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

[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).