D., II, 332, _332_. Cobb, Mary, II, 117. Cobbett, W., I, _177_, 200, 399. Cobden, R., II, 217. Cocker, I, _42_; II, 64, 173, 251, 307. Cody, P., II, 208. Coke, E., II, _331_. Colburn, Z., I, _86_. Colenso, I, _63_, 247; II, 191. Collins, J., I, _107_; II, 297, 300, 302, 313. Colvill, W. H., II, 68. Cometic astrology, I, 128. Comets, I, 128; II, 68, 83. Cominale, C., I, _162_, 162. Compton, S. J. A., II, _19_. Computation, Paradoxes of, II, 251, 267. Condamine, C. M. de la, II, _301_. Conduitt, John, I, _397_. Conduitt, Mrs., I, _136_. Congregation of the Index, I, 90. Converse propositions, I, 295. Convocation at Oxford, I, 96. Cooke, Margaret, I, _310_. Cooper, A. A. (Shaftsbury), II, _181_. Copernicus, I, 5, 6, _76_, 90, 121, 172, 380; II, 165, 335. Copley, J. S., I, _198_. Cormouls, I, 225. Cosmology, I, 172. {378} Cotes, R., II, _301_. Cottle, Mrs., II, 97, _97_, 161. Craig, J., I, _129_, 129. Creed, Mathematics of a, I, 329. Cribb, T., I, _314_. Crotus, J., I, 318. Cruickshank, G., I, _186_. Cube, Duplication of, I, 349. Cumyns, Eliza, I, 299. Cunningham, I, 172, _172_. Curabelle, I, _221_. Curious Calculations, II, 66. Curll, E., II, _279_. Cusa, I, _44_, 47, 360. Custom, II, 324. Cyclometry, II, 208. (_See Squaring of the Circle._) Cyclopaedias, Review of, II, 280.

D'Alembert, I, _382_; II, 283, 364. Dalgarno, I, 116, _117_. Dalton, J., I, _255_. D'Arblay, Mme., I, _190_. Darwin, E., II, _8_. Darwinism, Primitive, I, 344. Dary, M., II, _305_. Daval, P., II, _298_. Davies, T. S., II, 151, _151_, 188. Day, A., I, 295, _295_. De Baruel, I, 165. De Beaune. (_See Beaune._) De Becourt, II, 277, _277_. Debenham, J., I, _393_. De Causans. (_See Causans._) Dechales. (_See de Challes._) De Challes, I, _45_. Decimal coinage, II, 80, 168, 169. Decimals run riot, II, 80. Dee, J., II, _302_. De Faure, I, 149. De la Leu, I, _297_. Delambre, I, _160_, 167, 354; II, 165. Democritus, II, _34_. De Moivre, I, 24, _376_; II, 298. De Molieres, I, _220_. De Molina, I, _297_. Demonville, I, 291, 293. De Morgan, A., I, 191, 383; II, 194. --Refusal of LL. D., I, 191. De Morgan, G. C., I, 383. De Morgan, Mrs., I, _196_; II, 194. Denison, J., I, 348, 353. Desaguliers, I, _153_, 156, 157. Desargues, I, _119_, 221. Descartes, I, 5, 59, 105, 132, 165, 204, 220; II, 94. De Serres, II, _60_. De Sluse. (_See Sluse._) De Thou, I, 51, _111_, 113; II, 295. De Vausenville, I, 12. Devonshire, Duke of (7th), I, _290_. Diamandi, I, 86. Didacus Astunica, I, 90. Diderot, II, _4_, 283, 339. Digby, K., I, _108_. Digges, T., and L., II, _302_. Dionysius Exiguus, I, _360_. Dircks, H., II, 138, _138_. Discoverers and discoveries, II, 206. Discovery, Basis of, I, 85. D'Israeli, I., I, _115_, 118, 136, 188, 227. Ditton, I, _133_, 133. Division, Nature of, II, 248. Dobson, J., I, _234_, 234. Dodson, J., II, _312_. Dodt, I, _52_. Doggerel verse, I, 341. Dolland, I, _377_. Double Vahu Process, II, 360. Douglas, G., I, _232_. Drach, S. M., II, _317_. Drayson, G. A. W., II, _132_, 132. Dryden, II, _71_. Dual arithmetic, II, 186. Duchesne, I, _52_. Dumortier, I, 313. Duncan, A., I, _179_. Dunkin, E., II, _349_. Duodecimal scale, II, 68. Duplication Problem, I, 349. Dupuy, J. and P., II, _295_. Dutens, L., II, _90_. Dyer, G., I, _178_.

Earth, Figure of, II, 54. Easter, I, 359. Easter Day Paradoxes, I, 353. Ebrington, Thos., I, _247_. Edgeworth, Maria, I, _191_. Editorial System, I, 15. Edleston, I, _140_; II, 296. Edwards, J., I, _144_. Edwards, T., I, _112_. Eirenaeus Philalethes, I, _125_, 125, 126. Eldon, Lord (1st), II, _197_. Elephant story, I, 58. Elizabeth, Queen, I, 128. Ellenborough, Baron, I, _181_. {379} Ellicot, I, 24. Ellis, I, _76_, 82. Engel, I, 230. English language, Origin of, I, 215. Enriques, F., II, _367_. Epps, J., I, _153_; II, 143. Equation of fifth degree, I, 250, 373. Erasmus, I, 110. Erastus, I, _65_. Erichsen, I, 163. Ersch, II, _193_, 282. Erskine, T., II, _127_. Esperanto, Forerunner of, I, 116. Euclid, I, 5, 43; II, 118, 151. --Without Axioms, I, 287. Eudoxus, II, _164_. Euler, I, 221, _382_; II, 3, 4, 303, 331, 339. Eusebius, II, _220_. Eustace, J. C., II, _46_. Eutocius, I, _41_; II, 60. Evelyn, J., I, _108_. Everett, J., I, _346_. Evidence, I, 57, 58.

Faber. (_See Stapulensis._) Fairfax, Mary, I, _242_. Falco, I, 53. Faraday, M., II, _351_. Faure, de, I, 149; II, 238. Fawcett, H., II, _249_. Ferguson, J., II, _20_. Fermat, I, 122, 221; II, _300_. Ferrari, S., II, 68. Fiction, New era in, I, 189. Fienus, I, _74_, 74. Filopanti, Q. B., II, _93_. Finaeus, I, _50_, 50, 113. Finleyson, J., I, 314, _314_. Flamsteed, I, _87_, 309; II, 45, 143, 302, 306. Fletcher, I, 378. Fludd, II, _318_. Fly-leaf Paradox, II, 264. Folkes, M., I, _136_; II, 301. Fontenelle, I, _103_. Forbes, D., I, _237_. Forman, W., I, 296, _296_, 306. Forster, T. I. M., I, 320, _320_. Foscarini, I, _90_. Foster, S., II, _310_. Fourier, II, _66_. Fox, G., I, _397_. Francis, P., II, _96_. Francoeur, I, _365_. Frankland, W. B., I, 230, 287. Franklin, J., II, _265_. Freedom of opinion, Growth of, I, 265. Freher, A., II, 319. French academy on circle squaring, I, 163. Frend, W., I, _196_, 196, 206, 208, 252. Fresnel, II, _48_. Fromondus, I, _74_, 74, 99. Frost, I. and J., I, 394. Fry, Elizabeth, I, 224. Fuller, T., I, _86_. Fulton, R., I, _148_.

Gadbury, J., I, _115_, 115. Galbraith, J. A., II, 372. Galileo, I, 5, 6, 32, _76_, 82, 83, 96, 122, 381. Galle, J. G., I, _386_; II, 7. Galloway, I, _56_, 57; II, 143. Gamblers, I, 280. Garrick, I, 21. Gascoigne, W., II, _299_. Gassendi, I, _107_. Gauss, I, 86, 107, 310. Gemistus, G., I, _188_. Gentleman's Monthly, Miscellany, I, 208. Gephryander. (_See Salicetus._) Gergonne, I, _336_. Ghetaldi, I, _83_; II, 59. Ghost paradox, II, 47. Giddy (Gilbert), II, _174_. Gilbert, Davies, II, 66, _174_. Gilbert, William, I, 6, _68_, 68, 76. Gillot, II, _315_. Glazier (Glazion), II, 7. Godwin, F., I, _103_. Godwin, W., I, _174_. Golius, I, _106_. Gompertz, B., I, _378_. Goulburn, I, _288_. Goulden, S., II, 88. Graham, I, 24. Grandamicus, I, _104_, 104. Granger, J., I, _156_. Grant, A. R., II, 131. Grant, R., I, _392_; II, 131. Grassi, O., I, _262_. Grassini, I, _231_. Graunt, J., I, 113, _114_, 154. Gravity, I, 151, 244, 348, 353. {380} --Newton's apple, I, 136. Greek numerals, II, _77_. Greene, R., I, _135_, 135. Greenhill, Sir G., I, 136. Greenwich observatory, I, 87. Gregg, T. D., II, 75, _75_. Gregorian Calendar, I, 363. Gregory, D., I, _66_; II, 301. Gregory, J., I, _118_, 118, 207; II, 302. Gregory O., II, _71_. Gregory, Pope, I, 362. Grevil, I, _202_. Grey, C., (2d Earl), I, _315_; II, 247. Grosart, I, _141_, 141, 145. Grove, W. R., II, _320_. Gruber, II, _193_, 282. Gruenberger, I, _70_. Grynaeus, I, _66_. Guaricus, I, _43_. Guillim, J., II, _28_. Guldin, I, _83_. Gumpach, Von, II, 137, _137_. Gunning, H., I, _198_. Gurney. (_See Fry, E._) Guthrie, W., I, _395_.

Hailes, J. D., II, 135, _135_. Hailesean system of astronomy, II, 135. Hale, M., I, _123_, 123. Hales, S., I, _123_. Hall, B., II, _181_. Hallam, I, 159. Halley, I, 24, _124_, 311; II, 301, 332. Halliwell-Phillips, II, _148_, 296. Hamilton, W., I, _112_, 117, 331, 335, 339, 341, 342; II, 52, 53, 111. Hamilton, W. Rowan, I, _332_; II, 104, 256, 343. Hanover, King of, I, 201. Hardy, C., I, _298_. Hardy, T., I, _178_. Harriot, T., II, _302_. Harvey, I, _76_, 78; II, 201. Hauff, I, _230_. Haughton, S., II, 372. Hauksbee, F., I, _156_. Hayes, C., I, _132_, 132. Heath, D. D., I, _76_. Heinfetter, H., II, 94, _94_. Helmont, J. B. van, I, _125_. Henson, II, 8. Heraclitus, II, _34_. Herbart, J. F., I, 253, _253_; II, 78. Herigone, II, _59_. Herschel, J., I, _80_, 299, 326, 383, 386; II, 88, 95, 181, 255, 261, 262. Herschel, W., I, _81_, 151, 192, 225, 233, 299; II, 288, 348. Heywood, F., II, _49_. Hicks, J. P., II, _67_. Higgins, G., I, _257_, 274. Hilarius, Pope, I, _359_. Hill, J., I, 21, 22, 23, 24. Hill, Rev. R., I, _192_. Hill, Sir R., I, _165_, 232. Hind, J. R., I, _384_. Hippocrates, II, _59_. Hoax, An interesting, I, 163. --Lunar Caustic, I, 288. --Moon (Herschel), I, 326; II, 131. Hobbes, I, _105_, 109, 143, 144; II, 80. Hobhouse, J. C., II, _126_. Hodder, J., II, _265_. Hodge, C. B., I, 114. Hodges, W., I, 237. Hoffmann, J. J., II, _282_. Hoffmann, J. J. I. von, I, _230_. Holloway, B., I, _237_. Holmes, O. W., I, 109. Holyoake, G. J., I, _399_, 399. Hone, W., I, 124, 180, 184, 185. Hook, T. E., II, _261_. Hooke, I, _77_; II, 300. Hooker, R., II, _201_. Hopkins, J., II, 41. Horace, I, 40. Horne, G., I, _152_, 152, 154, 155, 236. Horne, J., I, _178_. Horner, L., I, _176_. Horner, W. G., II, _66_, 151, 187. Houlston, W., II, 156, _156_. Howard, E., I, 131. Howison, W., I, 256, _256_. Howitt, W., II, 193, _193_. Howley, I, 63. Hulls, I, _147_, 147; II, 8. Hume, J., I, _352_; II, 174. Husain Rifki, II, 16. Hussein Effendi, II, 15. Hutchinson, J., I, 154, _154_. Hutton, C., I, _153_, 161; II, 303, 340. Huyghens, I, _100_, 133; II, 300.

Imaginary numbers, II, 186. Impalement by request, II, 133. Inaudi, I, 86. Index Expurgatorius, I, 90. {381} Infant prodigies, I, 86. Inglis, J. B., II, _52_. Inglis, R. H., I, _352_. Ingliz Selim Effendi, II, 15. Innocent I., I, _359_. Irving, E., II, _54_. Ivory, J., II, 142, _142_.

Jabir ben Aflah, II, _59_. Jack, R., I, 149. Jacotot, J., I, 278, _278_. Jameson, Mrs., II, _63_. Jeffreys, G., I, _183_. Jenner, E., II, _205_. Jesuit contributions, I, 164. Johnson, H. C., I, 350. Johnson, S., I, 20, _190_, 259; II, 117. Johnston, W. H., II, 67. Jombert, I, _161_. Jonchere, I, _146_, 146. Jones, W., I, _135_; II, 298, 301. Jones, Rev. W., I, _237_. Jonson, B., I, 13. Journals, Three classes of, II, 144.

Kantesian Jeweler, I, 258. Karsten, I, _230_. Kaestner, I, _43_, 110, 112. Kater, I, 11. Keckermann, I, 3. Keill, J., II, _302_. Kepler, I, 52, _76_, 82, 381; II, 166. Kerigan, T., I, _308_, 353. Keroualle, De, II, 50. Kersey, I, 107. King, Wm., I, _246_. Kircher, Adolphe, I, 229. Kircher, Athanasius, I, _103_. Kirkringius, T., I, 125, _125_. Kittle, I, 236. Klein, F., II, 367. Knight, C., II, _109_, 280, 289. Knight, G., I, 151, _151_. Knight, R. P., II, _274_. Knight, Wm., I, _97_. Koenig, S., I, _150_.

Lacomme, I, 46. La Condamine, II, _301_. Lacroix, I, 41, 159, 207. Lactantius, I, 33, _96_. Lagrange, I, 221, _288_, 313, 382; II, 86. Laing, F. H., II, _186_, 186. Lalande, I, _159_. Lamb, C., I, 178; II, 270. Lambert, J. H., I, _336_; II, 214, 367. Lambert, John, II, _309_. Language, Test of, II, 327. Lansbergius, I, _70_, 70. Laplace, I, 24, _255_, 382; II, 1, 340. Lardner, D., II, _253_. Lardner, N., I, 14; II, _221_. Laud, I, _145_. Lauder, W., I, 297. Laurent, P., I, _309_, 309. Laurie, J., II, 4. Laurie, P., II, _42_. Laurus, I, 381. Law, Edmund, I, _181_. Law, Edward, I, _181_. Law, W., I, 168, _254_; II, 317. Le Coq, I, _86_. Lee, R., I, _66_. Lee, S., I, _131_. Lee, W., I, 157. Legate, I, _59_. Legendre, I, _229_; II, 215, 367. Legh, P., II, _68_, 83. Leibnitz, I, 5, 7; II, 46. Leo, St., I, _359_. Leverrier, I, _43_, 82, 383, 386, 388, 390; II, 7, 135, 140, 303. Lewis, G. C., II, 162, _162_. Libri, I, _40_, 62; II, 295. Lilius, Aloysius, I, 362. Lilly, I, _115_; II, 302. Lipen, M., I, _298_. Little, J., I, 206. Livingston, R., I, _148_. Locke, J., I, _142_, 142, 144; --and Socinianism, I, 142. Locke, R., I, 146. Locke, R. A., I, _326_; II, 86, 131. Logan, W. E., I, _337_. Logic, Formal, I, 158; II, 75. --Has no paradoxes, I, 330. London Mathematical Society, I, 383. London, University of, I, 259; II, 71. Long, G., II, _290_. Long, J. St. J., II. _38_, 205. Longitude problems, I, 132, 146, 249. Longley, C. T., I, _325_. Longomontanus, I, _105_, 105. Lottery, I. 281. Lovett, R., I, 165, _166_. Lowe, R., II, _169_. Lowndes, W. T., I. _402_. Lubbock, J., I, _279_; II, 148. {382} Lucas, F., II, _28_. Lucian, I, _102_. Lunar Caustic Joke, I, 288. Lunn, J. R., II, _66_. Lydiat, T., II, _302_. Lyndhurst, I, _198_.

Macclesfield, Earls of, I, 7; II, _296_, 301. Macclesfield, Letters, II, 296. MacElshender, II, 87. Machin, J., II, _301_. Mackey, John, I, 349. Mackey, S. A., I, _256_. Maclear, T., II, _181_. Macleod, H. D., II, 184, _184_. Magic, I, 118. Magna Charta, I, 25. Magnus, I, 42. Maitland, S., I, _63_, 163. Malacarne, I, 119. Malden, H., II, _162_. Malius, II, _342_. Mallemens, II, _333_. Mankind gullible, I, 115. Manning, H. E., (Card.), II, _233_. Mansel, H. L., II, _162_. Marcelis, J., I, _129_, 129. Maret, II, _3_. Margarita Philosophica. (_See Reisch._) Marryat, Capt., II, _87_. Marsh, H., I, _199_, 271. Martin, B., I, _152_, 153. Martin, R., II, _236_. Maseres, F., I, _197_, 203. Mason, M., II, _132_. Mathematical Illustrations of Doctrine, II, 70; --Psychology, I, 253; --Society, I, 374, 376, 382; --Theology, I, 149. Mathematics, Condensed history of, II, 58. Matter to Spirit, II, 194. Maty, I, 23. Maupertuis, II, _301_. Maurice, F. D., II, _101_. Maurolycus, I, _121_. Maxwell, A., I, _102_. Meadley, G. W., I, _223_. Mechanics Magazine, II, 141, 145. Medici, Cosmo de, II, _295_. Medicine, Status of, I, 266. Melanchthon, II, _323_. Menestrier, I, _127_, 127. Mercator, G., II, _92_. Mercator's projection, I, 84. Mersenne, I, _106_, 107; II, 295, 297. Meslier, J., II, _195_. Meteorologist, An early, I, 320. Meteorology, I, 327. Metius, A. and P., I, _52_, _99_, 99. Meton, II, 167. Metric System, Forerunner of, I, 171. Meziriac, I, 161. Milbanke, A. I., I, 225. Mill, Jas., I, 260. Miller, Joe, I, _182_. Miller, S., I, 167. Mills, Elizabeth, W., II, 7. Milne, J., I, _286_. Milner, I., I, _251_, 251. Milner, J., II, _23_. Milner's lamp, I, 252. Milward, II, _250_. Miracles _vs_. Nature, II, 6. Mitchell, J., I, _242_. Moliere, I, _232_. Molina, A. C. de, I, _297_. Mollendorff, von, II, _3_, 338. Mondeux, I, 86. Montague, C., II, _311_. Montmort, P. R. de, II, _301_. Montucla, I, 40, 45, 54, 65, 117, 120, 159, 163; II, 60. Moon Hoax, I, 326; II, 131. Moon, Nature of, II, 84; --Rotation of, II, 4, 19, 84, 87. More, Hannah, I, _189_, 192. More, Henry, I, 123. Moore, Dr. John, I, _190_. Moore, Sir John, I, _190_. Morgan, S., I, 6. Morgan, T., I, 191. Morgan, W., I, _223_, 224. Morhof, I, _61_. Morin, I, _99_, 99. Morinus, J. B., I, 149. Morland, S., II, _302_. Mormonism, II, 69. Morrison, R. J., I, _321_; II, 43. Mose, H., II, _266_. Mottelay, I, 68. Motti, II, 60. Mouton, I, _172_; II, 300. Muggleton, I, 394, _395_. Multiplication, Nature of, II, 251. Murchison, R. I., I, _384_. Murhard, I, _43_, 298. {383} Murphy, A., II, _308_. Murphy, J. L., II, 54, _54_. Murphy, P., I, _327_, 398. Murphy, R., I, 349, _349_. Murray, J., I, _186_; II, 145. Murray, L., II, _326_. Murray, Mungo, II, 310. Musgrave, T., I, _324_. Mydorge, I, _298_. Mystrom, J. W., II, 182. Mythological paradoxes, I, 256.

Names of Religious Bodies, II, 22. Napier, J., I, 5, 66, _67_, 82. Napoleon, Doubts as to, I, 246. Nautical Almanac, I, 300; II, 147. Neal, I, _98_. Negative numbers, I, 196, 203. Neile, W., II, _190_. Neptune, Discovery of, I, 387; II, 140. (_See Adams, Leverrier._) Nesse, C, I, _128_, 128. Newcomb, S., I, 162. Newcomen, T., I, _147_. Newton, Sir Isaac, I, 5, 6, 8, 24, 39, 84, 88, 130, 136, 139, 144, 145, 148, 152, 154, 155, 162, 165, 167, 197, 225, 237, 242, 257, 282, 296, 297, 309, 311, 382, 394, 395, 396, 397; II, 2, 70, 184, 297, _302_, 305. Newton, John, II, _305_. Nicene Creed, I, 371. Nichol, J. P., II, _289_. Nicholas. (_See Cusa._) Nichols, J., I, _175_. Nicolas, N. H., I, _354_. Nicollet, I, _326_; II, 131. Nicolson, W., I, _201_. Nieuwentijt, II, _333_. Nizzoli, M., II, 275. Non-Euclidean geometry, II, 83. Northampton, Marquis of (2d), II, _19_. Novum Organum Moralium, II, 74. Number, Mystery of, I, 55, 56, 169. Number of the Beast (666), I, 55, 130, 272, 298, 352; II, 77, 159, 217, 218, 361, 373. Numeral system, II, 68. Nursery rhymes, II, 150.

Occam, Wm. of, II, _40_. Odgers, N., II, 191, _191_. Oinopides of Chios, II, _59_. Oldenburgh, H., II, _300_, 302. Orthodox Paradoxes, II, 363. Orthography, Paradoxes of, II, 267. Ortwinus, I, 319. Oughtred, W., II, _298_, 303. Owenson, I, _191_. Ozanam, I, _161_, 312.

Pagi, I, 32. Paine, T., I, 173, _173_, 271. Paley, W., I, _222_; II, 226. Palmer, C., I, 225. Palmer, H., I, _141_, 141, 145. Palmer, J., II, _253_. Palmer, T. F., II, _254_. Palmer, W., II, _37_. Palmerston, Viscount (3d), I, _290_, 352. Palmezeaux, I, 167. Panizzi, A., I, _151_. Papist, II, 26. Paracelsus, II, 322. Paradox defined, I, 2, 31. Paradox, religious, I, 236. Paradoxers in general, II, 352. Parallels, Theory of, I, 229, 344. Pardies, I. G., II, _300_. Park, Mungo, II, _91_, 132. Parker, F., II, _94_. Parker, G. (Earl of Macclesfield), II, _296_. Parr, S., I, 173, _173_, 175, 176, 184. Parsey, I, 293, _293_. Partridge, J., I, _305_. Pasbergius, I, 381. Pascal, I, 39, 119, 122, _220_, _221_; II, 73. Pascal's Hexagram, I, 221. Passot, I, 279, _279_. Passover, I, 358, 372. Patriotic paradox, I, 231. Paucton, I, _172_. Paulian, I, 165, _165_. Peacock, Geo., I, _196_, 350. Peacock, T. L., I, _190_, 340. Pearce, A. J., II, 43. Pearne, T., I, _239_. Peel, Sir R., I, 290, _352_. Peel, W. Y., I, _290_. Pelerin, J., II, _324_. Pell, J., I, _105_, 105, 107; II, 300, 302, 312. Pepys, I, _113_, 114. Perigal, H., II, 19, _20_. {384} Perpetual motion, I, 118, 348; II, 55, 138. Perspective, New theory of, I, 293. Peters, W., II, 11, 315. Petitioning Comet, I, 127. Petrie, W. M. F., I, _328_. Petty, I, _114_; II, 300. Philalethes, Eirenaeus, I, _125_, 125, 126. Philalethes, Eugenius, I, _255_. Phillips, R., I, 242, _242_, 245. Philo of Gadara, I, 40, _40_. Philosopher's stone, I, 118, 125. Philosophical atheists, II, 1. Philosophy and Religion, II, 37. Phonetic spelling, II, 81. [pi], values of, I, 11, 43, 45, 46, 52, 69, 100, 110, 129, 135, 146, 245, 283, 284, 294, 347, 348, 349, 350; II, 60, 63, 105, 110, 118, 135, 156, 209, 279, 315, 316. Pighius, I, _372_. Pike, S., I, 236, _236_. Pindar, P., II, _272_. Piozzi, Mrs., I, _235_; II, 272. Piscator, B., II, 25. Pitman, F., II, 81, _81_. Place, F., I, _199_. Planets inhabitable, I, 100, 102. Plato, I, 5. Platt, H., I, _126_, 126. Playfair, J., I, _233_. Pletho, G., I, _188_. Pliny, II, 280. Ploucquet, I, _336_, 337. Poe, E. A., II, 132. Poincare, I, 136. Poisson, I, _292_; II, 2. Pollock, J. F., II, _174_. Pons, II, _45_. Pope, Wm., I, 277, _277_. Porta, I, _68_, 68, 83. Porteus, B., I, _193_, 203. Porteus, H. F. A., II, 157, _157_. Porus, I, 44. Powell, Baden, II, _267_. Powell, W. S., I, _222_. Pratt, H. F. A., II, 157, _157_. Pratt, O., II, _69_. Predaval, Count de, I, _348_. Prescot, B., I, 270, _270_, 278. Prester John, I, 70, _71_, 152. Price, R., I, _223_. Probability, Discourse on, I, 279. Proclus, I, 188, _188_. Prodigies, Youthful, I, 219, 332. Pronunciation, II, 330. Protestant and Papal Christendom, II, 33. Protimalethes, II, 6. Ptolemy, I, 5, 33, _380_. Pullicino, II, 61, _61_. Pusey, I, _64_. Pyramids, The, I, 328; II, 95, 136. Pythagoras, II, _59_.

Quadrature problem. (_See Squaring the circle._) Quarles, F., II, _277_. Quintilian, II, 280. Quotem, C., I, 399.

Rabelais, I, _102_. Rainbow Paradox, II, 334. Ramachandra, Y., I, _374_. Ramchundra, I, 374. Ramus, I, 5. Recalcati, II, 208, 314. Recorde, R., II, _328_. Reddie, Jas., II, 183, _183_, 344, 360. Reeve, J., I, _395_. Regiomontanus, I, _48_, 360. Reisch, I, _45_; II, 281. Religion and Philosophy, II, 37. Religious bodies, Names of, II, 22; --customs, Attacks on, I, 177; --Insurance, I, 345; --Paradox, I, 236; --Tract society, I, 192. Remigius, I, _50_. Reuchlin, J., II, _323_. Revelations, Napier on, I, 66. Revilo, (O. Byrne), I, 241, 329, _329_. Reyneau, C. R., II, _301_. Rheticus, I, _69_; II, 372. Rhonius, II, 300. Ribadeneira, P. de, II, _62_. Riccioli, I, _96_. Richards, G., II, _270_. Rigaud, J., II, _299_. Rigaud, S. J., II, _299_. Rigaud, S. P., I, _140_; II, 298, 313. Ringelbergh, J. S., II, _281_. Ripley, G., I, _126_, 126. Ritchie, W., I, 295, _295_. Ritterhusius, I, _60_. Rive, J.-J., I, _160_. Robertson, Jas., I, _237_. Roberval, I, _105_, 122. {385} Robinson, B., I, _148_, 148. Robinson, H. C., I, _314_; II, 52, 275. Robinson, R., I, _177_. Robinson, T. R., II, _181_. Roblin, J., II, 136. Rogers, S., II, _260_. Roget, P. M., I, _398_. Roomen, A. van, I, _110_. Ross, J. C., I, _303_. Rosse, I, 26. Rossi, G., I, 231, _231_. Rotation of the Moon, II, 4, 19. Rough, W., I, 198. Rowning, J., I, _155_. Royal Astronomical Society, I, 27; --Forerunner of, I, 374. Royal Society, I, 21, 22, 24-30, 56, 57, 136, 153, 163, 164, 165. Rudio, I, 159; II, 367. Rudolff, C., II, 373. Russell, Earl (1st), I, _296_. Rutherford, W., II, _109_.

Sabatier, A., II, _267_. Sabellius, I, _241_. Sacrobosco, I, _360_. Sadler, T., I, _238_, 241. Saint-Martin, I, 167, _168_, 206. St.-Mesmin, M. de., I, 280. St. Vincent, G. de., I, _110_, 117. St. Vitus, Patron of Cyclometers, II, 60. Sales, de, I, 167. Salicetus, I, 64. Salisbury, Earl of (1st), II, _330_. Salmasius, Claudius, II, _168_. Salusbury, Hester, I, _235_. Sanchez, Petro, I, 229, _229_. Sanders, W., I, 207. Sanderson, R., I, _135_. Sara, R., I, _297_. Saunderson, N., I, _377_; II, 301. Scaliger, I, _44_, 110, 111, 112, 113; II, 238. Scevole de St. Marthe, I, 113. Schooten, Van, II, _59_. Schopp, I, _60_. Schott, I, _64_; II, 64. Schumacher, H. C., I, _107_; II, 297. Schwab, I, _230_. Scientific paradoxes, I, 232. Scott, Michael, I, _38_. Scott's Devils, I, 38. Scott, W., I, 20, 27, 38, 39, 155, _191_. Scripture and Science, II, 261. Search, John, I, 247. Selden, J., II, _250_. Senarmont, II, _48_. Serres, De, II, _60_. Shaftesbury, Earl of, II, _181_. Shakespeare, I, 13. Shanks, II, _63_, 65, 109. Shaw, P., I, _142_. Sheepshanks, J., I, _147_. Sheepshanks, R., I, _290_. Shelley, I, 174. Shepherd, S., I, _124_. Sherburne, E., II, _295_. Sheridan, R. B., I, _175_. Sheridan, T., I, _175_. Shoberl, F., II, _270_. Shrewsbury, I, _108_. Siddons, Mrs., I, 189. Simms, W., I, _152_. Simplicius, II, _164_. Simpson, T., I, 377; II, 304. Simson, R., I, _197_, 202, 233. Sinclair, G., I, _207_. Slander Paradoxes, II, 138. Sloane, I, 24. Sluse, R. de, I, _118_, 118; II, 300. Smith, Adam, II, _112_. Smith, Jas., I, _46_; II, 103, _103_, 154, 236, 237, 238, 241, 336, 360. Smith, Jas., II, _217_. Smith, Jas. (Shepherd), II, _55_, 193. Smith, Joseph, II, _69_. Smith, Richarda, I, _242_. Smith, Thomas, I, 346, _346_. Smith, Wm., II, _152_. Smyth, C. P., I, _328_; II, 65. Snell, I, _75_, 75. Socinianism, I, 142, 143. Socinus, I, 3, _143_. Socrates Scholasticus, I, _358_. Sohncke, L. A., II, _131_. Somerville, Mrs., I, _242_. South, J., II, _181_. Southcott, Joanna, II, _58_, 97, 239. Spearman, R., I, _237_. Speculative thought in England, I, 374. Spedding, I, _76_, 82, 142. Speed, J., I, _201_. Speke, I, _70_. Spelling, phonetic, II, 81. Spence, W., I, _231_, 231. Spencer, Earl (3d), II, _9_. {386} Spinoza, I, 3, _37_. Spiritualism, II, 47, 55, 207. Spurius Cassius Viscellinus, II, _342_. Spurius Maelius, II, _342_. Squaring the circle, I, 8, 42, 44, 46, 47, 50, 52, 53, 69, 70, 75, 109, 117, 119, 129, 135, 146, 149, 159, 163, 164, 347, 348, 374; II, 10, 11, 60, 105, 154, 156, 208, 278, 314. Staeckel, I, 230. Stanhope, P. D., (Earl of Chesterfield), II, _298_. Stapulensis, I, _44_; II, 324. Star polygons, I, 229. Starkie, G., I, _126_, 126. Statter, D., II, 80. Steamship suggested, I, 147. Steel, Jas., II, 68. Stenography, II, 81. Stephens, I, _44_; II, 324. Stephenson, G., II, _138_. Stephenson, R., II, _138_. Stevin, I, _83_, 313; II, 59. Stewart, D., II, _53_. Stewart, R., I, _186_. Stifel, M., II, _373_. Strafford, Earl of, I, _240_. Stratford, W. S., I, _300_. Street, T., I, _124_. Stukely, W., I, _236_. Suffield, G., II, _66_. Suidas, II, _29_. Sumner, C. R., I, _324_. Sumner, J. B., I, _324_. Sun as an electric space, II, 41. Supernatural, The, II, 193. Suvaroff, II, _85_. Swastika, II, 231. Swedenborg, E., I, _255_. Swift, I, 19, 133. Sylvester, J. J., II, _336_. Symington, W., I, _148_. Symons, II, 4, 5, 20, 84, 85. Sympathetic powder, I, 108. Synesius, I, 125.

Talbot, G., I, _22_, _108_. Talbot's powder, I, 108. Tartaglia, II, 59. Tasse, I, _106_. Tate, J., I, _199_. Tauler, J., II, _322_. Taylor, Brook, II, _301_. Taylor, John, I, _352_; II, 95. Taylor, Robt., I, _270_. Taylor, T., I, 188, _188_. Teissier, I, _113_. Temple, H. J., I, 290. Tenterden, Chief Justice, I, _181_. Thales, II, _59_, 83. Theism independent of Revelation, I, 399. Thelwall, J., I, _178_. Theodoretus, I, _358_. Theological Paradoxes, I, 316. Theology, Mathematical, I, 129, 149. Theophrastus, II, _167_. Thiebault, II, _3_, 338. Thom, D., II, _226_, 240. Thom, J. H., II, _226_. Thompson, P., I, _7_. Thompson, T. P., I, _252_, 287, 344; II, 83, 185. Thomson, Dr., I, 21. Thomson, W., I, _325_. Thorn, W., II, 158, _158_, 360. Thorndike, H., II, _313_. Thrale, Mrs., I, _235_. Thurlow, Baron, I, _222_. Thyraeus, I, 50. Tides, New theory of, I, 393. Tombstones of mathematicians, I, 106. Tonal System, II, 182. Tooke, H., I, _178_. Torriano, E., I, 250. Towneley, II, 300. Townley, C., II, _300_. Trisection problem, I, 118; II, 10, 12, 13, 15. Troughton, I, _152_. Turnor, E., I, _137_. Tycho Brahe, I, 5, _76_, 381; II, 302, 335.

Upton, W., II, 12, _12_, 15. Ursus, I, _52_.

Valentine, B., I, _125_, 125. Van Ceulen, I, 52, 70, 100. Van de Weyer, I, _313_. Van Etten, I, _161_. Van Helmont, I, _125_, 125. Van Roomen, I, _110_. Van Schooten, II, _59_. Vaughan, T., I, _255_. Victorinus, I, _359_. Viete, I, _51_; II, 210, 295. Virgil, St., I, 32, _33_, 34, 99. {387} Virginia, University of, I, 233. Viscellinus, II, _342_. Vitruvius, II, _281_. Vivian, T., I, 172, _172_. Vogel, A. F., I, 373. Voltaire, I, 103, 165, 166, 167, 168, 248; II, 268. Von Gumpach, II, 137, _137_. Von Hutten, I, 318. Von Wolzogen. (_See Wolzogen._) Vyse, R. W. H., I, _328_.

Walker, W. E., II, _316_. Walkingame, F., II, _173_. Wallich, N., II, _14_. Wallis, J., I, 107, 109, 110; II, 299, 313. Walpole, I, _23_, 131. Walsh, John, I, 260, _260_; II, 157. Wapshare, J., II, _230_. Warburton, H., I, _349_. Warburton, Wm., I, _55_, 112; II, 174. Ward, S., II, _299_. Waring, E., I, _203_, 222. Warner, W., II, _302_, 312. Warren, S., II, _340_. Watkins, J., II, _270_. Watson, Bp., I, _223_. Watt, R., I, _102_, 402. Watts, I., II, 18. Weddle, T., II, _187_. Wentworth, Thos., I, _240_. Wharton, I, 115. Whately, R., I, 246, _246_, 324. Whately's Paradox, I, 246. Whewell, I, _101_, 101, 273, 314, 380; II, 104, 246, 247. Whigs, II, 22. Whiston, J., I, _147_. Whiston, W., I, 133, _133_, 146, 156, 311. White, H. K., II, _271_. White, J. B., I, 248. White, R., I, 11. Whitford, I, 105. Whitworth, W. A., II, _344_. Whizgig, On the, I, 254. Wightman, I, 59. Wilberforce, W., II, _236_. Wilkins, J., I, 96, _100_, 116, 226. Williams, J. B., I, _378_. Williams, T., I, 171, _171_. Wilson, Sir J., I, _221_. Wilson, J. M., II, _344_. Wilson, R., II, 7, _7_. Wilson's Theorem, I, _222_. Wingate, E., II, _308_. Winter, I, 46. Wirgman, T., I, 258, _258_. Wiseman, N. P. S., II, _26_, 61, 294. Wolcot, J. (Peter Pindar), II, _272_. Wollstonecraft, I, 173, _173_. Wolzogen, I, _106_. Wood, A., I, _98_. Wood, John, I, _233_. Wood, Wm., I, 246, _246_. Woodley, W., I, 307, _307_. Wordsworth, II, 273. Wright, E., I, 84. Wright, T., I, 151, _151_, 152, 153. Wright, W., II, 9. Wronski, I, 249, _250_. Wrottesley, J. (Baron), II, _181_.

Young, B., II, _69_. Young, J. W. A., II, 367. Young, T., I, 24, 30, _250_. Youthful Prodigies, I, 219. Yvon, I, _297_.

Zach, von, II, _45_, 196. Zachary, Pope, I, 32, 34. Zadkiel, I, _321_; II, 43. Zetetic Astronomy, II, 88. Zodiac, II, 136. Zytphen, II, _335_.

* * * * *

Notes

Transcriber's note: References to Notes in Volume I are shown as in the printed book, with the resequenced footnote numbers in the Project Gutenberg Edition (EText-No. 23100) added thus {123}.

[1] See Vol. I, page 255, note 6 {584}.

[2] "I have no need for this hypothesis."

[3] "Ah, it is a beautiful hypothesis; it explains many things."

[4] "What we know is very slight; what we don't know is immense."

[5] Brewster relates (_Life of Sir Isaac Newton_, Vol. II, p. 407) that, a short time before his death, Newton remarked: "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

[6] See Vol. I, p. 292, note 1 {632}.

[7] "What is all that!"

[8] "I have some good news to tell you: at the Bureau of Longitudes they have just received a letter from Germany announcing that M. Bessel has verified by observation your theoretical discoveries on the satellites of Jupiter."

[9] "Man follows only phantoms."

[10] See Vol. I, page 382, note 13 {786}.

[11] Dieudonne Thiebault (1733-1807) was a Jesuit in his early life, but he left the order and took up the study of law. In 1765 he went to Prussia and became a favorite of Frederick the Great. He returned to France in 1785 and became head of the Lycee at Versailles.

[12] _Memories of Twenty Years of Residence in Berlin._ There was a second French and an English edition in 1805.

[13] Richard Joachim Heinrich von Mollendorff (1724-1816) began his career as a page of Frederick the Great (1740) and became field marshal (1793) and commander of the Prussian army on the Rhine (1794).

[14] Hugues Bernard Maret (1763-1839) was not Duc de Bassano in 1807, this title not being conferred upon him until 1809. He was ambassador to England in 1792 and to Naples in 1793. Napoleon made him head of the cabinet and his special confidant. The Bourbons exiled him in 1816.

[15] Denis Diderot (1713-1784), whose _Lettre sur les aveugles_ (1749) introduced him to the world as a philosopher, and whose work on the _Encyclopedie_ is so well known.

[16] "Sir, (a + b^{n}) / n = x, whence God exists; answer!"

[17] This was one James Laurie of Musselburgh.

[18] Jelinger Cookson Symons (1809-1860) was an office-holder with a decided leaning towards the improvement of education and social conditions. He wrote _A Plea for Schools_ (1847), _The Industrial Capacities of South Wales_ (1855), and _Lunar Motion_ (1856), to which last work the critic probably refers.

[19] "Protimalethes" followed this by another work along the same line the following year, _The Independence of the Testimony of St. Matthew and St. John tested and vindicated by the theory of chances_.

[20] Wilson had already taken up the lance against science in his _Strictures on Geology and Astronomy, in reference to a supposed want of harmony between these sciences and some parts of Divine Revelation_, Glasgow, 1843. He had also ventured upon poetry in his _Pleasures of Piety_, Glasgow, 1837.

[21] Mrs. Borron was Elizabeth Willesford Mills before her marriage. She made an attempt at literature in her _Sibyl's Leaves_, London (printed at Devonport), 1826.

[22] See Vol. I, page 386, note 10 {801}.

[23] See Vol. I, page 43, notes 7 {32} and 8 {33}.

[24] His flying machine, designed in 1843, was one of the earliest attempts at aviation on any extensive scale.

[25] Erasmus Darwin (1731-1802) was the grandfather of Charles Darwin. The work here mentioned had great influence, being translated into French, Portuguese, and Italian. Canning parodied it in his _Loves of the Triangles_.

[26] See Vol. I, page 147, note 1 {312}.

[27] The notes on this page were written on the day of the funeral of Wilbur Wright, June 1, 1912, the man who realized all of these prophecies, and then died a victim of municipal crime,--of typhoid fever.

[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the Reform Bill was greatly indebted for its final success.

[29] This was published in London in 1851 instead of 1848.

[30] This appeared in 1846.

[31] This was done in _The Circle Squared_, published at Brighton in 1865.

[32] It first appeared in 1847, under the title, _The Scriptural Calendar and Chronological Reformer, 1848. Including a review of tracts by Dr. Wardlaw and others on the Sabbath question. By W. H. Black._ The one above mentioned, for 1849, was printed in 1848, and was also by Black (1808-1872). He was pastor of the Seventh Day Baptists and was interested in archeology and in books. He catalogued the manuscripts of the Ashmolean Museum at Oxford.

[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's Physioglyphics_, London, 1844; _Pars prima. Geometria vindicata; antiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli, Circulique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at Southampton), 1847; _The Uptonian Trisection_, London, 1866; and _The Circle Squared_, London, 1872.

[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1 + [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or 1/2 [root]3 = 1.

[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at Serampore when the East India Company took over the control in 1807. He entered the British medical service and was invalided to England in 1828. His _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was recognized as a standard. He became vice-president of the Linnean Society, F. R. S., and fellow of the Royal Asiatic Society.

[36] But if [theta] = 90 deg. this asserts that

cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg. . sin 225 deg.) / [root](sin^2 270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg. . sin 450 deg. . sin^2 90 deg.),

or that

1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1 . 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2),

so that De Morgan must have made some error in copying.

[37] John Bonnycastle (died in 1821) was professor of mathematics at Woolwich. His edition of Bossut's _History of Mathematics_ (1803), and his works on elementary mathematics were well known.

[38] The bibliographies give Husain Rifki as the translator, a practical geometry as the work, and 1802 as the date.

[39] See Vol. I, page 309, note 2 {670}.

[40] Probably in _The Improvement of the Mind_ which Isaac Watts (1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and the _Hymns_, by which he is still well known, in 1707.

[41] Spencer Joshua Alwyne Compton, second Marquis of Northampton (1790-1851), was a poet, a scientist, and a statesman. He was president of the Royal Society from 1838 to 1849.

[42] Besides the writings here mentioned Perigal published a work on _Geometric Maps_ (London, 1853), and _Graphic Demonstrations of Geometric Problems_ (1891).

[43] See Vol. II, page 5, note 18.

[44] James Ferguson (1710-1776) was a portrait painter, an astronomer, and a popular writer and lecturer on various subjects.

[45] In the old ballad of King Alfred and the Shepherd, when the latter is tempting the disguised king into his service, he says:

"Of whig and whey we have good store, And keep good pease-straw fire."

_Whig_ is then a preparation of milk. But another commonly cited derivation may be suspected from the word _whiggamor_ being used before _whig_, as applied to the political party; _whig_ may be a contraction. Perhaps both derivations conspired: the word _whiggamor_, said to be a word of command to the horses, might contract into _whig_, and the contraction might be welcomed for its own native meaning.--A. De M.

[46] This was p. 147 in the first edition.

[47] St. Augustine (354-430) was bishop of Hippo. His _Confessiones_, in 13 books, was written in 397, and his _De Civitate Dei_ in 426.

[48] "He was wont to indulge in certain Punic subtleties lest he should weary the reader by much speaking."

[49] John Milner (1751-1826), bishop of Castabala, a well-known antiquarian.

[50] It will be said that when the final happiness is spoken of in "sure and certain hope," it is _the_ Resurrection, generally; but when afterwards application is made to the individual, simple "hope" is all that is predicated which merely means "wish?" I know it: but just before the general declaration, it is declared that it _has_ pleased God of his great mercy to _take unto Himself_, the soul of our dear brother: and between the "hopes" hearty thanks are given that it _has_ pleased God to deliver our dear brother out of the miseries of this wicked world, with an additional prayer that the number of the elect may shortly be accomplished. All which means, that our dear brother is declared to be taken to God, to be in a place not so miserable as this world--a description which excludes the "wicked place"--and to be of the elect. Yes, but it will be said again! do you not know that when this Liturgy was framed, all who were not in the road to Heaven were excommunicated burial service read over them. Supposing the fact to have been true in old time, which is a very spicy supposition, how does that excuse the present practice? Have you a right _always_ to say what you believe _cannot always_ be true, because you think it was once _always_ true? Yes, but, choose whom you please, you cannot be _certain_ He is _not_ gone to Heaven. True, and choose which Bishop you please, you cannot be demonstratively _certain_, he is _not_ a concealed unbeliever: may I therefore say of the whole bench, _singulatim et seriatim_, that they _are_ unbelievers? No! No! The voice of common sense, of which common logic is a part, is slowly opening the eyes of the multitude to the unprincipled reasoning of theologians. Remember 1819. What chance had Parliamentary Reform when the House of Commons thanked the Manchester sabre-men? If you do not reform your Liturgy, it will be reformed for you, and sooner than you think! The dishonest interpretations, by defence of which even the minds of children are corrupted, and which throw their shoots into literature and commerce, will be sent to the place whence they came: and over the door of the established organization for teaching religion will be posted the following notice:

"Shift and Subterfuge, Shuffle and Dodge, No longer here allowed to lodge!"

All this ought to be written by some one who belongs to the Establishment: in him, it would be quite prudent and proper; in me, it is kind and charitable.--A. De M.

[51] But few do have access to it, for the work is not at all common, and this Piscator is rarely mentioned.

[52] This derivation has been omitted.--S. E. De M.

[53] A blow for a blow. Roland and Oliver were two of the paladins of Charlemagne whose exploits were so alike that each was constantly receiving credit for what the other did. Finally they met and fought for five days on an island in the Rhine, but even at the end of that period it was merely a drawn battle.

[54] "In the name of the church."

[55] "From the chair," officially.

[56] Nicholas Patrick Stephen Wiseman (1802-1865), whose elevation to the archbishopric of Westminster and the cardinalate (1850) led to the act prohibiting Roman Catholics from assuming episcopal titles in England, a law that was never enforced.

[57] He was born in 1812 and was converted to Catholicism in 1839. He founded the _Tablet_ in London in 1840, removing its office to Dublin in 1849. He became M. P. in 1852, and at the time of his death (1855) he was preparing a memorial to the Pope asking him to annul the proclamation of an Irish bishop prohibiting his priests from taking part in politics.

[58] John Guillim (1565-1621) was the first to systematize and illustrate the whole science of heraldry. He published _A display of Heraldrie: manifesting a more easie accesse to the knowledge thereof_ in 1610.

[59] "Faith."

[60] "Faithful."

[61] "For the faith vindicated."

[62] The words are of the same root, and hence our word _fiddle_. Some suppose this root means a _rope_, which, as that to which you trust, becomes, in one divergence, confidence itself--just as a _rock_, and other words, come to mean reliance--and in another, a little string.--A. De M.

[63] The Greek lexicographer, a Christian, living after 1000 A. D. His lexicon was first printed at Milan in 1499.

[64] _Skindapsos._

[65] This was John William Burgon (1813-1888), Gresham professor of theology (1867) and dean of Chichester. He was an ultra-conservative, opposing the revised version of the New Testament, and saying of the admission of women to the university examinations that it was "a thing inexpedient and immodest."

[66] _Ekklesia_, or _ecclesia_.

[67] _Ennomos ekklesia._

[68] "Without doubt I shall perish forever."

[69] "Every man is an animal." "Sortes is a man." "Sortes is an animal."

[70] "For a special purpose."

[71] Heraclitus of Ephesus, the weeping philosopher, 6th century B. C.

[72] Democritus, the laughing philosopher, founder of the atomistic theory, 5th century B. C.

[73] "Ends to which."

[74] "Ends from which."

[75] "In just as many syllables," "With just as many letters," "In just as many words."

[76] "I shall make a way," "I shall find a way."

[77] The notion that the Evil Spirit is a functionary liable to be dismissed for not attending to his duty, is, so far as my reading goes, utterly unknown in theology. My first wrinkle on the subject was the remark of the Somersetshire farmer upon Palmer the poisoner-- "Well! if the Devil don't take he, he didn't ought to be allowed to be devil no longer."--A. De M.

William Palmer (1824-1856) was a member of the Royal College of Surgeons and practised medicine at London. He was hanged in 1856 for having poisoned a friend and was also suspected of having poisoned his wife and brother for their insurance money, besides being guilty of numerous other murders. His trial was very much in the public attention at the time.

[78] Advantages and dangers.

[79] The old priory of St. Mary of Bethlehem in London, was used as an asylum for the insane. The name was corrupted to Bedlam.

[80] Referring to the common English pronunciation of St. John, almost Sinjin. John St. John Long (1798-1834), an Irishman by birth, practised medicine in London. He claimed to have found a specific for rheumatism and tuberculosis, but upon the death of one of his patients in 1830 he was tried for manslaughter. He died of tuberculosis four years later, refusing to take his own treatment.

[81] William of Occam (d. 1349), so called from his birthplace, Ockham, in Surrey. He was a Franciscan, and lectured on philosophy in the Sorbonne.

[82] He signs himself "James Hopkins, schoolmaster," and this seems to have been his only published effort.

[83] Joseph Ady (1770-1852) was a famous swindler. One of his best-known schemes was to send out letters informing the recipients that they would learn something to their advantage on payment of a certain sum. He spent some time in prison.

[84] Sir Peter Laurie (c. 1779-1861) was worth referring to, for he was prominent as a magistrate and was honored because of his interest in all social reforms. He made a fortune as a contractor, became sheriff of London in 1823, and was knighted in the following year. He became Lord Mayor of London in 1832.

[85] See Vol. I, page 321, note 2 {691}. The _Astronomy in a nutshell_ appeared in 1860. _The Herald of Astrology_ was first published in London in 1831, "by Zadkiel the Seer." It was continued as _The Astrological Almanac_ (London, 1834), as _Zadkiel's Almanac and Herald of Astrology_ (_ibid._, 1835, edited by R. J. Morrison, and subsequently by A. J. Pearce), and as _Raphael's Prophetic Almanac_ (1840-1855).

[86] See Vol. I, page 172, note 3 {382}.

[87] See Vol. I, page 87, note 4 {133}.

[88] Franz Xaver, Freiherr von Zach (1754-1832) was director of the observatory at Seeberge near Gotha. He wrote the _Tabulae speciales aberrationis et mutationis_ (1806-7), _Novae et correctae tabulae solis_ (1792), and _L'attraction des montagnes et ses effets sur le fil a plomb_ (1814).

[89] Jean Louis Pons (1761-1831) was connected with the observatory at Marseilles for thirty years (1789-1819). He later became director of the observatory at Marlia, near Lucca, and subsequently filled the same office at Florence. He was an indefatigable searcher for comets, discovering 37 between 1801 and 1827, among them being the one that bears Encke's name.

[90] This hypothesis has now become an established fact.

[91] John Chetwode Eustace (c. 1762-1815) was born in Ireland. Although a Roman Catholic priest he lived for a time at Cambridge where he did some tutoring. His _Classical Tour_ appeared in 1813 and went through several editions.

[92] "Crimes should be exposed when they are punished, but disgraceful acts should be hidden."

[93] Henri Hureau de Senarmont (1808-1862) was professor of mineralogy at the _Ecole des mines_ and examiner at the _Ecole polytechnique_ at Paris.

[94] Augustin Jean Fresnel (1788-1827), "Ingenieur des ponts et chaussees," gave the first experimental proofs of the wave theory of light. He studied the questions of interference and polarization, and determined the approximate velocity of light.

[95] "As is my custom."

[96] Francis Heywood (1796-1858) made the first English translation of Kant's _Critick of Pure Reason_ (1838, reprinted in 1848). The _Analysis_ came out, as here stated, in 1844.

[97] Louise Renee de Keroualle, Duchess of Portsmouth and Aubigny (1649-1734), was a favorite of Charles II. She used her influence to keep him under the control of Louis XIV.

[98] William Chiffinch (c. 1602-1688) was page of the king's bed-chamber and keeper of the private closet to Charles II. He was one of the king's intimates and was an unscrupulous henchman.

[99] "Well devised."

[100] "John Bellingham Inglis. His _Philobiblion_ "translated from the first edition (of Ricardus d'Aungervile, Bishop of Durham), 1473," appeared at London in 1832. It was republished in America (Albany, N. Y.) in 1864.

[101] "What are you laughing at?"

[102] See Vol. I, page 314, note 4 {681}.

[103] See Vol. I, page 112, note 7 {211}.

[104] Referring to Hamilton's edition of the _Collected Works of Dugald Stewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered that Stewart (1753-1828) taught mathematics at the University of Edinburgh before he took up philosophy.

[105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols., Edinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in philosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow.

[106] Edward Irving (1792-1834), the famous preacher. At first he assisted Dr. Chalmers at Glasgow, but in 1822 he went to London where he met with great success. A few years later he became mentally unbalanced and was finally expelled from his church (1832) for heresy. He was a great friend of Carlyle.

[107] He also wrote a number of other paradoxes, including _An Essay towards a Science of Consciousness_ (1838), _Instinctive Natural Religion_ (1858), _Popular Treatise on the structure, diseases, and treatment of the human teeth_ (1837), and _On Headache_ (1859).

[108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and a mystic, with a philosophy that was wittily described as "Oriental pantheism translated into Scotch." He was editor of several journals.

[109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in which she announced herself as the woman spoken of in Revelations xii. She had at one time as many as 100,000 disciples, and she established a sect that long survived her.

[110] Thales, c. 640-548 B. C.

[111] Pythagoras, 580-501 B. C.

[112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of Euripides and Pericles. Plutarch speaks of him as having squared the circle.

[113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that Oinopides was the first to show how to let fall a perpendicular to a line from an external point.

[114] Bryson and Antiphon, contemporaries of Socrates, invented the so-called method of exhaustions, one of the forerunners of the calculus.

[115] He wrote, c. 440 B. C., the first elementary textbook on mathematics in the Greek language. The "lunes of Hippocrates" are well known in geometry.

[116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy and spherical trigonometry. The _Gebri filii Affla Hispalensis de astronomia libri_ IX was published at Nuremberg in 1533.

[117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great algebraist. His _Artis magnae sive de regulis Algebrae_ was published at Nuremberg in 1545.

[118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan.

[119] See note 5 {98}, Vol. I, page 69.

[120] See note 10 {124}, Vol. I., page 83.

[121] See note 9 {123}, Vol. I, page 83.

[122] Pierre Herigone lived in Paris the first half of the 17th century. His _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not at all original.

[123] Franciscus van Schooten (died in 1661) was professor of mathematics at Leyden. He edited Descartes's _La Geometrie_.

[124] Florimond de Beaune (1601-1652) was the first Frenchman to write a commentary on Descartes's _La Geometrie_. He did some noteworthy work in the theory of curves.

[125] See note 3 {23}, Vol. I, page 41.

[126] Olivier de Serres (b. in 1539) was a writer on agriculture. Montucla speaks of him in his _Quadrature du cercle_ (page 227) as having asserted that the circle is twice the inscribed equilateral triangle, although, as De Morgan points out, this did not fairly interpret his position.

[127] Anghera wrote not only the three works here mentioned, but also the _Problemi del piu alto interesse scientifico, geometricamente risoluti e dimostrati_, Naples, 1861. His quadrature was defended by Giovanni Motti in a work entitled _Matematica Vera. Falsita del sistema ciclometrico d'Archimede, quadratura del cerchio d'Anghera, ricerca algebraica dei lati di qualunque poligono regolare inscritto in un circolo_, Voghera, 1877. The _Problemi_ of 1861 contains Anghera's portrait, and states that he lived at Malta from 1849 to 1861. It further states that the Malta publications are in part reproduced in this work.

[128] This was his friend Paolo Pullicino whose _Elogio_ was pronounced by L. Farrugia at Malta in 1890. He wrote a work _La Santa Effegie della Blata Vergine Maria_, published at Valetta in 1868.

[129] St. Vitus, St. Modestus, and St. Crescentia were all martyred the same day, being torn limb from limb after lions and molten lead had proved of no avail. At least so the story runs.

[130] The reference is to Cardinal Wiseman. See Vol. II, page 26, note 56.

[131] "Worthy of esteem."

[132] Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born at Toledo in 1526 and died in 1611. He held high position in the Jesuit order. The work referred to is the _Flos Sanctorum o libro de las vidas de los santos_, of which there was an edition at Barcelona in 1643. His life of Loyola (1572) and _Historia ecclesiastica del Cisma del reino de Inglaterra_ were well known.

[133] Caesar Baronius (1538-1607) was made a cardinal in 1595 and became librarian at the Vatican in 1597. The work referred to appeared at Rome in 1589.

[134] Mrs. Jameson's (1794-1860) works were very popular half a century ago, and still have some circulation among art lovers. The first edition of the work mentioned appeared in 1848.

[135] The barnyard cock.

[136] Shanks did nothing but computing. The title should, of course, read "to 607 Places of _Decimals_." He later carried the computation to 707 decimal places. (_Proc. Roy. Society_, XXI, p. 319.) He also prepared a table of prime numbers up to 60,000. (_Proc. Roy. Society_, XXII, p. 200.)

[137] See Vol. I, page 42, note 4 {24}.

[138] See Vol. I, page 64, note 1 {78}.

[139] See Vol. I, page 328, note 1 {704}.

[140] George Suffield published _Synthetic Division in Arithmetic_, to which reference is made, in 1863.

[141] John Robert Lunn wrote chiefly on Church matters, although he published a work on motion in 1859.

[142] Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime professor in the Military School at Paris, and later at the _Ecole polytechnique_. He is best known by his _Theorie analytique de la chaleur_ (Paris, 1822), in which the Fourier series is used. The work here referred to is the _Analyse des equations determinees_ (Paris, 1831).

[143] William George Horner (1786-1837) acquired a name for himself in mathematics in a curious manner. He was not a university man nor was he a mathematician of any standing. He taught school near Bristol and at Bath, and seems to have stumbled upon his ingenious method for finding the approximate roots of numerical higher equations, including as a special case the extracting of the various roots of numbers. Davies Gilbert presented the method to the Royal Society in 1819, and it was reprinted in the _Ladies' Diary_ for 1838, and in the _Mathematician_ in 1843. The method was original as far as Horner was concerned, but it is practically identical with the one used by the Chinese algebraist Ch'in Chiu-shang, in his _Su-shu Chiu-chang_ of 1247. But even Ch'in Chiu-shang can hardly be called the discoverer of the method since it is merely the extension of a process for root extracting that appeared in the _Chiu-chang Suan-shu_ of the second century B. C.

[144] He afterwards edited Loftus's _Inland Revenue Officers' Manual_ (London, 1865). The two equations mentioned were x^3 - 2x = 5 and y^3 - 90y^2 + 2500y - 16,000 = 0, in which y = 30 - 10x. Hence each place of y is the complement of the following place of x with respect to 9.

[145] Probably the John Power Hicks who wrote a memoir on T. H. Key, London, 1893.

[146] Possibly the one who wrote on the quadrature of the circle in 1881.

[147] As it is. But what a pity that we have not 12 fingers, with duodecimal fractions instead of decimals! We should then have 0.6 for 1/2, 0.4 for 1/3, 0.8 for 2/3, 0.3 for 1/4, 0.9 for 3/4, and 0.16 for 1/8, instead of 0.5, 0.333+, 0.666+, 0.25, 0.75, and 0.125 as we now have with our decimal system. In other words, the most frequently used fractions in business would be much more easily represented on the duodecimal scale than on the decimal scale that we now use.

[148] He wrote Hints for an _Essay on Anemology and Ombrology_ (London, 1839-40) and _The Music of the Eye_ (London, 1831).

[149] Brigham Young (1801-1877) was born at Whitingham, Vermont, and entered the Mormon church in 1832. In 1840 he was sent as a missionary to England. After the death of Joseph Smith he became president of the Mormons (1847), leading the church to Salt Lake City (1848).

[150] Joseph Smith (1805-1844) was also born in Vermont, and was four years the junior of Brigham Young. The _Book of Mormon_ appeared in 1827, and the church was founded in 1830. He was murdered in 1844.

[151] Orson Pratt (1811-1881) was one of the twelve apostles of the Mormon Church (1835), and made several missionary journeys to England. He was professor of mathematics in the University of Deseret (the Mormon name for Utah). Besides the paper mentioned Pratt wrote the _Divine Authenticity of the Book of Mormon_ (1849), _Cubic and Biquadratic Equations_ (1866), and a _Key to the Universe_ (1866).

[152] "It does not follow."

[153] Dryden (1631-1700) published his _Religio Laici_ in 1682. The use of the word "proportion" in the sense of ratio was common before his time, but he uses it in the sense of having four terms; that is, that price is to price as offence is to offence.

[154] Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as professor of mathematics at Woolwich. He was, with De Morgan, much interested in founding the University of London. He wrote on astronomy (1793), mechanics (1806), practical mathematics (1825), and Christian evidences (1811).

[155] See Vol. I, page 220, note 6 {482}. The _Pensees_ appeared posthumously in 1670.

[156] "The right thing to do is not to wager at all." "Yes, but you ought to wager; you have started out; and not to wager at all that God exists is to wager that he does not exist."

[157] He lived about 300 A.D., in Africa, and wrote _Libri septem adversus Gentes_. This was printed at Rome in 1542-3.

[158] Pierre Bayle (1647-1706) was professor of philosophy at the Prostestant University at Sedan from 1675 until its dissolution in 1681. He then became professor at Rotterdam (1681-1693). In 1684 he began the publication of his journal of literary criticism _Nouvelles de la Republique des Lettres_. He is best known for his erudite _Dictionnaire historique et critique_ (1697).

[159] "But Christ himself does not prove what he promises. It is true. For, as I have said, there cannot be any absolute proof of future events. Therefore since it is a condition of future events that they cannot be grasped or comprehended by any efforts of anticipation, is it not more reasonable, out of two alternatives that are uncertain and that are hanging in doubtful expectation, to give credence to the one that gives some hope rather than to the one that offers none at all? For in the former case there is no danger if, as is said to threaten, it becomes empty and void; while in the latter case the danger is greatest, that is, the loss of salvation, if when the time comes it is found that it was not a falsehood."

[160] Gregg wrote several other paradoxes, including the following: _The Authentic Report of the extraordinary case of Tresham Dames Gregg ... his committal to Bridewell for refusing to give his recognizance_ (Dublin, 1841), _An Appeal to Public Opinion upon a Case of Injury and Wrong ... in the case of a question of prerogative that arose between_ [R. Whately] _... Archbishop of Dublin and the author_ (London, 1861), _The Cosmology of Sir Isaac Newton proved to be in accordance with the Bible_ (London, 1871), _The Steam Locomotive as revealed in the Bible_ (London 1863) and _On the Sacred Law of 1866, conferring perpetual life with immunity from decay and disease. A cento of decisive scriptural oracles strangely discovered_ (London and Dublin, 1875). These titles will help the reader to understand the man whom De Morgan so pleasantly satirizes.

[161] See Vol. I, page 261, note 2 {592}.

[162] "They have found it."

[163] The late Greeks used the letters of their alphabet as numerals, adding three early alphabetic characters. The letter [chi] represented 600, [xi] represented 60, and [digamma] stood for 6. This gives 666, the number of the Beast given in the Revelation.

[164] "Allowing for necessary exceptions."

[165] Mr. Gregg is not alone in his efforts to use the calculus in original lines, as any one who has read Herbart's application of the subject to psychology will recall.

[166] See Vol. I, page 105, note 4 {188}; page 109, note 1 {197}.

[167] The full title shows the plan,--_The Decimal System as a whole, in its relation to time, measure, weight, capacity, and money, in unison with each other._ But why is this so much worse than the French plan of which we have only the metric system and the decimal division of the angle left?

[168] One of the brothers of Sir Isaac Pitman (1813-1897), the inventor of modern stenography. Of these brothers, Benjamin taught the art in America, Jacob in Australia, and Joseph, Henry, and Frederick in England.

[169] For example, _The Phonographic Lecturer_ (London, 1871 etc.), _The Phonographic Student_ (1867, etc.), and _The Shorthand Magazine_ (1866, etc.).

[170] See Vol. II, page 68, note 148.

[171] It involves the theory of non-Euclidean geometry, Euclid's postulate of parallels being used in proving this theorem.

[172] Referring to the fact that none of the works of Thales is extant.

[173] The author was one B. Bulstrode. Parts 4 and 5 were printed at Calcutta.

[174] See Vol. II, page 5, note 18.

[175] See Vol. I, page 85, note 2 {129}.

[176] Alexander Vasilievich Suvaroff (1729-1800), a Russian general who fought against the Turks, in the Polish wars, and in the early Napoleonic campaigns. When he took Ismail in 1790 he sent this couplet to Empress Catherine.

[177] "Newton hath determined rightly," "Newton hath not determined rightly."

[178] See Vol. I, page 288, note 3 {621}.

[179] See Vol. I, page 326, note 1 {700}.

[180] "With great honor."

[181] Apparently unknown to biographers. He seems to have written nothing else.

[182] Captain Marryat (1792-1848) published _Snarley-yow, or the Dog Fiend_ in 1837.

[183] He is not known to biographers, and published nothing else under this name.

[184] See Vol. I, page 80, note 5 {119}.

[185] He published a _Family and Commercial Illustrated Almanack and Year Book ... for 1861_ (Bath, 1860).

[186] Louis Dutens (1730-1812) was born at Tours, but went to England as a young man. He made the first collection of the works of Leibnitz, against the advice of Voltaire, who wrote to him: "Les ecrits de Leibnitz sont epars comme les feuilles de la Sybille, et aussi obscurs que les ecrits de cette vieille." The work appeared at Geneva, in six volumes, in 1769.

[187] Mungo Park (1771-1806), the first European to explore the Niger (1795-6). His _Travels in the Interior of Africa_ appeared in 1799. He died in Africa.

[188] Gerhard Mercator (1512-1594) the well-known map maker of Louvain. The "Mercator's Projection" was probably made as early as 1550, but the principle of its construction was first set forth by Edward Wright (London, 1599).

[189] Quirico Barilli Filopanti wrote a number of works and monographs. He succeeded in getting his _Cesare al Rubicone_ and _Degli_ _usi idraulici della Tela_ in the _Memoria letta ... all' Accademia delle Scienze in Bologna_ (1847, 1866). He also wrote _Dio esiste_ (1881), _Dio Liberale_ (1880), and _Sunto della memoria sulle geuranie ossia di alcune singolari relazioni cosmiche della terra e del cielo_ (1862).

[190] The periods of disembodiment may be interesting. They will be seen from the following dates: Descartes (1596-1650), William III (1650-1702); Roger Bacon (1214 to c. 1294), Boccaccio (1313-1375). Charles IX was born in 1550 and died in 1574.

[191] His real name was Frederick Parker, and he wrote several works on the Greek language and on religion. Among these were a translation of the New Testament from the Vatican MS. (1864), _The Revealed History of Man_ (1854), _An Enquiry respecting the Punctuation of Ancient Greek_ (1841), and _Rules for Ascertaining the sense conveyed in Ancient Greek Manuscripts_ (1848, the seventh edition appearing in 1862).

[192] See Vol. I, page 352, second note 1 {736}.

The literature on the subject of the Great Pyramid, considered from the standpoint of metrology, is extensive.

[193] See Vol. I, page 80, note 5 {119}.

[194] Sir Philip Francis (1740-1818) was a Whig politician. The evidence that he was the author of the _Letters of Junius_ (1769-1772) is purely circumstantial. He was clerk in the war office at the time of their publication. In 1774 he was made a member of the Supreme Council of Bengal, and was a vigorous opponent of Warren Hastings, the two fighting a duel in 1780. He entered parliament in 1784 and was among the leaders in the agitation for parliamentary reform.

[195] Mrs. Cottle published a number of letters that attracted attention at the time. Among these were letters to the emperor of France and king of Sardinia (1859) relating to the prophecies of the war between France and Austria; to G. C. Lavis and Her Majesty's Ministers (1859) relating to her claims as a prophetess; and to the "Crowned Heads" at St. James, the King of Prussia, and others (1860), relating to certain passages of Scripture. She also wrote _The Lamb's Book of Life for the New Jerusalem Church and Kingdom, interpreted for all nations_ (1861).

[196] See Vol. I, page 315, note 2 {685}, and Vol. II, page 58, note 109.

[197] A Congregational minister, who published a number of sermons, chiefly obituaries, between 1804 and 1851. His _Frailty of Human Life_, two sermons delivered on the occasion of the death of Princess Charlotte, went through at least three editions.

[198] He was secretary of the Congregational Board and editor of the _Congregational Year Book_ (from 1846) and the _Congregational Manual_.

[199] Frederick Denison Maurice (1805-1872) began his preaching as a Unitarian but entered the Established Church in 1831, being ordained in 1834. He was professor of English and History at King's College, London, from 1840 to 1853. He was one of the founders of Queen's College for women, and was the first principal of the Working Men's College, London. The subject referred to by De Morgan is his expression of opinion in his _Theological Essays_ (1853) that future punishment is not eternal. As a result of this expression he lost his professorship at King's College. In 1866 he was made Knightbridge Professor of Casuistry, Moral Theology, and Moral Philosophy at Cambridge.

[200] See Vol. I, page 46, note 1 {42}. Besides the books mentioned in this list he wrote _The Ratio between Diameter and Circumference demonstrated by angles, and Euclid's Theorem, Proposition 32, Book I, proved to be fallacious_ (Liverpool, 1870). This is the theorem which asserts that the exterior angle of a triangle is equal to the sum of the two opposite interior angles, and that the sum of the interior angles equals two right angles. He also published his _Curiosities of Mathematics_ in 1870, a work containing an extensive correspondence with every one who would pay any attention to him. De Morgan was then too feeble to show any interest in the final effort of the subject of some of his keenest satire.

[201] See Vol. I, page 332, note 4 {709}.

[202] See Vol. I, page 101, note 4 {174}.

[203] "The circle-squaring disease"; literally, "the circle-measuring disease."

[204] See Vol. II, page 63, note 136.

[205] William Rutherford (c. 1798-1871), teacher of mathematics at Woolwich, secretary of the Royal Astronomical Society, editor of _The Mathematician_, and author of various textbooks. _The Extension of [pi] to 440 places_, appeared in the _Proceedings_ of the Royal Society in 1853 (p. 274).

[206] Charles Knight (1791-1873) was associated with De Morgan for many years. After 1828 he superintended the publications of the Society for the Diffusion of Useful Knowledge, to which De Morgan contributed, and he edited the _Penny Cyclopedia_ (1833-1844) for which De Morgan wrote the articles on mathematics.

[207] Sir William Hamilton. See Vol. I, page 112, note 7 {211}.

[208] Adam Smith (1723-1790) was not only known for his _Wealth of Nations_ (1776), but for his _Theory of Moral Sentiments_ (1759), published while he was professor of moral philosophy at Glasgow (1752-1764). He was Lord Rector of the university in 1787.

[209] See Vol. I, page 332, note 4 {709}.

[210] "Whip."

[211] "Terrible lash."

[212] "An accomplished fact [an accomplished fault]."

[213] See _Extracts from the Diary and Letters of Mrs. Mary Cobb_, London, 1805.

[214] "Gentle in manner."

[215] "Brave in action." The motto of Earl Newborough was "Suaviter in modo, fortiter in re."

[216] "Reduction to an absurdity," a method of proof occasionally used in geometry and in logic.

[217] "He has lost the right of being moved (struck) by evidence."

[218] For _radix quadratus_. The usual root sign is supposed to be derived from _r_ (for radix), and at one time _q_ was commonly used for square, as in Viete's style of writing Aq for A^2.

[219] The Garde Douloureuse was a castle in the marches of Wales and received its name because of its exposure to attacks by the Welsh.

[220] "Out of the fight."

[221] "Hidden."

[222] John Cam Hobhouse (1786-1869), Baron Broughton, was committed to Newgate for two months in 1819 for his anonymous pamphlet, _A Trifling Mistake_. This was a great advertisement for him, and upon his release he was at once elected to parliament for Westminster. He was a strong supporter of all reform measures, and was Secretary for War in 1832. He was created Baron Broughton de Gyfford in 1851.

[223] Thomas Erskine (1750-1823), the famous orator. He became Lord Chancellor in 1806, but sat in the House of Commons most of his life.

[224] The above is explained in the MS. by a paragraph referring to some anagrams, in one of which, by help of the orthography suggested, a designation for this cyclometer was obtained from the letters of his name.--S. E. De M.

[225] "A personal verb agrees with its subject."

[226] See Vol. I, page 326, note 1 {700}.

[227] See Vol. I, page 326, note 2 {701}.

[228] Apparently unknown to biographers.

[229] The _Bibliotheca Mathematica_ of Ludwig Adolph Sohncke (1807-1853), professor of mathematics at Koenigsberg and Halle, covered the period from 1830 to 1854, being completed by W. Engelmann. It appeared in 1854.

[230] See Vol. I, page 392, note 2 {805}.

[231] See Vol. I, page 43, note 7 {32}.

[232] See Vol. II, page 91, note 187.

[233] Mason made a notable balloon trip from London to Weilburg, in the Duchy of Nassau, in November, 1836, covering 500 miles in 18 hours. He published an account of this trip in 1837, and a work entitled _Aeronautica_ in 1838.

[234] William Harrison Ainsworth (1805-1885) the novelist.

[235] On this question see Vol. I, page 326, note 2 {701}.

[236] Major General Alfred Wilks Drayson, author of various works on geology, astronomy, military surveying, and adventure.

[237] Hailes also wrote several other paradoxes on astronomy and circle squaring during the period 1843-1872.

[238] See Vol. I, page 43, note 8 {33}.

[239] See Vol. I, page 43, note 7 {32}.

[240] "Very small errors are not to be condemned."

[241] He seems to have written nothing else.

[242] Besides the paradoxes here mentioned by De Morgan he wrote several other works, including the following: _Abriss der Babylonisch-Assyrischen Geschichte_ (Mannheim, 1854), _A Popular Inquiry into the Moon's rotation on her axis_ (London, 1856), _Practical Tables for the reduction of the Mahometan dates to the Christian kalendar_ (London, 1856), _Grundzuege einer neuen Weltlehre_ (Munich, 1860), and _On the historical Antiquity of the People of Egypt_ (London, 1863).

[243] Dircks (1806-1873) was a civil engineer of prominence, and a member of the British Association and the Royal Society of Edinburgh. He wrote (1863) on "Pepper's Ghost," an ingenious optical illusion invented by him. There was a second edition of the _Perpetuum Mobile_ in 1870.

[244] George Stephenson (1781-1848), the inventor of the first successful steam locomotive. His first engine was tried in 1814.

[245] Robert Stephenson (1803-1859), the only son of George. Most of the early improvements in locomotive manufacture were due to him. He was also well known for his construction of great bridges.

[246] "In its proper place."

[247] "A fool always finds a bigger fool to admire him."

[248] See Vol. I, page 43, note 7 {32}.

[249] See Vol. I, page 43, note 8 {33}.

[250] See Vol. I, page 85, note 2 {129}.

[251] See Vol. I, page 390, note 1 {390}.

[252] From 1823 to 1852 it was edited by I. C. Robertson; from 1852 to 1857 by R. A. Brooman; and from 1857 to 1863 by Brooman and E. J. Reed.

[253] Sir James Ivory (1765-1842) was, as a young man, manager of a flax mill in Scotland. In 1804 he was made professor of mathematics at the Royal Military College, then at Marlow and later at Sandhurst. He was deeply interested in mathematical physics, and there is a theorem on the attraction of ellipsoids that bears his name. He was awarded three medals of the Royal Society, and was knighted together with Herschel and Brewster, in 1831.

[254] See Vol. I, page 56, note 1 {64}.

[255] See Vol. I, page 153, note 5 {338}.

[256] See Vol. I, page 309, note 2 {670}.

[257] See Vol. I, page 87, note 4 {133}.

[258] George Canning (1770-1857), the Tory statesman and friend of Scott, was much interested in founding the _Quarterly Review_ (1808) and was a contributor to its pages.

[259] See Vol. I, page 186, note 14 {418}.

[260] See Vol. II, page 141, note 252.

[261] De Morgan had a number of excellent articles in this publication.

[262] See Vol. I, page 279, note 1 {611}.

[263] James Orchard Halliwell (1820-1889), afterwards Halliwell-Phillips, came into prominence as a writer at an early age. When he was seventeen he wrote a series of lives of mathematicians for the _Parthenon_. His _Rara Mathematica_ appeared when he was but nineteen. He was a great bibliophile and an enthusiastic student of Shakespeare.

[264] This was written at the age of twenty-two.

[265] The subject of this criticism is of long past date, and as it has only been introduced by the author as an instance of faulty editorship, I have omitted the name of the writer of the libel, and a few lines of further detail.--S. E. De M.

[266] "Condemned souls."

[267] The editor of the _Mechanics' Magazine_ died soon after the above was written.--S. E. De M.

[268] Thomas Stephens Davies (1795-1851) was mathematical master at Woolwich and F. R. S. He contributed a series of "Geometrical Notes" to the _Mechanics' Magazine_ and edited the _Mathematician_. He also published a number of text-books.

[269] See Vol. II, page 66, note 143.

[270] The _Dictionary of Greek and Roman Biography_ (1849), edited by Sir William Smith (1813-1893), whose other dictionaries on classical and biblical matters are well known.

[271] "O J. S.! This is the worst! the greatest possible injury!"

[272] See Vol. I, page 44, note 9 {34} and page 110, note 5 {201}.

[273]

"If there's a man whom the judge's pitiless sentence awaiteth, His head condemned to penalties and tribulations, Let neither penitentiaries tire him with laborer's burdens Nor let his stiffened hands be harrassed by work in the mines. He must square the circle! For what else do I care?--all Known punishments this one task hath surely included."

[274] Houlston was in the customs service. He also published _Inklings of Areal Autometry_, London, 1874.

[275] This is Frederick C. Bakewell. He had already published _Natural Evidence of a Future Life_ (London, 1835), _Philosophical Conversations_ (London, 1833, with other editions), and _Electric Science_ (London, 1853, with other editions).

[276] Henry F. A. Pratt had already published _A Dissertation on the power of the intercepted pressure of the Atmosphere_ (London, 1844) and _The Genealogy of Creation_ (1861). Later he published a work _On Orbital Motion_ (1863), and _Astronomical Investigations_ (1865).

[277] See Vol. I, page 260, note 1 {591}.

[278] Thomas Rawson Birks (1810-1883), a theologian and controversialist, fellow of Trinity College, Cambridge, and (1872) professor of moral philosophy in that university. He wrote _Modern Rationalism_ (1853), _The Bible and Modern Thought_ (1861), _The First Principles of Moral Science_ (1873), and _Modern Physical Fatalism and the Doctrine of Evolution_ (1876), the last being an attack on Herbert Spencer's _First Principles_.

[279] Pseudonym for William Thorn. In the following year (1863) he published a second work, _The Thorn-Tree: being a History of Thorn Worship_, a reply to Bishop Colenso's work entitled _The Pentateuch and the Book of Joshua critically examined_.

[280] Besides _The Pestilence_ (1866) he published _The True Church_ (1851), _The Church and her destinies_ (1855), _Religious reformation imperatively demanded_ (1864), and _The Bible plan unfolded_ (second edition, 1872).

[281] See Vol. II, page 97, note 195.

[282] Sir George Cornewall Lewis (1806-1863) also wrote an _Essay on the Origin and Formation of the Romance Languages_ (1835), an _Essay on the Government of Dependencies_ (1841), and an _Essay on Foreign Jurisdiction and the Extradition of Criminals_ (1859). He was Chancellor of the Exchequer in 1855 and Home Secretary in 1859.

[283] Henry Malden (1800-1876), a classical scholar, fellow of Trinity College, Cambridge, and professor of Greek at University College (1831-1876), then (1831) the University of London. He wrote a _History of Rome to 390 B. C._ (1830), and _On the Origin of Universities and Academical Degrees_ (1835).

[284] Henry Longueville Mansel (1820-1871), theologian and metaphysician, reader in theology at Magdalen College, Oxford (1855), and professor of ecclesiastical history and Dean of St. Paul's (1866). He wrote on metaphysics, and his Bampton Lectures (1858) were reprinted several times.

[285] "Hejus gave freely, gave freely. God is propitious, God is favorable to him who gives freely. God is honored with a banquet of eggs at the cross roads, the god of the world. God, with benignant spirit, desired in sacrifice a goat, a bull to be carried within the precincts of the holy place. God, twice propitiated, blesses the pit of the sacred libation."

[286] Eudoxus of Cnidus (408-355 B. C.) had much to do with the early scientific astronomy of the Greeks. The fifth book of Euclid is generally attributed to him. His astronomical works are known chiefly through the poetical version of Aratus mentioned in note 13, page 167.

[287] Simplicius, a native of Cilicia, lived in the 6th century of our era. He was driven from Athens by Justinian and went to Persia (531), but he returned later and had some fame as a teacher.

[288] See Vol. I, page 160, note 3 {348}.

[289] See Vol. I, page 76, note 3 {112}.

[290] "Through right and wrong."

[291] "It is therefore to arrive at this parallelism, or to preserve it, that Copernicus feared to be obliged to have recourse to this equal and opposite movement which destroys the effect which he attributed so freely to the first, of deranging the parallelism."

[292] A contemporary of Plato and a disciple of Aristotle.

[293] Meton's solstice, the beginning of the Metonic cycles, has been placed at 432 B. C. Ptolemy states that he made the length of the year 365-1/4 + 1/72 days.

[294] Aratus lived about 270 B. C., at the court of Antigonus of Macedonia, and probably practiced medicine there. He was the author of two astronomical poems, the [Greek: Phainomena], apparently based on the lost work of Eudoxus, and the [Greek: Dioseeia] based on Aristotle's _Meteorologica_ and _De Signis Ventorum_ of Theophrastus.

[295] "The nineteen (-year) cycle of the shining sun."

[296] Claudius Salmasius (1588-1653), or Claude Saumaise, was a distinguished classicist, and professor at the University of Leyden. The word [Greek: eleioio] means Elian, thus making the phrase refer to the brilliant one of Elis.

[297] Sir William Brown (1784-1864). In 1800 the family moved to Baltimore, and there the father, Alexander Brown, became prominent in the linen trade. William went to Liverpool where he acquired great wealth as a merchant and banker. He was made a baronet in 1863.

[298] Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow of Magdalen College, Oxford (1835). He went to Australia in 1842 and was very successful at the bar. He returned to England in 1850 and became leader writer on the _Times_. He was many years in parliament, and in 1880 was raised to the peerage.

[299] See Vol. I, page 42, note 4 {24}.

[300] Francis Walkingame (fl. about 1751-1785), whose _Tutor's Assistant_ went through many editions from 1751-1854.

[301] Davies Gilbert (1767-1839). His family name was Giddy, but he assumed his wife's name. He sat in parliament from 1806 to 1832. In 1819 he secured the establishment of the Cape of Good Hope observatory. He was Treasurer (1820-1827) and President (1827-1830) of the Royal Society.

[302] See Vol. I, page 55, note 2 {63}.

[303] Sir Jonathan Frederick Pollock (1783-1870) entered parliament in 1831 and was knighted in 1834.

[304] Joseph Hume (1777-1855) entered parliament in 1812 and for thirty years was leader of the Radical party.

[305] "What! when I say, 'Nicole, bring me my slippers,' is that prose?"

[306] Captain Basil Hall (1788-1844), a naval officer, carried on a series of pendulum observations in 1820-1822, while on a cruise of the west coast of North America. The results were published in 1823 in the _Philosophical Transactions_. He also wrote two popular works on travel that went through numerous editions.

[307] Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His name is connected with philanthropic work and factory legislation.

[308] See Vol. I, page 207, note 12 {469}.

[309] See Vol. I, page 80, note 5 {119}.

[310] Sir Thomas Maclear (1794-1879), an Irishman by birth, became Astronomer Royal at the Cape of Good Hope in 1833. He was an indefatigable observer. He was knighted in 1860.

[311] Thomas Romney Robinson (1792-1882), another Irish astronomer of prominence. He was a deputy professor at Trinity College, Dublin, but took charge of the Armagh observatory in 1823 and remained there until his death.

[312] Sir James South (1785-1867) was in early life a surgeon, but gave up his practice in 1816 and fitted up a private observatory. He contributed to the science of astronomy, particularly with respect to the study of double stars.

[313] Sir John Wrottesley (1798-1867), second Baron Wrottesley. Like Sir James South, he took up the study of astronomy after a professional career,--in his case in law. He built a private observatory in 1829 and made a long series of observations, publishing three star catalogues. He was president of the Astronomical Society from 1841 to 1843, and of the Royal Society from 1854 to 1857.

[314] He seems to have written nothing else.

[315] See Vol. II, page 68, note 147.

[316] "The wills are free, and I wish neither the one nor the other."

[317] "The force of inertia conquered."

[318] Reddie also wrote _The Mechanics of the Heavens_, referred to later in this work. He must not be confused with Judge James Reddie (1773-1852), of Glasgow, who wrote on international law, although this is done in the printed edition of the British Museum catalogue, for he is mentioned by De Morgan somewhat later as alive in 1862.

[319] Henry Dunning Macleod (1821-1902), a lawyer and writer on political economy, was a Scotchman by birth. He wrote on economical questions, and lectured on banking at Cambridge (1877) and at King's College, London (1878). He was a free lance in his field, and was not considered orthodox by the majority of economists of his time. He was an unsuccessful candidate for the chairs of political economy at Cambridge (1863), Edinburgh (1871), and Oxford (1888).

[320] See Vol. I, page 252, note 2 {576}.

[321] Francis Henry Laing (1816-1889) was a graduate of Queen's College, Cambridge, and a clergyman in the Church of England until 1846, when he entered the Church of Rome. He taught in various Jesuit colleges until 1862, when his eccentricity was too marked to warrant the Church in allowing him to continue. He published various controversial writings during his later years. Of course if he had known the works of Wessel, Gaus, Buee, Argand, and others, he would not have made such a sorry exhibition of his ignorance of mathematics.

[322] See Vol. I, page 329, note 1 {705}. The book went into a second edition in 1864.

[323] Thomas Weddle (1817-1853) was, at the time of publishing this paper, a teacher in a private school. In 1851 he became professor of mathematics at Sandhurst. He contributed several papers to the _Cambridge and Dublin Mathematical Journal_, chiefly on geometry.

[324] See Vol. II, page 109, note 205.

[325] See Vol. II, page 66, note 143.

[326] See Vol. II, page 151, note 268.

[327] George Barrett (1752-1821) worked from 1786 to 1811 on a set of life insurance and annuity tables. He invented a plan known as the "columnar method" for the construction of such tables, and as De Morgan states, this was published by Francis Baily, appearing in the appendix to his work on annuities, in the edition of 1813. Some of his tables were used in Babbage's _Comparative View of the various Institutions for the Assurance of Lives_ (1826).

[328] See Vol. I, page 309, note 2 {670}.

[329] This was his _Practical short and direct Method of Calculating the Logarithm of any given Number, and the Number corresponding to any given Logarithm_ (1849).

[330] This is William Neile (1637-1670), grandson of Richard Neile (not Neal), Archbishop of York. At the age of 19, in 1657, he gave the first rectification of the semicubical parabola. Although he communicated it to Brouncker, Wren, and others, it was not published until 1639, when it appeared in John Wallis's _De Cycloide_.

[331] I myself "was a considerable part."

[332] He also wrote _A Glance at the Universe_ ("2d thousand" in 1862), and _The Resurrection Body_ (1869).

[333] See Vol. I, page 63, note 1 {74}.

[334] As Swift gave it in his _Poetry. A Rhapsody_, it is as follows:

"So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em. And so proceed _ad infinitum_."

[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based on radium disintegration stand the test. This would mean, according to MacCurdy's estimate, 60,000,000 years since life first appeared on the earth.

[336] De Morgan wrote better than he knew, for this work, the _Allgemeine Encyclopaedie der Wissenschaften und Kuenste_, begun at Leipsic in 1818, is still (1913) unfinished. Section I, A-G, consists of 99 parts in 56 volumes; Section II, H-N, consists of 43 volumes and is not yet completed; and Section III, O-Z, consists of 25 volumes thus far, with most of the work still to be done. Johann Samuel Ersch (1766-1828), the founder, was head librarian at Halle. Johann Gottfried Gruber (1774-1851), his associate, was professor of philosophy at the same university.

[337] William Howitt (1792-1879) was a poet, a spiritualist, and a miscellaneous writer. He and his wife became spiritualists about 1850. He wrote numerous popular works on travel, nature and history.

[338] See Vol. II, page 55, note 108.

[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and A. B. was De Morgan.

[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a skeptic, but preached only strict orthodoxy to his people. It was only in his manuscript, _Mon Testament_, that was published after his death, and that caused a great sensation in France, that his antagonism to Christianity became known.

[341] Baron Zach relates that a friend of his, in a writing intended for publication, said _Un esprit doit se frotter contre un autre_. The censors struck it out. The Austrian police have a keen eye for consequences.--A. De M.

"One mind must rub against another." On Baron Zach, see Vol. II, page 45, note 4.

[342] Referring to the first Lord Eldon (1751-1838), who was Lord Chancellor from 1799 to 1827, with the exception of one year.

[343] "Sleeping power."

[344] "Causes sleep."

[345] Richard Hooker (c. 1554-1600), a theologian, "the ablest living advocate of the Church of England as by law established."

[346] See Vol. I, page 76, note 3 {112}.

[347] "Other I,"--other self.

[348] This "utter rejection" has been repeated (1872) by the same writer.--S. E. De M.

[349] Edward Jenner (1749-1823) was a physician and biologist. His first experiments in vaccination were made in 1796, and his discovery was published in 1798.

[350] See Vol. II, page 38, note 80.

[351] "You will go most safely in the middle (way)."

[352] Pierre Joseph Arson was known early in the 19th century for his controversy with Hoene Wronski the mathematician, whom he attacked in his _Document pour l'histoire des grands fourbes qui ont figure sur la terre_ (1817-1818).

[353] "We enter the course by night and are consumed by fire."

[354] See Vol. I, page 51, note 3 {51}.

[355] See Vol. I, page 336, note 8 {713}.

[356] See Vol. I, page 137, note 8 {286}.

[357] See Vol. I, page 229, note 2 {515}.

[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who was prominent in his advocacy of the repeal of the Corn Laws.

[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his brother Horatio he wrote numerous satires. His _Horace in London_ (1813) imitated the Roman poet. His works were collected and published in 1840.

[360] Samuel Butler (1612-1680), the poet and satirist, author of _Hudibras_ (1663-1678).

[361] "Is it not fine to be sure of one's action when entering in a combat with another? There, push me a little in order to see. NICOLE. Well! what's the matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the rascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me _en tierce_, before you pushed _en quarte_, and you did not give me time to parry."

[362] John Abernethy (1764-1831), the famous physician and surgeon.

[363] See Vol. I, page 102, note 5 {175}.

[364] "With what measure ye mete, it shall be measured to you again."

[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the Council of Nicaea, and author of a _History of the Christian Church_ in ten books (c. 324 A. D.).

[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of the first to advocate the scientific study of early Christian literature.

[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of the Greek Testament (1849-1861).

[368] The work was _The Number and Names of the Apocalyptic Beasts: with an explanation and application. Part I._ London, 1848, as mentioned below. Thom also wrote _The Assurance of Faith, or Calvinism identified with Universalism_ (London, 1833), and various other religious works.

[369] See Vol. I, page 222, note 14 {490}.

[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was long a minister in that church, preaching in the Renshaw Street Chapel from 1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy conducted by James Martineau and Henry Giles in response to a challenge by thirteen Anglican Clergy. In 1839 Thom contributed four lectures and a letter to this controversy. Among his religious works were a _Life of Blanco White_ (1845) and _Hymns, Chants, and Anthems_ (1854).

[371] The spelling of these names is occasionally changed to meet the condition that the numerical value of the letters shall be 666, "the number of the beast" of Revelations. The names include Julius Caesar; Valerius Jovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the Christians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as Pope Sylvester II from 999 to 1003, known to mathematicians for his abacus and his interest in geometry, and accused by his opponents as being in league with the devil; Linus, the second Bishop of Rome, the successor of Peter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605 to 1621, and who excommunicated all Venice in 1606 for its claim to try ecclesiastics before lay tribunals, thus taking a position which he was forced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7 {307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455 and persecuted the orthodox Christians in Africa; Boniface III, who was pope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83}); Mohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and who reigned as Pope Pius VI from 1775 to 1799, dying in captivity because he declined to resign his temporal power to Napoleon; Bonaparte; and, under [Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984 during the absence of Boniface VII in Constantinople.

[372] The Greek words and names are also occasionally misspelled so as to fit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he latine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the Italian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan), [Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho niketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes blaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of old), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos] (Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout fibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e. e. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios] (baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa he papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek: saxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he alazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet); [Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord over the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek: papeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina] (Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note 10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks] (cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N. Boneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender), [Greek: to megatherion] (the megathereum, the beast).

[373] James Wapshare, whose _Harmony of the Word of God in Spirit and in Truth_ appeared in 1849.

[374] The literature relating to the _Swastika_ is too extended to permit of any adequate summary in these notes.

[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he became a Roman Catholic priest in 1851, and became Cardinal in 1875. He succeeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a number of religious works.

[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman. He worked with Cobden for free trade, peace, and reform of the electorate.

[377] "The fallacy of many questions."

[378] William Wilberforce (1759-1833), best known for his long fight for the abolition of the slave trade.

[379] Richard Martin (1754-1834), high sheriff of County Galway and owner of a large estate in Connemara. Curiously enough, he was known both for his readiness in duelling and for his love for animals. He was known as "Humanity Martin," and in 1822 secured the passage of an act "to prevent the cruel and improper treatment of cattle." He was one of the founders (1824) of the Royal Society for the Prevention of Cruelty to Animals. He is usually considered the original of Godfrey O'Malley in Lever's novel, _Charles O'Malley_.

[380] See Vol. I, page 149, note 1 {323}, also text on same page.

[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110.

[382] "Penitential seat."

[383] "Well placed upon the cushion."

[384] See Vol. II, page 58, note 109.

[385] "He has lost the right of being influenced by evidence."

[386] "Hung up."

[387] "A few things to the wise, nothing to the unlettered."

[388] The fallacy results from dividing both members of an equation by 0, x - 1 being the same as 1 - 1, and calling the quotients finite.

[389] "If you order him to the sky he will go."

[390] _Similia similibus curanter_, "Like cures like," the homeopathic motto.

[391] "Without harm to the proprieties."

[392] "What are you doing? I am standing here."

[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva hault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le poulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre toute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que fermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit lentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict de la gausche, et de la gausche ce que avoit faict de la dextre.--A. De M.

[394] _Suaviter in modo, fortiter in re_, "Gentle in manners, firm in action."

[395] See Vol. I, page 101, note 4 {174}.

[396] See Vol. I, page 315, note 3 {686}.

[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite of this handicap he became professor of political economy at Cambridge and sat in parliament for a number of years. He championed the cause of reform and in particular he was prominent in the protection of the native interests of India. The establishing of the parcels post (1882) took place while he was postmaster general (1880-1884).

[398] Of course the whole thing depends upon what definition of division is taken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to allow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics.

[399] Richard Milward (1609-1680), for so the name is usually given, was rector of Great Braxted (Essex) and canon of Windsor. He was long the amanuensis of John Selden, and the _Table Talk_ was published nine years after Milward's death, from notes that he left. Some doubt has been cast upon the authenticity of the work owing to many of the opinions that it ascribes to Selden.

[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental scholar. He sat in the Long Parliament, and while an advocate of reform he was not an extremist. He was sent to the Tower for his support of the resolution against "tonnage and poundage," in 1629. His _History of Tythes_ (1618) was suppressed at the demand of the bishops. His _De Diis Syriis_ (1617) is still esteemed a classic on Semitic mythology.

[401] See Vol. I, page 42, note 4 {24}.

[402] See Vol. II, page 249, note 398.

[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set forth a plan for forwarding the mails by stage coaches instead of by postmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general of the post office in 1786 and was dismissed six years later for arbitrarily suspending a deputy. He had been verbally promised 2-1/2% on the increased revenue, but Pitt gave him only a pension of L3000. In 1813 he was awarded L50,000 in addition to his pension.

[404] Dionysius Lardner (1793-1859), professor of natural philosophy in London University (now University College). His _Cabinet Cyclopaedia_ (1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and Lardner on various branches of mathematics, and there were many other well-known contributors. Lardner is said to have made $200,000 on a lecture tour in America.

[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and in 1785 took a charge in Dundee. He was arrested for sedition because of an address that it was falsely alleged that he gave before a society known as the "Friends of Liberty." As a matter of fact the address was given by an uneducated weaver, and Palmer was merely asked to revise it, declining to do even this. Nevertheless he was sentenced to Botany Bay (1794) for seven years. The trial aroused great indignation.

[406] See Vol. I, page 80, note 5 {119}.

[407] See Vol. II, page 244, note 394.

[408] See Vol. I, page 352, note 1 {731}.

[409] See Vol. I, page 332, note 4 {709}.

[410] "The lawyers are brought into court; let them accuse each other."

[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined the laureateship on the death of Wordsworth (1850). Byron, his pretended friend, wrote a lampoon (1818) ridiculing his cadaverous appearance.

[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized as Mr. Wagg in _Vanity Fair_. The _John Bull_ was founded in 1820 and Hook was made editor.

[413] "On pitying the heretic."

[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all S is P. Celarent: No M is P, all S is M, hence no S is P.

[415] "Simply," "According to which," "It does not follow."

[416]

"O sweet soul, what good shall I declare That heretofore was thine, since such are thy remains!"

[417] "Stupid fellow!"

[418] Christopher Barker (c. 1529-1599), also called Barkar, was the Queen's printer. He began to publish books in 1569, but did no actual printing until 1576. In 1575 the Geneva Bible was first printed in England, the work being done for Barker. He published 38 partial or complete editions of the Bible from 1575 to 1588, and 34 were published by his deputies (1588-1599).

[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to London to learn the printer's trade. He returned in 1717 and started a printing house. Benjamin, his brother, was apprenticed to him but ran away (1723). James published the _New England Courant_ (1721-1727), and Benjamin is said to have begun his literary career by writing for it.

[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in 1661, and later kept a boarding school in Bromley-by-Bow. His famous arithmetic appeared at London in 1661 and went through many editions. It was the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was long thought to have been the first arithmetic published in America, and it was the first English one. There was, however, an arithmetic published much earlier than this, in Mexico, the _Sumario compendioso ... con algunas reglas tocantes al Aritmetica_, by "Juan Diaz Freyle," in 1556.

[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane, London.

