Chapter 7

Ḥabash,9,92Hager, J. (G.),28,32Halliwell,59,85Hankel,93Hārūn al-Rashīd,97,106Havet,110Heath, T. L.,125Hebrew numerals,127Hecatæus,75Heiberg, J. L.,55,85,148Heilbronner,5Henry, C.,5,31,55,87,120,135Heriger,122Hermannus Contractus,123Herodotus,76,78Heyd,75Higden,136Hill, G. F.,52,139,142Hillebrandt, A.,15,74Hilprecht, H. V.,28Hindu forms, early,12Hindu number names,42Hodder,62Hoernle,43,49Holywood,seeSacroboscoHopkins, E. W.,12Horace,79,80Ḥosein ibn Moḥammed al-Maḥallī,6Hostus, M.,56Howard, H. H.,29Hrabanus Maurus,72Huart,7Huet,33Hugo, H.,57Humboldt, A. von,62Huswirt,58Iamblichus,81Ibn Abī Ya‛qūb,9Ibn al-Adamī,92Ibn al-Bannā,93Ibn Khordāḍbeh,101,106Ibn Wahab,103India, history of,14writing in,18Indicopleustes,83Indo-Bactrian numerals,19Indrājī,23Isḥāq ibn Yūsuf al-Ṣardafī,93Jacob of Florence,57Jacquet, E.,38Jamshid,56Jehan Certain,59Jetons,58,117Jevons, F. B.,76Johannes Hispalensis,48,88,124John of Halifax,seeSacroboscoJohn of Luna,seeJohannes HispalensisJordan, L.,58,124Joseph Ispanus (Joseph Sapiens),115Justinian,104Kále, M. R.,26Karabacek,56Karpinski, L. C.,126,134,138Kātyāyana,39Kaye, C. R.,6,16,43,46,121Keane, J.,75,82Keene, H. G.,15Kern,44Kharoṣṭhī,19,20Khosrū,82,91Kielhorn, F.,46,47Kircher, A.,34Kitāb al-Fihrist,seeFihristKleinwächter,32Klos,62Köbel,4,58,60,119,123Krumbacher, K.,57Kuckuck,62,133Kugler, F. X.,51Lachmann,85Lacouperie,33,35Lalitavistara,15,17Lami, G.,57La Roche,61Lassen,39Lāṭyāyana,39Lebœuf,135Leonardo of Pisa,5,10,57,64,74,120,128-133Lethaby, W. R.,142Levi, B.,13Levias,3Libri,73,85,95Light of Asia,16Luca da Firenze,144Lucas,128Mahābhārata,18Mahāvīrācārya,53Malabar numerals,36Malayalam numerals,36Mannert,81Margarita Philosophica,146Marie,78Marquardt, J.,85Marshman, J. C.,17Martin, T. H.,30,62,85,113Martines, D. C.,58Māshāllāh,3Maspero,28Mauch,142Maximus Planudes,2,57,66,93,120Megasthenes,77Merchants,114Meynard,8Migne,87Mikami, Y.,56Milanesi,128Moḥammed ibn ‛Abdallāh,92Moḥammed ibn Aḥmed,6Moḥammed ibn ‛Alī ‛Abdī,8Moḥammed ibn Mūsā,seeAl-KhowārazmīMolinier,123Monier-Williams,17Morley, D.,126Moroccan numerals,68,119Mortet, V.,11Moseley, C. B.,33Moṭahhar ibn Ṭāhir,7Mueller, A.,68Mumford, J. K.,109Muwaffaq al-Dīn,93Nabatean forms,21Nallino,4,54,55Nagl, A.,55,110,113,126Nānā Ghāt inscriptions,20,22,23,40Narducci,123Nasik cave inscriptions,24Naẓīf ibn Yumn,94Neander, A.,75Neophytos,57,62Neo-Pythagoreans,64Nesselmann,58Newman, Cardinal,96Newman, F. W.,131Nöldeke, Th.,91Notation,61Note,61,119Noviomagus,45,61,119,150Null,61Numerals,Algerian,68astrological,150Brāhmī,19-22,83early ideas of origin,1Hindu,26Hindu, classified,19,38Kharoṣṭhī,19-22Moroccan,68Nabatean,21origin,27,30,31,37supposed Arabic origin,2supposed Babylonian origin,28supposed Chaldean and Jewish origin,3supposed Chinese origin,28,32supposed Egyptian origin,27,30,69,70supposed Greek origin,33supposed Phœnician origin,32tables of,22-27,36,48,49,69,88,140,143,145-148O'Creat,5,55,119,120Olleris,110,113Oppert, G.,14,75Pali,22Pañcasiddhāntikā,44Paravey,32,57Pātalīpuṭra,77Patna,77Patrick, R.,119Payne, E. J.,106Pegolotti,107Peletier,2,62Perrot,80Persia,66,91,107Pertz,115Petrus de Dacia,59,61,62Pez, P. B.,117"Philalethes,"75Phillips, G.,107Picavet,105Pichler, F.,141Pihan, A. P.,36Pisa,128Place value,26,42,46,48Planudes,seeMaximus PlanudesPlimpton, G. A.,56,59,85,143,144,145,148Pliny,76Polo, N. and M.,107Prändel, J. G.,54Prinsep, J.,20,31Propertius,80Prosdocimo de' Beldomandi,137Prou,143Ptolemy,54,78Putnam,103Pythagoras,63Pythagorean numbers,13Pytheas of Massilia,76Rabbi ben Ezra,60,127Radulph of Laon,60,113,118,124Raets,62Rainer,seeGemma FrisiusRāmāyana,18Ramus,2,41,60,61Raoul Glaber,123Rapson,77Rauhfuss,seeDasypodiusRaumer, K. von,111Reclus, E.,14,96,130Recorde,3,58Reinaud,67,74,80Reveillaud,36Richer,110,112,115Riese, A.,119Robertson,81Robertus Cestrensis,97,126Rodet,5,44Roediger, J.,68Rollandus,144Romagnosi,81Rosen, F.,5Rotula,60Rudolff,85Rudolph,62,67Ruffi,150Sachau,6Sacrobosco,3,58,133Sacy, S. de,66,70Sa‛dī,102Śaka inscriptions,20Samū'īl ibn Yaḥyā,93Śāradā characters,55Savonne,60Scaliger, J. C.,73Scheubel,62Schlegel,12Schmidt,133Schonerus,87,119Schroeder, L. von,13Scylax,75Sedillot,8,34Senart,20,24,25Sened ibn ‛Alī,10,98Sfortunati,62,150Shelley, W.,126Siamese numerals,36Siddhānta,8,18Ṣifr,57Sigsboto,55Sihāb al-Dīn,67Silberberg,60Simon,13Sinān ibn al-Fatḥ,93Sindbad,100Sindhind,97Sipos,60Sirr, H. C.,75Skeel, C. A.,74Smith, D. E.,11,17,53,86,141,143Smith, V. A.,20,35,46,47Smith, Wm.,75Smṛti,17Spain,64,65,100Spitta-Bey,5Sprenger,94Śrautasūtra,39Steffens, F.,116Steinschneider,5,57,65,66,98,126Stifel,62Subandhus,44Suetonius,80Suleimān,100Śūnya,43,53,57Suter,5,9,68,69,93,116,131Sūtras,13Sykes, P. M.,75Sylvester II,seeGerbertSymonds, J. A.,129

Ḥabash,9,92Hager, J. (G.),28,32Halliwell,59,85Hankel,93Hārūn al-Rashīd,97,106Havet,110Heath, T. L.,125Hebrew numerals,127Hecatæus,75Heiberg, J. L.,55,85,148Heilbronner,5Henry, C.,5,31,55,87,120,135Heriger,122Hermannus Contractus,123Herodotus,76,78Heyd,75Higden,136Hill, G. F.,52,139,142Hillebrandt, A.,15,74Hilprecht, H. V.,28Hindu forms, early,12Hindu number names,42Hodder,62Hoernle,43,49Holywood,seeSacroboscoHopkins, E. W.,12Horace,79,80Ḥosein ibn Moḥammed al-Maḥallī,6Hostus, M.,56Howard, H. H.,29Hrabanus Maurus,72Huart,7Huet,33Hugo, H.,57Humboldt, A. von,62Huswirt,58

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,seeSacrobosco

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

Iamblichus,81Ibn Abī Ya‛qūb,9Ibn al-Adamī,92Ibn al-Bannā,93Ibn Khordāḍbeh,101,106Ibn Wahab,103India, history of,14writing in,18Indicopleustes,83Indo-Bactrian numerals,19Indrājī,23Isḥāq ibn Yūsuf al-Ṣardafī,93

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

Indrājī,23

Isḥāq ibn Yūsuf al-Ṣardafī,93

Jacob of Florence,57Jacquet, E.,38Jamshid,56Jehan Certain,59Jetons,58,117Jevons, F. B.,76Johannes Hispalensis,48,88,124John of Halifax,seeSacroboscoJohn of Luna,seeJohannes HispalensisJordan, L.,58,124Joseph Ispanus (Joseph Sapiens),115Justinian,104

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,seeSacrobosco

John of Luna,seeJohannes Hispalensis

Jordan, L.,58,124

Joseph Ispanus (Joseph Sapiens),115

Justinian,104

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

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,seeFihrist

Kleinwächter,32

Klos,62

Köbel,4,58,60,119,123

Krumbacher, K.,57

Kuckuck,62,133

Kugler, F. X.,51

Lachmann,85Lacouperie,33,35Lalitavistara,15,17Lami, G.,57La Roche,61Lassen,39Lāṭyāyana,39Lebœuf,135Leonardo of Pisa,5,10,57,64,74,120,128-133Lethaby, W. R.,142Levi, B.,13Levias,3Libri,73,85,95Light of Asia,16Luca da Firenze,144Lucas,128

Lachmann,85

Lacouperie,33,35

Lalitavistara,15,17

Lami, G.,57

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

Mahābhārata,18Mahāvīrācārya,53Malabar numerals,36Malayalam numerals,36Mannert,81Margarita Philosophica,146Marie,78Marquardt, J.,85Marshman, J. C.,17Martin, T. H.,30,62,85,113Martines, D. C.,58Māshāllāh,3Maspero,28Mauch,142Maximus Planudes,2,57,66,93,120Megasthenes,77Merchants,114Meynard,8Migne,87Mikami, Y.,56Milanesi,128Moḥammed ibn ‛Abdallāh,92Moḥammed ibn Aḥmed,6Moḥammed ibn ‛Alī ‛Abdī,8Moḥammed ibn Mūsā,seeAl-KhowārazmīMolinier,123Monier-Williams,17Morley, D.,126Moroccan numerals,68,119Mortet, V.,11Moseley, C. B.,33Moṭahhar ibn Ṭāhir,7Mueller, A.,68Mumford, J. K.,109Muwaffaq al-Dīn,93

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 ‛Abdallāh,92

Moḥammed ibn Aḥmed,6

Moḥammed ibn ‛Alī ‛Abdī,8

Moḥammed ibn Mūsā,seeAl-Khowārazmī

Molinier,123

Monier-Williams,17

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

Nabatean forms,21Nallino,4,54,55Nagl, A.,55,110,113,126Nānā Ghāt inscriptions,20,22,23,40Narducci,123Nasik cave inscriptions,24Naẓīf ibn Yumn,94Neander, A.,75Neophytos,57,62Neo-Pythagoreans,64Nesselmann,58Newman, Cardinal,96Newman, F. W.,131Nöldeke, Th.,91Notation,61Note,61,119Noviomagus,45,61,119,150Null,61Numerals,Algerian,68astrological,150Brāhmī,19-22,83early ideas of origin,1Hindu,26Hindu, classified,19,38Kharoṣṭhī,19-22Moroccan,68Nabatean,21origin,27,30,31,37supposed Arabic origin,2supposed Babylonian origin,28supposed Chaldean and Jewish origin,3supposed Chinese origin,28,32supposed Egyptian origin,27,30,69,70supposed Greek origin,33supposed Phœnician origin,32tables of,22-27,36,48,49,69,88,140,143,145-148

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,58

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,22-27,36,48,49,69,88,140,143,145-148

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

O'Creat,5,55,119,120

Olleris,110,113

Oppert, G.,14,75

Pali,22Pañcasiddhāntikā,44Paravey,32,57Pātalīpuṭra,77Patna,77Patrick, R.,119Payne, E. J.,106Pegolotti,107Peletier,2,62Perrot,80Persia,66,91,107Pertz,115Petrus de Dacia,59,61,62Pez, P. B.,117"Philalethes,"75Phillips, G.,107Picavet,105Pichler, F.,141Pihan, A. P.,36Pisa,128Place value,26,42,46,48Planudes,seeMaximus PlanudesPlimpton, G. A.,56,59,85,143,144,145,148Pliny,76Polo, N. and M.,107Prändel, J. G.,54Prinsep, J.,20,31Propertius,80Prosdocimo de' Beldomandi,137Prou,143Ptolemy,54,78Putnam,103Pythagoras,63Pythagorean numbers,13Pytheas of Massilia,76

Pali,22

Pañcasiddhāntikā,44

Paravey,32,57

Pātalīpuṭra,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,seeMaximus Planudes

Plimpton, G. A.,56,59,85,143,144,145,148

Pliny,76

Polo, N. and M.,107

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

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

Rabbi ben Ezra,60,127

Radulph of Laon,60,113,118,124

Raets,62

Rainer,seeGemma Frisius

Rāmāyana,18

Ramus,2,41,60,61

Raoul Glaber,123

Rapson,77

Rauhfuss,seeDasypodius

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,6Sacrobosco,3,58,133Sacy, S. de,66,70Sa‛dī,102Śaka inscriptions,20Samū'īl ibn Yaḥyā,93Śāradā characters,55Savonne,60Scaliger, J. C.,73Scheubel,62Schlegel,12Schmidt,133Schonerus,87,119Schroeder, L. von,13Scylax,75Sedillot,8,34Senart,20,24,25Sened ibn ‛Alī,10,98Sfortunati,62,150Shelley, W.,126Siamese numerals,36Siddhānta,8,18Ṣifr,57Sigsboto,55Sihāb al-Dīn,67Silberberg,60Simon,13Sinān ibn al-Fatḥ,93Sindbad,100Sindhind,97Sipos,60Sirr, H. C.,75Skeel, C. A.,74Smith, D. E.,11,17,53,86,141,143Smith, V. A.,20,35,46,47Smith, