The Hindu-Arabic Numerals Part 9

Calandri, 59, 81 Caldwell, R., 19 Calendars, 133 Calmet, 34 Cantor, M., 5, 13, 30, 43, 84 {155} Capella, 86 Cappelli, 143 Caracteres, 87, 113, 117, 119 Cardan, 119 Carmen de Algorismo, 11, 134 Casagrandi, 132 Casiri, 8, 10 Ca.s.siodorus, 72 Cataldi, 62 Cataneo, 3 Caxton, 143, 146 Ceretti, 32 Ceylon numerals, 36 Chalfont, F. H., 28 Champenois, 60 Characters, _see_ Caracteres Charlemagne, 103 Chasles, 54, 60, 85, 116, 122, 135 Cha.s.sant, L. A., 142 Chaucer, 121 Chiarini, 145, 146 Chiffre, 58 Chinese numerals, 28, 56 Chinese zero, 56 Cifra, 120, 124 Cipher, 58 Circulus, 58, 60 Clichtoveus, 61, 119, 145 Codex Vigila.n.u.s, 138 Codrington, O., 139 Coins dated, 141 Colebrooke, 8, 26, 46, 53 Constantine, 104, 105 Cosmas, 82 Cossali, 5 Counters, 117 Courteille, 8 c.o.xe, 59 Crafte of Nombrynge, 11, 87, 149 Crusades, 109 Cunningham, A., 30, 75 Curtze, 55, 59, 126, 134 Cyfra, 55

Dagomari, 146 D'Alviella, 15 Dante, 72 Dasypodius, 33, 67, 63 Daunou, 135 Delambre, 54 Devan[=a]gar[=i], 7 Devoulx, A., 68 Dhruva, 49 Dicaearchus of Messana, 77 Digits, 119 Diodorus Siculus, 76 Du Cange, 62 Dumesnil, 36 Dutt, R. C., 12, 15, 18, 75 Dvived[=i], 44

East and West, relations, 73-81, 100-109 Egyptian numerals, 27 Eisenlohr, 28 Elia Misrachi, 57 Enchiridion Algorismi, 58 Enestrom, 5, 48, 59, 97, 125, 128 Europe, numerals in, 63, 99, 128, 136 Eusebius Caesariensis, 142 Euting, 21 Ewald, P., 116

Fazzari, 53, 54 Fibonacci, _see_ Leonardo of Pisa Figura nihili, 58 Figures, 119. _See_ numerals.

Fihrist, 67, 68, 93 Finaeus, 57 Firdus[=i], 81 Fitz Stephen, W., 109 Fleet, J. C., 19, 20, 49 {156} Florus, 80 Flugel, G., 68 Francisco de Retza, 142 Francois, 58 Friedlein, G., 84, 113, 116, 122 Froude, J. A., 129

Gandh[=a]ra, 19 Garbe, 48 Gasbarri, 58 Gautier de Coincy, 120, 124 Gemma Frisius, 2, 3, 119 Gerber, 113 Gerbert, 108, 110-120, 122 Gerhardt, C. I., 43, 56, 93, 118 Gerland, 88, 123 Gherard of Cremona, 125 Gibbon, 72 Giles, H. A., 79 Ginanni, 81 Giovanni di Danti, 58 Glarea.n.u.s, 4, 119 Gnecchi, 71, 117 [.G]ob[=a]r numerals, 65, 100, 112, 124, 138 Gow, J., 81 Grammateus, 61 Greek origin, 33 Green, J. R., 109 Greenwood, I., 62, 119 Guglielmini, 128 Gulist[=a]n, 102 Gunther, S., 131 Guyard, S., 82

