The Hindu-Arabic Numerals c13: Index

The Hindu-Arabic Numerals c13

Language: English

Index

c13.1

Abbo of Fleury, 122 'Abdallāh ibn al-Ḥasan, 92 'Abdallatīf ibn Yūsuf, 93 'Abdalqādir ibn 'Alī al-Sakhāwī, 6 Abenragel, 34 Abraham ibn Meïr ibn Ezra, *see* Rabbi ben Ezra Abū 'Alī al-Ḥosein ibn Sīnā, 74 Abū 'l-Ḥasan, 93, 100 Abū 'l-Qāsim, 92 Abū 'l-Ṭeiyib, 97 Abū Naṣr, 92 Abū Roshd, 113 Abu Sahl Dunash ibn Tamim, 65, 67 Adelhard of Bath, 5, 55, 97, 119, 123, 126 Adhemar of Chabanois, 111 Aḥmed al-Nasawī, 98 Aḥmed ibn 'Abdallāh, 9, 92 Aḥmed ibn Moḥammed, 94 Aḥmed ibn 'Omar, 93 Akṣaras, 32 Alanus ab Insulis, 124 Al-Baġdādī, 93 Al-Battānī, 54 Albelda (Albaida) MS., 116 Albert, J., 62 Albert of York, 103 Al-Bīrūnī, 6, 41, 49, 65, 92, 93 Alcuin, 103 Alexander the Great, 76 Alexander de Villa Dei, 11, 133 Alexandria, 64, 82 Al-Fazārī, 92 Alfred, 103 Algebra, etymology, 5 Algerian numerals, 68 Algorism, 97 Algorismus, 124, 126, 135 Algorismus cifra, 120 Al-Ḥaṣṣār, 65 'Alī ibn Abī Bekr, 6 'Alī ibn Aḥmed, 93, 98 Al-Karābīsī, 93 Al-Khowārazmī, 4, 9, 10, 92, 97, 98, 125, 126 Al-Kindī, 10, 92 Almagest, 54 Al-Maġrebī, 93 Al-Maḥallī, 6 Al-Māmūn, 10, 97 Al-Manṣūr, 96, 97 Al-Mas'ūdī, 7, 92 Al-Nadīm, 9 Al-Nasawī, 93, 98 Alphabetic numerals, 39, 40, 43 Al-Qāsim, 92 Al-Qass, 94 Al-Sakhāwī, 6 Al-Ṣardafī, 93 Al-Sijzī, 94 Al-Sūfī, 10, 92 Ambrosoli, 118 Aṅkapalli, 43 Apices, 87, 117, 118 Arabs, 91-98 Arbuthnot, 141

c13.2

Archimedes, 15, 16 Arcus Pictagore, 122 Arjuna, 15 Arnold, E., 15, 102 Ars memorandi, 141 Āryabhaṭa, 39, 43, 44 Aryan numerals, 19 Aschbach, 134 Ashmole, 134 Aśoka, 19, 20, 22, 81 Aṣ-ṣifr, 57, 58 Astrological numerals, 150 Atharva-Veda, 48, 50, 55 Augustus, 80 Averroës, 113 Avicenna, 58, 74, 113

c13.3

Babylonian numerals, 28 Babylonian zero, 51 Bacon, R., 131 Bactrian numerals, 19, 30 Bæda, 2, 72 Bagdad, 4, 96 Bakhṣālī manuscript, 43, 49, 52, 53 Ball, C. J., 35 Ball, W. W. R., 36, 131 Bāṇa, 44 Barth, A., 39 Bayang inscriptions, 39 Bayer, 33 Bayley, E. C., 19, 23, 30, 32, 52, 89 Beazley, 75 Bede, *see* Bæda Beldomandi, 137 Beloch, J., 77 Bendall, 25, 52 Benfey, T., 26 Bernelinus, 88, 112, 117, 121 Besagne, 128 Besant, W., 109 Bettino, 36 Bhandarkar, 18, 47, 50