[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was printed by the Society for the Diffusion of Useful Knowledge.

[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe but was really nothing more than a "clerc tonsure." He lived at Court and was pensioned to write against the philosophers of the Voltaire group. He posed as the defender of morality, a commodity of which he seems to have possessed not the slightest trace.

[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was during his ambitious reign that Galileo was summoned to Rome to make his recantation (1633), the exact nature of which is still a matter of dispute.

[425] This Baden Powell (1796-1860) was the Savilian professor of geometry (1827-1860) at Oxford.

[426] "Memoirs of the famous bishop of Chiapa, by which it appears that he had butchered or burned or drowned ten million infidels in America in order to convert them. I believe that this bishop exaggerated; but if we should reduce these sacrifices to five million victims, this would still be admirable."

[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested in astronomy and caused the Alphonsine Tables to be prepared. These table were used by astronomers for a long time. It is said that when the Ptolemaic system of the universe was explained to him he remarked that if he had been present at the Creation he could have shown how to arrange things in a much simpler fashion.

[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824), and a poet of no mean ability.

[429] The "Aboriginal Britons," an excellent poem, by Richards. (Note by Byron.)--A. De M.

[430] John Watkins (d. after 1831), a teacher and miscellaneous writer.

[431] Frederic Shoberl (1775-1853), a miscellaneous writer.

[432] He wrote, besides the _Aboriginal Britons_, _Songs of the Aboriginal Bards_ (1792), _Modern France: a Poem_ (1793), _Odin, a drama_ (1804), _Emma, a drama on the model of the Greek theatre_ (1804), _Poems_ (2 volumes, 1804), and a _Monody on the Death of Lord Nelson_ (1806).

[433] Henry Kirke White (1785-1806), published his first volume of poems at the age of 18. Southey and William Wilberforce became interested in him and procured for him a sizarship at St. John's College, Cambridge. He at once showed great brilliancy, but he died of tuberculosis at the age of 21.

[434] John Wolcot, known as Peter Pindar (1738-1819), was a London physician. He wrote numerous satirical poems. His _Bozzy and Piozzi, or the British Biographers_, appeared in 1786, and reached the 9th edition in 1788.

[435] See Vol. I, page 235, note 8 {532}.

[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems, and coins, many of his pieces being now in the British Museum. He sat in parliament for twenty-six years (1780-1806), but took no active part in legislation. He opposed the acquisition of the Elgin Marbles, holding them to be of little importance. His _Analytical Inquiry into the Principles of Taste_ appeared in 1808.

[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a time professor at the University of Parma. His _Observationes in M. Tullium Ciceronem_ appeared at Pratalboino in 1535. It was revised by his nephew under the title _Thesaurus Ciceronianus_ (Venice, 1570).

[438] See Vol. I, page 314, note 4 {681}.

[439]

"Like the geometer, who bends all his powers To measure the circle, and does not succeed, Thinking what principle he needs."

[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases of the Bible and numerous elegies. In the early days of the revolutionary struggle he sided with the Royalists. One of his most popular works was the _Emblems_ (1635), with illustrations by William Marshall.

[441] Regnault de Becourt wrote _La Creation du monde, ou Systeme d'organisation primitive suivi de l'interpretation des principaux phenomenes et accidents que se sont operes dans la nature depuis l'origine de univers jusqu'a nos jours_ (1816). This may be the work translated by Dalmas.

[442] "Because it lacks a holy prophet."

[443] Anghera. See Vol. II, page 60, note 127.

[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and pamphleteer. He was for a time at "The Peacock without Temple Bar," and later at "The Dial and Bible against St. Dunstan's Church." He was fined repeatedly for publishing immoral works, and once stood in the pillory for it. He is ridiculed in the _Dunciad_ for having been tossed in a blanket by the boys of Westminster School because of an oration that displeased them.

[445] See Vol. II, page 109, note 206.

[446] Encyclopaedia.

[447] Author of the _Historia Naturalis_ (77 A.D.)

[448] Author of the _De Institutione Oratorio Libri_ XII (c. 91 A.D.)

[449] His _De Architectures Libri_ X was not merely a work on architecture and building, but on the education of the architect.

[450] Cyclophoria.

[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art of printing either at Bruges or Cologne, and between 1471 and 1477 set up a press at Westminster. Tradition says that the first book printed in England was his _Game and Playe of Chesse_ (1474). The _Myrrour of the Worlde and th'ymage of the same_ appeared in 1480. It contains a brief statement on arithmetic, the first mathematics to appear in print in England.

[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date of the _Margarita Philosophica_. The first edition appeared at Freiburg in 1503.

[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans (1486) and Emperor (1493-1519).

[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy and mathematics in various cities of France and Germany. His _Institutionum astronomicarum libri III_ appeared at Basel in 1528, his _Cosmographia_ at Paris in 1529, and his _Opera_ at Leyden in 1531.

[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and theology at his birthplace, Herborn, in Nassau, and later at Weissenberg. He published several works, including the _Elementale mathematicum_ (1611), _Systema physicae harmonicae_ (1612), _Methodus admirandorum mathematicorum_ (1613), _Encyclopaedia septem tomis distincta_ (1630), and the work mentioned above.

[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at his birthplace, Basel. He also wrote the _Epitome metrica historiae universalis civilis et sacrae ab orbe condito_ (1686).

[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but kind-hearted freethinker. His _Cyclopaedia, or an Universal Dictionary_ was translated into French and is said to have suggested the great _Encyclopedie_.

[458] _Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des metiers, par un societe de gens de lettres. Mis en ordre et publie par M. Diderot, et quant a la partie mathematique, par M. d'Alembert._ Paris, 1751-1780, 35 volumes.

[459] "From the egg" (state).

[460] See Vol. I, page 382, note 12 {785}.

[461] See Vol. II, page 4, note 15.

[462] "In morals nothing should serve man as a model but God; in the arts, nothing but nature."

[463] _Encyclopedie Methodique, ou par ordre de matieres._ Paris, 1782-1832, 166-1/2 volumes.

[464] See Vol. II, page 193, note 336.

[465] _Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge._ London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40 volumes.

[466] See Vol. I, page 137, note 8 {286}.

[467] See Vol. I, page 80, note 5 {119}.

[468] De Morgan should be alive to satirize some of the statements on the history of mathematics in the eleventh edition.

[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at Glasgow and a popular lecturer on the subject. He lectured in the United States in 1848-1849. His _Views of the Architecture of the Heavens_ (1838) was a very popular work, and his _Planetary System_ (1848, 1850) contains the first suggestion for the study of sun spots by the aid of photography.

[470] See Vol. II, page 109, note 206.

[471] George Long (1800-1879), a native of Poulton, in Lancashire, was called to the University of Virginia when he was only twenty-four years old as professor of ancient languages. He returned to England in 1828 to become professor of Greek at London University. From 1833 to 1849 he edited the twenty-nine volumes of the _Penny Cyclopaedia_. He was an authority on Roman law.

[472] A legal phrase, "Qui tam pro domina regina, quam pro se ipso sequitur,"--"Who sues as much on the Queen's account as on his own."

[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge (1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen years at the bar he published some two hundred mathematical papers. In 1863 he became professor of mathematics at Cambridge, and so remained until his death. His collected papers, nine hundred in number, were published by the Cambridge Press in 13 volumes (1889-1898). He contributed extensively to the theory of invariants and covariants. De Morgan's reference to his coining of new names is justified, although his contemporary, Professor Sylvester, so far surpassed him in this respect as to have been dubbed "the mathematical Adam."

[474] See Vol. II, page 26, note 56.

[475] See Vol. I, page 111, note 3 {207}.

[476] See Vol. I, page 87, note 6 {135}.

[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With the collaboration of his brother and Nicolas Rigault he published the 1620 and 1626 editions of De Thou's History. He also wrote on law and history. His younger brother, Jacques (died in 1656), edited his works. The two had a valuable collection of books and manuscripts which they bequeathed to the Royal Library at Paris.

[478] See Vol. I, page 51, note 3 {51}.

[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo.

[480] See Vol. I, page 40, note 4 {20}.

[481] See Vol. I, page 106, note 4 {188}.

[482] Sir Edward Sherburne (1618-1702), a scholar of considerable reputation. The reference by De Morgan is to _The Sphere of Marcus Manilius_, in the appendix to which is a _Catalogue of Astronomers, ancient and modern_.

[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out with the best equipment then available. He was President of the Royal Society in 1752.

[484] See Vol. II, page 148, note 263.

[485] See Vol. I, page 140, note 7 {296}.

[486] See Vol. I, page 106, note 4 {188}.

[487] Edward Bernard (1638-1696), although Savilian professor of astronomy at Oxford, was chiefly interested in archeology.

[488] See Vol. I, page 107, note 1 {190}.

[489] See Vol. I, page 107, note 1 {190}.

[490] See Vol. I, page 135, note 3 {281}.

[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well known for the letters written to his son which were published posthumously (1774).

[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and an astronomer of some ability.

[493] See Vol. I, page 376, note 1 {766}.

[494] William Oughtred (c. 1573-1660), a fellow of King's College, Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known arithmetic and trigonometry of his time. His _Arithmeticae in Numero & Speciebus Institutio ... quasi Clavis Mathematicae est_ (1631) went through many editions and appeared in English as _The Key to the Mathematicks new forged and filed_ in 1647.

[495] See Vol. I, page 140, note 5 {294}.

[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of Westminster School (1846) and head master of Queen Elizabeth's School at Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow fever the following year.

[497] He also wrote a memoir of his father, privately printed at Oxford in 1883.

[498] See Vol. I, page 69, note 3 {96}.

[499] See Vol. I, page 106, note 4 {188}.

[500] William Gascoigne was born at Middleton before 1612 and was killed in the battle of Marston Moor in 1644. He was an astronomer and invented the micrometer with movable threads (before 1639).

[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for refusing to sign the covenant. He became professor of astronomy at Oxford (1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor of the Garter (1671). He is best known for his solution of Kepler's problem to approximate a planet's orbit, which appeared in his _Astronomia geometrica_ in 1656.

[502] See Vol. I, page 110, note 2 {198}.

[503] See Vol. I, page 100, note 2 {172}.

[504] See Vol. I, page 107, note 1 {190}.

[505] See Vol. I page 114, note 6 {220}.

[506] See Vol. I, page 77, note 4 {118}.

[507] See Vol. I, page 125, note 3 {253}.

[508] See Vol. I, page 105, note 2 {186}.

[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City of Bremen, his birthplace, and afterwards became a private teacher in London. He became secretary of the Royal Society and contributed on physics and astronomy to the _Philosophical Transactions_.

[510] Thomas Brancker, or Branker (1636-1676) wrote the _Doctrinae sphaericae adumbratio et usus globorum artificialium_ (1662) and translated the algebra of Rhonius with the help of Pell. The latter work appeared under the title of _An Introduction to Algebra_ (1668), and is noteworthy as having brought before English mathematicians the symbol / for division. The symbol never had any standing on the Continent for this purpose, but thereafter became so popular in England that it is still used in all the English-speaking world.

[511] See Vol. I, page 118, note 1 {230}.

[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated at London and Leyden. He became a professor at Leyden, and later held the chair of mathematics at the College de France. He wrote chiefly on geography.

[513] See Vol. II, page 297, note 487.

[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome at the Convent of St. Panteleon. He wrote several works on geometry, astronomy, and physics.

[515] See Vol. I, page 172, note 2 {381}.

[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient languages and later of mathematics and physics at the College of Pau, and afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He wrote on geometry, astronomy and physics.

[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse, and died in 1665. Although connected with the parliament of Toulouse, his significant work was in mathematics. He was one of the world's geniuses in the theory of numbers, and was one of the founders of the theory of probabilities and of analytic geometry. After his death his son published his edition of Diophantus (1670) and his _Varia opera mathematica_ (1679).

[518] This may be Christopher Townley (1603-1674) the antiquary, or his nephew, Richard, who improved the micrometer already invented by Gascoigne.

[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He invented a screw micrometer with movable threads (1666) and made many improvements in astronomical instruments.

[520] See Vol. I, page 66, note 9 {86}.

[521] See Vol. I, page 124, note 7 {248}.

[522] John Machin (d. 1751) was professor of astronomy at Gresham College (1713-1751) and secretary of the Royal Society. He translated Newton's _Principia_ into English. His computation of [pi] to 100 places is given in William Jones's _Synopsis palmariorum matheseos_ (1706).

[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until his marriage. He was a gentleman of leisure and devoted himself to the study of mathematics, especially of probabilities.

[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and physics at Cambridge, and editor of the second edition of Newton's _Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains "Cotes's Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had lived we had known something."

[525] See Vol. I, page 135, note 3 {281}.

[526] See Vol. I, page 377, note 4 {769}.

[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at Angers. His _Analyse demontree, ou Maniere de resoudre les problemes de mathematiques_ (1708) was a successful attempt to popularize the theories of men like Descartes, Newton, Leibnitz, and the Bernoullis.

[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student of mathematics and physics. His _Methodus incrementorum directa et inversa_ (1715) was the first treatise on the calculus of finite differences. It contained the well-known theorem that bears his name.

[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut (1735) to measure an arc of a meridian in Lapland. He was head of the physics department in the Berlin Academy from 1745 until 1753. He wrote _Sur la figure de la terre_ (1738) and on geography and astronomy.

[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and was one of those sent by the Academy of Sciences to measure an arc of a meridian in Peru (1735). The object of this and the work of Maupertuis was to determine the shape of the earth and see if Newton's theory was supported.

[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris Academy of Sciences and was sent with Bouguer to Peru, for the purpose mentioned in the preceding note. He wrote on the figure of the earth, but was not a scientist of high rank.

[532] See Vol. I, page 136, note 5 {283}.

[533] See Vol. II, page 296, note 483.

[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).

[535] See Vol. I, page 160, note 5 {350}.

[536] See Vol. I, page 87, note 4 {133}.

[537] See Vol. I, page 132, note 2 {272}.

[538] See Vol. I, page 118, second note 1 {231}.

[539] The name of Newton is so well known that no note seems necessary. He was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in 1727.

[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710, is said to have been the first to teach the Newtonian physics by direct experiment, the apparatus being invented by him for the purpose. He wrote on astronomy and physics. His _Epistola de legibus virium centripetarum_, in the Philosophical Transactions for 1708, accused Leibnitz of having obtained his ideas of the calculus from Newton, thus starting the priority controversy.

[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise, named Stratioticos_ (1579), and completed _A geometrical practise, named Pantometria_ (1571) that had been begun by his father, Leonard Digges.

[542] John Dee (1527-1608), the most famous astrologer of his day, and something of a mathematician, wrote a preface to Billingsley's translation of Euclid into English (1570).

[543] See Vol. I, page 76, note 3 {112}.

[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter Raleigh, who sent him to survey Virginia (1585). He was one of the best English algebraists of his time, but his _Artis Analyticae Praxis ad Aequationes Algebraicas resolvendas_ (1631) did not appear until ten years after his death.

[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life chiefly to the study of chronology, writing upon the subject and taking issue with Scaliger (1601).

[546] See Vol. I, page 69, note 3 {96}.

[547] Walter Warner edited Harriot's _Artis Analyticae Praxis_ (1631). Tarporley is not known in mathematics.

[548] See Vol. I, page 105, note 2 {186}.

[549] See Vol. I, page 115, note 3 {224}.

[550] See Vol. II, page 300, note 509.

[551] See Vol. I, page 107, note 1 {190}.

[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some years he was assistant to John Pell, then ambassador to Switzerland. He wrote on arithmetical instruments invented by him (1673), on hydrostatics (1697) and on church history (1658).

[553] See Vol. I, page 153, note 4 {337}.

[554] See Vol. I, page 85, note 2 {129}.

[555] See Vol. I, page 43, note 8 {33}.

[556] See Vol. I, page 43, note 7 {32}.

[557] See Vol. I, page 382, note 13 {786}. The history of the subject may be followed in Braunmuehl's _Geschichte der Trigonometrie_.

[558] See Vol. I, page 377, note 3 {768}.

[559] See Vol. I, page 108, note 2 {192}.

[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_ (1669), and _The general Doctrine of Equation_ (1664).

[561] John Newton (1622-1678), canon of Hereford (1673), educational reformer, and writer on elementary mathematics and astronomy.

[562] See Vol. I, page 87, note 4 {133}.

[563] "The average of the two equal altitudes of the sun before and after dinner."

[564] See Vol. I, page 42, note 4 {24}.

[565] London, 1678. It went though many editions.

[566] "This I who once ..."

[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He then went on the stage and met with some success at Covent Garden. His first comedy, _The Apprentice_ (1756) was so successful that he left the stage and took to play writing. His translation of Tacitus appeared in 1793, in four volumes.

[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess Henrietta Maria and remained there several years. He wrote _L'usage de la regle de proportion_ (Paris, 1624, with an English translation in 1626), _Arithmetique Logarithmetique_ (Paris, 1626, with an English translation in 1635), and _Of Natural and Artificial Arithmetick_ (London, 1630, revised in 1650-1652), part I of which was one of the most popular textbooks ever produced in England.

[569] John Lambert (1619-1694) was Major-General during the Revolution and helped to draw up the request for Cromwell to assume the protectorate. He was imprisoned in the Tower by the Rump Parliament. He was confined in Guernsey until the clandestine marriage of his daughter Mary to Charles Hatton, son of the governor, after which he was removed (1667) to St. Nicholas in Plymouth Sound.

[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham College in March, 1636, but resigned in November of that year, being succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and Foster succeeded him. He wrote on dialling and made a number of improvements in geometric instruments.

[571] "Twice of the word a minister," that is, twice a minister of the Gospel.

[572] This is _The Lives of the Professors of Gresham College to which is prefixed the Life of the Founder, Sir Thomas Gresham_, London, 1740. It was written by John Ward (c. 1679-1758), professor of rhetoric (1720) at Gresham College and vice-president (1752) of the Royal Society.

[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the Treasury in 1692, and was created Baron Halifax in 1700 and Viscount Sunbury and Earl of Halifax in 1714. He introduced the bill establishing the Bank of England, the bill becoming a law in 1694. He had troubles of his own, without considering Newton, for he was impeached in 1701, and was the subject of a damaging resolution of censure as auditor of the exchequer in 1703. Although nothing came of either of these attacks, he was out of office during much of Queen Anne's reign.

[574] See Vol. II, page 302, note 547.

[575] See Vol. I, page 105, note 2 {186}.

[576] James Dodson (d. 1757) was master of the Royal Mathematical School, Christ's Hospital. He was De Morgan's great-grandfather. The _Anti-Logarithmic Canon_ was published in 1742.

[577] See Vol. I, page 106, note 4 {188}.

[578] See Vol. I, page 110, note 2 {198}.

[579] Richard Busby, (1606-1695), master of Westminster School (1640) had among his pupils Dryden and Locke.

[580] See Vol. I, page 107, note 1 {190}.

[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge (1620-1646), and Prebend of Westminster (1661), was a well-known theological writer of the time.

[582] See Vol. I, page 140, note 5 {294}.

[583] See Vol. I, page 108, note 2 {192}.

[584] "Labor performed returns in a circle."

[585] See Vol. II, page 208.

[586] "Whatever objections one may make to the above arguments, one always falls into an absurdity."

[587] See Vol. II. page 11, note 29. _The Circle Squared; and the solution of the problem adapted to explain the difference between square and superficial measurement_ appeared at Brighton in 1865.

[588] "And beyond that nothing."

[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery, reducing the price from 1s. each to 4d. a gross. He was a great collector of paintings and old violins.

[590] William Edward Walker wrote five works on circle squaring (1853, 1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham.

[591] Solomon M. Drach wrote _An easy Rule for formulizing all Epicyclical Curves_ (London, 1849), _On the Circle area and Heptagon-chord_ (London, 1864), _An easy general Rule for filling up all Magic Squares_ (London, 1873), and _Hebrew Almanack-Signs_ (London, 1877), besides numerous articles in journals.

[592] See Vol. I, page 168, note 3 {371}.

[593] See Vol. I, page 254, note 2 {580}.

[594] See Vol. I, page 98, note 6 {163}.

[595] Robert Fludd or Flud (1574-1637) was a physician with a large London practice. He denied the diurnal rotation of the earth, and was attacked by Kepler and Mersenne, and accused of magic by Gassendi. His _Apologia Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis aspersam, veritatis quasi Fluctibus abluens_ (Leyden, 1616) is one of a large number of works of the mystic type.

[596] Consult _To the Christianity of the Age. Notes ... comprising an elucidation of the scope and contents of the writings ... of Dionysius Andreas Freher_ (1854).

[597] Sir William Robert Grove (1811-1896), although called to the bar (1835) and to the bench (1853), is best known for his work as a physicist. He was professor of experimental philosophy (1840-1847) at the London Institution, and invented a battery (1839) known by his name. His _Correlation of Physical Forces_ (1846) went through six editions and was translated into French.

[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a mystic, closely in touch with the Gottesfreunde of Basel. His _Sermons_ first appeared in print at Leipsic in 1498.

[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von Hohenheim, and he took the name by which he is generally known because he held himself superior to Celsus. He was a famous physician and pharmacist, but was also a mystic and neo-Platonist. He lectured in German on medicine at Basel, but lost his position through the opposition of the orthodox physicians and apothecaries.

[600] See Vol. I, page 256, note 2 {588}.

[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg. He helped Luther with his translation of the Bible.

[602] Johann Reuchlin (1455-1522), the first great German humanist, was very influential in establishing the study of Greek and Hebrew in Germany. His lectures were mostly delivered privately in Heidelberg and Stuttgart. Unlike Melanchthon, he remained in the Catholic Church.

[603] Joseph Chitty (1776-1841) published his _Precedents of Pleading_ in 1808 and his _Reports of Cases on Practice and Pleading_ in 1820-23 (2 volumes).

[604] See Vol. I, page 44, note 1 {35}.

[605] See Vol. I, page 44, note 4 {38}.

[606] Jean Pelerin, also known as Viator, who wrote on perspective. His work appeared in 1505, with editions in 1509 and 1521.

[607] Henry Stephens. See Vol. I, page 44, note 3 {37}.

[608] The well-known grammarian (1745-1826). He was born at Swatara, in Pennsylvania, and practised law in New York until 1784, after which he resided in England. His grammar (1795) went through 50 editions, and the abridgment (1818) through 120 editions. Murray's friend Dalton, the chemist, said that "of all the contrivances invented by human ingenuity for puzzling the brains of the young, Lindley Murray's grammar was the worst."

[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics and medicine at Cambridge up to 1545. After that he taught mathematics at Oxford and practised medicine in London. His _Grounde of Artes_, published about 1540, was the first arithmetic published in English that had any influence. It went through many editions. The _Castle of Knowledge_ appeared in 1551. It was a textbook on astronomy and the first to set forth the Copernican theory in England. Like Recorde's other works it was written on the catechism plan. His _Whetstone of Witte ... containying thextraction of Rootes: The Cosike practise, with the rule of Equation: and the woorkes of Surde Nombres_ appeared in 1557, and it is in this work that the modern sign of equality first appears in print. The word "Cosike" is an adjective that was used for a long time in Germany as equivalent to algebraic, being derived from the Italian _cosa_, which stood for the unknown quantity.

[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of State under Elizabeth (1596-1603) and under James I (1603-1612).

[611] In America the German pronunciation is at present universal among mathematicians, as in the case of most other German names. This is due, no doubt, to the great influence that Germany has had on American education in the last fifty years.

[612] The latest transliteration is substantially K'ung-fu-tz[vu].

[613] The tendency seems to be, however, to adopt the forms used of individuals or places as rapidly as the mass of people comes to be prepared for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very common in America.

[614] Sir Edward Coke (1552-1634), the celebrated jurist.

[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a grandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef traveled in France and Italy and then taught mathematics in London. He wrote on astronomy and philosophy and also published in the _Acta Eruditorum_ (1686) his _Schediasma geometricum de nova infinitorum scientia_. _Quadratura circuli infinitis modis demonstrata_, and his _Monitum ad geometras_ (1687). Philippe was geographer of the Academy of Leyden. His _Introductionis in universam geographiam tam veterem quam novam libri sex_ appeared at Leyden in 1624, about the time of his death.

[616] See Vol. I, page 124, note 7 {248}.

[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at Purmerend. His _Considerationes circa Analyseos ad quantitates infinite parvas applicatae Principia et Calculi Differentialis usum_ (Amsterdam, 1694) was attacked by Leibnitz. He replied in his _Considerationes secundae_ (1694), and also wrote the _Analysis Infinitorum, seu Curvilineorum Proprietates ex Polygonorum Natura deductae_ (1695). His most famous work was on the existence of God, _Het Regt Gebruik der Werelt Beschouwingen_ (1718).

[618] "From a given line to construct" etc.

[619] "Pirates do not fight one another."

[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor of philosophy at the College du Plessis, in Paris, for 34 years. The work to which De Morgan refers is probably the _Fameux Probleme de la quadrature du cercle, resolu geometriquement par le cercle et a ligne droite_ that appeared in 1683.

[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}.

[622] Wilhelm Frederik von Zytphen also published the _Tidens Stroem_, a chronological table, in 1840. The work to which De Morgan refers, the _Solens Bevaegelse i Verdensrummet_, appeared first in 1861. De Morgan seems to have missed his _Nogl Ord om Cirkelens Quadratur_ which appeared in 1865, at Copenhagen.

[623] James Joseph Sylvester (1814-1897), professor of natural philosophy at University College, London (1837-1841), professor of mathematics at the University of Virginia (1841-1845), actuary in London (1845-1855), professor of mathematics at Woolwich (1877-1884) and at Johns Hopkins University, Baltimore (1877-1884), and Savilian professor of geometry at Oxford (1884-1894).

[624] See Vol. I, page 76, note 3 {112}.

[625] See Vol. II, page 205, note 349.

[626] See Vol. I, page 76, note 3 {112}.

[627] See Vol. I, page 46, note 1 {42}.

[628] See Vol. II, page 183, note 318.

[629] See Vol. I, page 321, note 2 {691}.

[630] James Mill, born 1773, died 1836.

[631] See Vol. II, page 3, note 11.

[632] See Vol. II, page 3, note 13.

[633] See Vol. II, page 3, note 14.

[634] This anecdote is printed at page 4 (Vol. II); but as it is used in illustration here, and is given more in detail, I have not omitted it.--S.E. De M.

[635] See Vol. II, page 4, note 15.

[636] See Vol. I, page 382, note 13 {786}.

[637] "Monsieur, (a + b^{n})/n = x, whence God exists; answer that!"

[638] "Monsieur, you know very well that your argument requires the development of x according to integral powers of n."

[639] See Vol. I, page 153, note 4 {337}.

[640] Thomas Love Peacock (1785-1866) an English novelist and poet.

[641] Perhaps Dr. Samuel Warren (1807-1877), the author of _Ten Thousand a Year_ (serially in Blackwood's in 1839; London, 1841).

[642] See Vol. I, page 255, note 6 {584}.

[643] "From many, one; much in little; Ultima Thule (the most remote region); without which not."

[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the poor in the famine of 440 B. C. and was assassinated by the patricians.

[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C. Put to death in 485.

[646] "O what a fine bearing, he said, that has no brain."

[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}.

[648] William Allen Whitworth, the author of the well-known _Choice and Chance_ (Cambridge, 1867), and other works.

[649] James Maurice Wilson, whose _Elementary Geometry_ appeared in 1868 and went through several editions.

[650] See Vol. II, page 183, note 315.

[651] "Force of inertia conquered," and "Victory in the whole heavens."

[652] "With all his might."

[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic philosopher and author of the _Principles of Human Knowledge_ (1710), _The Analyst, or a Discourse addressed to an Infidel Mathematician_ (1734), and _A Defense of Freethinking in Mathematics_ (1735). He asserted that space involves the idea of movement without the sensation of resistance. Space sensation less than the "minima sensibilia" is, therefore, impossible. From this he argues that infinitesimals are impossible concepts.

[654] See Vol. I, page 85, note 2 {129}.

[655] See Vol. I, page 81, note 6 {120}.

[656] Edwin Dunkin revised Lardner's _Handbook of Astronomy_ (1869) and Milner's _The Heavens and the Earth_ (1873) and wrote _The Midnight Sky_ (1869).

[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He was an assistant to Sir Humphrey Davy (1813) and became professor of chemistry at the Royal Institution, London, in 1827.

[658] "If you teach a fool he shows no joyous countenance; he cordially hates you; he wishes you buried."

[659] "Every man is an animal, Sortes is a man, therefore Sortes is an animal."

[660]

"May some choice patron bless each grey goose quill; May every Bavius have his Bufo still."--POPE, _Prologue to the Satires._

Bavius has become proverbial as a bad poet from the lines in Vergil's _Eclogues_ (III, 90):

"Qui Bavium non odit, amet tua carmina, Maevi, Atque idem jungat vulpes, et mulgeat hircos."

"He who does not hate Bavius shall love thy verses, O Maevius; and the same shall yoke foxes and shall milk he-goats."

Bavius and Maevius were the worst of Latin poets, condemned by Horace as well as Vergil.

[661] See Vol. II, page 158, note 279.

[662] "Honest," "useful," "handsome," "sweet."

[663] "Let not the fourth man attempt to speak."

[664]

"In those old times,--ah 'Twas just like this, ah!"

[665] See Vol. I, page 382, note 12 {785}.

[666] These remarks were never written.--S. E. De M.

[667]

"Fleas, flies, and friars, are masters who sadly the people abuse, And thistles and briars are sure growing grains to abuse. O Christ, who hatest strife and slayst all things in peace, Destroy where'er are rife, briars, friars, flies and fleas. Fleas, flies, and friars foul fall them these fifteen years For none that there is loveth fleas, flies, nor freres."

[668] "It is my plan to restore to an unskilled race the worthy arts of a better life."

[669] The first sentences of the first oration of Cicero against Catiline: "Quo usque tandem abutere, Catilina, patientia nostra?" (How long, O Catiline, will you abuse our patience?) "Quamdiu etiam furor iste tuus nos eludet?" (How long will this your madness baffle us?) "Nihilne te nocturnum praesidium Palati, ... nihil horum ora voltusque moverunt?" (Does the night watch of the Palatium, ... do the faces and expressions of all these men fail to move you?) "In te conferri ..." (This plague should have been inflicted upon you long ago, which you have plotted against us so long.)

[670] "Beware of the things that are marked."

[671] "Farewell, ye teachers without learning! See to it that at our next meeting we may find you strong in body and sound in mind."

[672] See Vol. I, page 336, note 8 {713}.

[673] See Vol. I, page 229, note 2 {515}.

[674] This proof, although capable of improvement, is left as in the original. Those who may be interested in the mathematics of the question, may consult F. Enriques, _Fragen der Elementargeometrie_ (German by Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, _Archimedes_, _Huygens_, _Lambert_, _Legendre_. _Vier Abhandlungen ueber die Kreismessung_, Leipsic, 1892; F. Klein, _Famous Problems of Elementary Geometry_ (English by Beman and Smith), Boston, 1895; J. W. A. Young, _Monographs on Modern Mathematics_, New York, 1911, Chap. IX (by the editor of the present edition of De Morgan.)

[675] See Vol. I, page 69, note 2 {95}.

[676] See Vol. I, page 137, note 8 {286}.

[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith and Haughton's _Scientific Manuals_. (Euclid, 1856; Algebra, 1860; Trigonometry, 1854; Optics, 1854, and others.)

[678] This note on Carlyle (1795-1881) is interesting. The translation of Legendre appeared in the same year (1824) as his translation of Goethe's _Wilhelm Meister_.

[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and Stifelius, was an Augustine monk but became a convert to Lutheranism. He was professor of mathematics at Jena (1559-1567). His edition of the _Coss_ appeared at Koenigsberg in 1553, the first edition having been published in 1525. The + and - signs first appeared in print in Widman's arithmetic of 1489, but for purposes of algebra this book was one of the first to make them known.

[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552. _Die Coss_ appeared in 1525 and his arithmetic in 1526.

* * * * *

Corrections made to printed original.

Page 9, "long-fostered prejudice": 'perjudice' in original.

Page 73, "Pensees, ch. 7": 'Pansees' in original.

Page 127, "and pulled out a plum": 'und' in original.

Page 147, "did not come forward": 'forword' in original.

Page 172, "come into general circulation": 'circulalation' in original.

Ibid., "the more difficult fractions which we have got": 'he have got' in original.

Page 192, "it has been stated": 'started' in original.

Page 216, "the obsolete word tetch of the same meaning": 'meaing' in original.

Page 228, "[Greek: dioklasianos]": 'dioklalasianos' in original.

Page 233. After `Henry E. Manning' were printed two paragraphs `Shilling versus Franc.' and `Teutonic Long Hundred 120 versus 100 or the Decimal question.' These appear to have been set in error, there is no applicable context.

Page 316, "in a manner depending upon the difference": 'maner' in original.

Page 322, "neither what Newton did, nor what was done before him.": 'not' (for 'nor') in original.

Page 344, "Victoria toto coelo": 'tolo' in original.

Page 368, "cannot be brought up to 1": 'up to +-' in original.

Page 371, "Q_2=b_2 Q_1+a_2": 'Q_2=b_2 Q_1-a_2' in original.

Note 50, "all who were not in the road to Heaven were excommunicated": 'excomunicated' in original.

Note 372, "[Greek: he alazoneia biou]": 'alaxoneia' in original.

Ibid., "Iapetos": 'Ispetos' in original.

Ibid., "Papeiskos": 'Paspeisoks' in original.

Ibid., "[Greek: dioklasianos]": 'dioklalasianos' in original.