[H.]abash, 9, 92 Hager, J. (G.), 28, 32 Halliwell, 59, 85 Hankel, 93 H[=a]r[=u]n al-Rash[=i]d, 97, 106 Havet, 110 Heath, T. L., 125 Hebrew numerals, 127 Hecataeus, 75 Heiberg, J. L., 55, 85, 148 Heilbronner, 5 Henry, C., 5, 31, 55, 87, 120, 135 Heriger, 122 Hermannus Contractus, 123 Herodotus, 76, 78 Heyd, 75 Higden, 136 Hill, G. F., 52, 139, 142 Hillebrandt, A., 15, 74 Hilprecht, H. V., 28 Hindu forms, early, 12 Hindu number names, 42 Hodder, 62 h.o.e.rnle, 43, 49 Holywood, _see_ Sacrobosco Hopkins, E. W., 12 Horace, 79, 80 [H.]osein ibn Mo[h.]ammed al-Ma[h.]all[=i], 6 Hostus, M., 56 Howard, H. H., 29 Hraba.n.u.s Maurus, 72 Huart, 7 Huet, 33 Hugo, H., 57 Humboldt, A. von, 62 Huswirt, 58

Iamblichus, 81 Ibn Ab[=i] Ya'q[=u]b, 9 Ibn al-Adam[=i], 92 Ibn al-Bann[=a], 93 Ibn Khord[=a][d.]beh, 101, 106 Ibn Wahab, 103 India, history of, 14 writing in, 18 Indicopleustes, 83 Indo-Bactrian numerals, 19 {157} Indr[=a]j[=i], 23 Is[h.][=a]q ibn Y[=u]suf al-[S.]ardaf[=i], 93

Jacob of Florence, 57 Jacquet, E., 38 Jamshid, 56 Jehan Certain, 59 Jetons, 58, 117 Jevons, F. B., 76 Johannes Hispalensis, 48, 88, 124 John of Halifax, _see_ Sacrobosco John of Luna, _see_ Johannes Hispalensis Jordan, L., 58, 124 Joseph Ispa.n.u.s (Joseph Sapiens), 115 Justinian, 104

Kale, M. R., 26 Karabacek, 56 Karpinski, L. C., 126, 134, 138 K[=a]ty[=a]yana, 39 Kaye, C. R., 6, 16, 43, 46, 121 Keane, J., 75, 82 Keene, H. G., 15 Kern, 44 Kharo[s.][t.]h[=i], 19, 20 Khosr[=u], 82, 91 Kielhorn, F., 46, 47 Kircher, A., 34 Kit[=a]b al-Fihrist, _see_ Fihrist Kleinwachter, 32 K[=l]os, 62 Kobel, 4, 58, 60, 119, 123 Krumbacher, K., 57 Kuckuck, 62, 133 Kugler, F. X., 51

Lachmann, 85 Lacouperie, 33, 35 Lalitavistara, 15, 17 Lami, G., 57 La Roche, 61 La.s.sen, 39 L[=a][t.]y[=a]yana, 39 Leboeuf, 135 Leonardo of Pisa, 5, 10, 57, 64, 74, 120, 128-133 Lethaby, W. R., 142 Levi, B., 13 Levias, 3 Libri, 73, 85, 95 Light of Asia, 16 Luca da Firenze, 144 Lucas, 128

Mah[=a]bh[=a]rata, 18 Mah[=a]v[=i]r[=a]c[=a]rya, 53 Malabar numerals, 36 Malayalam numerals, 36 Mannert, 81 Margarita Philosophica, 146 Marie, 78 Marquardt, J., 85 Marshman, J. C., 17 Martin, T. H., 30, 62, 85, 113 Martines, D. C., 58 M[=a]sh[=a]ll[=a]h, 3 Maspero, 28 Mauch, 142 Maximus Planudes, 2, 57, 66, 93, 120 Megasthenes, 77 Merchants, 114 Meynard, 8 Migne, 87 Mikami, Y., 56 Milanesi, 128 Mo[h.]ammed ibn 'Abdall[=a]h, 92 Mo[h.]ammed ibn A[h.]med, 6 Mo[h.]ammed ibn 'Al[=i] 'Abd[=i], 8 Mo[h.]ammed ibn M[=u]s[=a], _see_ Al-Khow[=a]razm[=i]

Molinier, 123 Monier-Williams, 17 {158} Morley, D., 126 Moroccan numerals, 68, 119 Mortet, V., 11 Moseley, C. B., 33 Mo[t.]ahhar ibn [T.][=a]hir, 7 Mueller, A., 68 Mumford, J. K., 109 Muwaffaq al-D[=i]n, 93

Nabatean forms, 21 Nallino, 4, 54, 55 Nagl, A., 55, 110, 113, 126 N[=a]n[=a] Gh[=a]t inscriptions, 20, 22, 23, 40 Narducci, 123 Nasik cave inscriptions, 24 Na[z.][=i]f ibn Yumn, 94 Neander, A., 75 Neophytos, 57, 62 Neo-Pythagoreans, 64 Nesselmann, 58 Newman, Cardinal, 96 Newman, F. W., 131 Noldeke, Th., 91 Notation, 61 Note, 61, 119 Noviomagus, 45, 61, 119, 150 Null, 61 Numerals, Algerian, 68 astrological, 150 Br[=a]hm[=i], 19-22, 83 early ideas of origin, 1 Hindu, 26 Hindu, cla.s.sified, 19, 38 Kharo[s.][t.]h[=i], 19-22 Moroccan, 68 Nabatean, 21 origin, 27, 30, 31, 37 supposed Arabic origin, 2 supposed Babylonian origin, 28 supposed Chaldean and Jewish origin, 3 supposed Chinese origin, 28, 32 supposed Egyptian origin, 27, 30, 69, 70 supposed Greek origin, 33 supposed Phoenician origin, 32 tables of, 22-27, 36, 48, 49, 69, 88, 140, 143, 145-148

O'Creat, 5, 55, 119, 120 Olleris, 110, 113 Oppert, G., 14, 75

Pali, 22 Pancasiddh[=a]ntik[=a], 44 Paravey, 32, 57 P[=a]tal[=i]pu[t.]ra, 77 Patna, 77 Patrick, R., 119 Payne, E. J., 106 Pegolotti, 107 Peletier, 2, 62 Perrot, 80 Persia, 66, 91, 107 Pertz, 115 Petrus de Dacia, 59, 61, 62 Pez, P. B., 117 "Philalethes," 75 Phillips, G., 107 Picavet, 105 Pichler, F., 141 Pihan, A. P., 36 Pisa, 128 Place value, 26, 42, 46, 48 Planudes, _see_ Maximus Planudes Plimpton, G. A., 56, 59, 85, 143, 144, 145, 148 Pliny, 76 Polo, N. and M., 107 {159} Prandel, J. G., 54 Prinsep, J., 20, 31 Propertius, 80 Prosdocimo de' Beldomandi, 137 Prou, 143 Ptolemy, 54, 78 Putnam, 103 Pythagoras, 63 Pythagorean numbers, 13 Pytheas of Ma.s.silia, 76

Rabbi ben Ezra, 60, 127 Radulph of Laon, 60, 113, 118, 124 Raets, 62 Rainer, _see_ Gemma Frisius R[=a]m[=a]yana, 18 Ramus, 2, 41, 60, 61 Raoul Glaber, 123 Rapson, 77 Rauhfuss, _see_ Dasypodius Raumer, K. von, 111 Reclus, E., 14, 96, 130 Recorde, 3, 58 Reinaud, 67, 74, 80 Reveillaud, 36 Richer, 110, 112, 115 Riese, A., 119 Robertson, 81 Robertus Cestrensis, 97, 126 Rodet, 5, 44 Roediger, J., 68 Rollandus, 144 Romagnosi, 81 Rosen, F., 5 Rotula, 60 Rudolff, 85 Rudolph, 62, 67 Ruffi, 150

Sachau, 6 Sacrobosco, 3, 58, 133 Sacy, S. de, 66, 70 Sa'd[=i], 102 ['S]aka inscriptions, 20 Sam[=u]'[=i]l ibn Ya[h.]y[=a], 93 ['S][=a]rad[=a] characters, 55 Savonne, 60 Scaliger, J. C., 73 Scheubel, 62 Schlegel, 12 Schmidt, 133 Schonerus, 87, 119 Schroeder, L. von, 13 Scylax, 75 Sedillot, 8, 34 Senart, 20, 24, 25 Sened ibn 'Al[=i], 10, 98 Sfortunati, 62, 150 Sh.e.l.ley, W., 126 Siamese numerals, 36 Siddh[=a]nta, 8, 18 [S.]ifr, 57 Sigsboto, 55 Sih[=a]b al-D[=i]n, 67 Silberberg, 60 Simon, 13 Sin[=a]n ibn al-Fat[h.], 93 Sindbad, 100 Sindhind, 97 Sipos, 60 Sirr, H. C., 75 Skeel, C. A., 74 Smith, D. E., 11, 17, 53, 86, 141, 143 Smith, V. A., 20, 35, 46, 47 Smith, Wm., 75 Sm[r.]ti, 17 Spain, 64, 65, 100 Spitta-Bey, 5 Sprenger, 94 ['S]rautas[=u]tra, 39 Steffens, F., 116 Steinschneider, 5, 57, 65, 66, 98, 126 Stifel, 62 {160} Subandhus, 44 Suetonius, 80 Suleim[=a]n, 100 ['S][=u]nya, 43, 53, 57 Suter, 5, 9, 68, 69, 93, 116, 131 S[=u]tras, 13 Sykes, P. M., 75 Sylvester II, _see_ Gerbert Symonds, J. A., 129

Tannery, P., 62, 84, 85 Tartaglia, 4, 61 Taylor, I., 19, 30 Teca, 55, 61 Tennent, J. E., 75 Texada, 60 Theca, 58, 61 Theophanes, 64 Thibaut, G., 12, 13, 16, 44, 47 Tibetan numerals, 36 Timotheus, 103 Tonstall, C., 3, 61 Trenchant, 60 Treutlein, 5, 63, 123 Trevisa, 136 Treviso arithmetic, 145 Trivium and quadrivium, 73 Tsin, 56 Tunis, 65 Turchill, 88, 118, 123 Turnour, G., 75 Tziphra, 57, 62 [Greek: tziphra], 55, 57, 62 Tzwivel, 61, 118, 145

Ujjain, 32 Unger, 133 Upanishads, 12 Usk, 121

Valla, G., 61 Van der Schuere, 62 Var[=a]ha-Mihira, 39, 44, 78 V[=a]savadatt[=a], 44 Vaux, Carra de, 9, 74 Vaux, W. S. W., 91 Ved[=a][.n]gas, 17 Vedas, 12, 15, 17 Vergil, 80 Vincent, A. J. H., 57 Vogt, 13 Voizot, P., 36 Vossius, 4, 76, 81, 84

Wallis, 3, 62, 84, 116 Wappler, E., 54, 126 Waschke, H., 2, 93 Wattenbach, 143 Weber, A., 31 Weidler, I. F., 34, 66 Weidler, I. F. and G. I., 63, 66 Weissenborn, 85, 110 Wertheim, G., 57, 61 Whitney, W. D., 13 Wilford, F., 75 Wilkens, 62 Wilkinson, J. G., 70 Willichius, 3 Woepcke, 3, 6, 42, 63, 64, 65, 67, 69, 70, 94, 113, 138 Wolack, G., 54 Woodruff, C. E., 32 Word and letter numerals, 38, 44 Wustenfeld, 74

Yule, H., 107

Zephirum, 57, 58 Zephyr, 59 Zepiro, 58 Zero, 26, 38, 40, 43, 45, 49, 51-62, 67 Zeuero, 58

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