c13.4

Bhāskara, 53, 55 Biernatzki, 32 Biot, 32 Björnbo, A. A., 125, 126 Blassière, 119 Bloomfield, 48 Blume, 85 Boeckh, 62 Boehmer, 143 Boeschenstein, 119 Boethius, 63, 70–73, 83–90 Boissière, 63 Bombelli, 81 Bonaini, 128 Boncompagni, 5, 6, 10, 48, 50, 123, 125 Borghi, 59 Borgo, 119 Bougie, 130 Bowring, J., 56 Brahmagupta, 52 Brāhmaṇas, 12, 13 Brāhmī, 19, 20, 31, 83 Brandis, J., 54 Bṛhat-Saṃhitā, 39, 44, 78 Brockhaus, 43 Bubnov, 65, 84, 110, 116 Buddha, education of, 15, 16 Büdinger, 110 Bugia, 130 Bühler, G., 15, 19, 22, 31, 44, 50 Burgess, 25 Bürk, 13 Burmese numerals, 36 Burnell, A. C., 18, 40 Buteo, 61

c13.5

Calandri, 59, 81 Caldwell, R., 19 Calendars, 133 Calmet, 34 Cantor, M., 5, 13, 30, 43, 84

c13.6

Capella, 86 Cappelli, 143 Caracteres, 87, 113, 117, 119 Cardan, 119 Carmen de Algorismo, 11, 134 Casagrandi, 132 Casiri, 8, 10 Cassiodorus, 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 Chassant, 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 Vigilanus, 138 Codrington, O., 139 Coins dated, 141 Colebrooke, 8, 26, 46, 53 Constantine, 104, 105 Cosmas, 82 Cossali, 5 Counters, 117 Courteille, 8 Coxe, 59 Crafte of Nombrynge, 11, 87, 149 Crusades, 109 Cunningham, A., 30, 75

c13.7

Curtze, 55, 59, 126, 134 Cyfra, 55

c13.8

Dagomari, 146 D'Alviella, 15 Dante, 72 Dasypodius, 33, 57, 63 Daunou, 135 Delambre, 54 Devanāgarī, 7 Devoulx, A., 68 Dhruva, 49, 50 Dicæarchus of Messana, 77 Digits, 119 Diodorus Siculus, 76 Du Cange, 62 Dumesnil, 36 Dutt, R. C., 12, 15, 18, 75 Dvivedī, 44

c13.9

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

c13.10

Fazzari, 53, 54 Fibonacci, *see* Leonardo of Pisa Figura nihili, 58 Figures, 119. *See* numerals. Fihrist, 67, 68, 93 Finaeus, 57 Firdusī, 81 Fitz Stephen, W., 109 Fleet, J. C., 19, 20, 50

c13.11

Florus, 80 Flügel, G., 68 Francisco de Retza, 142 François, 58 Friedlein, G., 84, 113, 116, 122 Froude, J. A., 129

c13.12

Gandhāra, 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 Glareanus, 4, 119 Gnecchi, 71, 117 Ġobār numerals, 65, 100, 112, 124, 138 Gow, J., 81 Grammateus, 61 Greek origin, 33 Green, J. R., 109 Greenwood, I., 62, 119 Guglielmini, 128 Gulistān, 102 Günther, S., 131 Guyard, S., 82

c13.13

Ḥabash, 9, 92 Hager, J. (G.), 28, 32 Halliwell, 59, 85 Hankel, 93 Hārūn al-Rashīd, 97, 106 Havet, 110 Heath, T. L., 125 Hebrew numerals, 127 Hecatæus, 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 Hoernle, 43, 49 Holywood, see Sacrobosco Hopkins, E. W., 12 Horace, 79, 80 Ḥosein ibn Moḥammed al-Maḥallī, 6 Hostus, M., 56 Howard, H. H., 29 Hrabanus Maurus, 72 Huart, 7 Huet, 33 Hugo, H., 57 Humboldt, A. von, 62 Huswirt, 58

c13.14

Iamblichus, 81 Ibn Abī Ya‘qūb, 9 Ibn al-Adamī, 92 Ibn al-Bannā, 93 Ibn Khordāḍbeh, 101, 106 Ibn Wahab, 103 India, history of, 14 writing in, 18 Indicopleustes, 83 Indo-Bactrian numerals, 19

c13.15

Indrājī, 23 Isḥāq ibn Yūsuf al-Ṣardafī, 93

c13.16

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 Ispanus (Joseph Sapiens), 115 Justinian, 104

c13.17

Kále, M. R., 26 Karabacek, 56 Karpinski, L. C., 126, 134, 138 Kātyāyana, 39 Kaye, C. R., 6, 16, 43, 46, 121 Keane, J., 75, 82 Keene, H. G., 15 Kern, 44 Kharoṣṭhī, 19, 20 Khosrū, 82, 91 Kielhorn, F., 46, 47 Kircher, A., 34 Kitāb al-Fihrist, *see* Fihrist Kleinwächter, 32 Klos, 62 Köbel, 4, 58, 60, 119, 123 Krumbacher, K., 57 Kuckuck, 62, 133 Kugler, F. X., 51

c13.18

Lachmann, 85 Lacouperie, 33, 35 Lalitavistara, 15, 17 Lami, G., 57

c13.19

La Roche, 61 Lassen, 39 Lāṭyāyana, 39 Lebœuf, 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

c13.20

Mahābhārata, 18 Mahāvīrācārya, 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 Māshāllāh, 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 Moḥammed ibn ʿAbdallāh, 92 Moḥammed ibn Aḥmed, 6 Moḥammed ibn ʿAlī ʿAbdī, 8 Moḥammed ibn Mūsā, *see* Al-Khowārazmī Molinier, 123 Monier-Williams, 17

c13.21

Morley, D., 126 Moroccan numerals, 68, 119 Mortet, V., 11 Moseley, C. B., 33 Moṭahhar ibn Ṭāhir, 7 Mueller, A., 68 Mumford, J. K., 109 Muwaffaq al-Dīn, 93

c13.22

Nabatean forms, 21 Nallino, 4, 54, 55 Nagl, A., 55, 110, 113, 126 Nānā Ghāt inscriptions, 20, 22, 23, 40 Narducci, 123 Nasik cave inscriptions, 24 Naẓīf ibn Yumn, 94 Neander, A., 75 Neophytos, 57, 62 Neo-Pythagoreans, 64 Nesselmann, 53 Newman, Cardinal, 96 Newman, F. W., 131 Nöldeke, Th., 91 Notation, 61 Note, 61, 119 Noviomagus, 45, 61, 119, 150 Null, 61 Numerals, algerian, 68 astrological, 150 Brāhmī, 19–22, 83 early ideas of origin, 1 Hindu, 26 Hindu, classified, 19, 38 Kharoṣṭhī, 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 Phœnician origin, 32 tables of, 22–27, 36, 48, 50, 69, 88, 140, 143, 145–148

c13.23

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

c13.24

Pali, 22 Pañcasiddhāntikā, 44 Paravey, 32, 57 Pātalīputra, 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

c13.25

Prändel, 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 Massilia, 76

c13.26

Rabbi ben Ezra, 60, 127 Radulph of Laon, 60, 113, 118, 124 Raets, 62 Rainer, *see* Gemma Frisius Rāmāyana, 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

c13.27

Sachau, 6 Sacrobosco, 3, 58, 133 Sacy, S. de, 66, 70 Sa'dī, 102 Śaka inscriptions, 20 Samū'il ibn Yaḥyā, 93 Śāradā 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 'Alī, 10, 98 Sfortunati, 62, 150 Shelley, W., 126 Siamese numerals, 36 Siddhānta, 8, 18 Ṣifr, 57 Sigsboto, 55 Sihāb al-Dīn, 67 Silberberg, 60 Simon, 13 Sinān ibn al-Fatḥ, 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 Smṛti, 17 Spain, 64, 65, 100 Spitta-Bey, 5 Sprenger, 94 Śrautasūtra, 39 Steffens, F., 116 Steinschneider, 5, 57, 65, 66, 98, 126 Stifel, 62

c13.28

Subandhus, 44 Suetonius, 80 Suleimān, 100 Śūnya, 43, 53, 57 Suter, 5, 9, 68, 69, 93, 116, 131 Sūtras, 13 Sykes, P. M., 75 Sylvester II, *see* Gerbert Symonds, J. A., 129

c13.29

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 τζίφρα, 55, 57, 62 Tzwivel, 61, 118, 145

c13.30

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

c13.31

Valla, G., 61 Van der Schuere, 62 Varāha-Mihira, 39, 44, 78 Vāsavadattā, 44 Vaux, Carra de, 9, 74 Vaux, W. S. W., 91 Vedāṅgas, 17 Vedas, 12, 15, 17 Vergil, 80 Vincent, A. J. H., 57 Vogt, 13 Voizot, P., 36 Vossius, 4, 76, 81, 84

c13.32

Wallis, 3, 62, 84, 116 Wappler, E., 54, 126 Wäschke, 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 Wüstenfeld, 74

c13.33

Yule, H., 107

c13.34

Zephirum, 57, 58 Zephyr, 59 Zepiro, 58 Zero, 26, 38, 40, 43, 45, 50, 51–62, 67 Zeuero, 58

c13.35

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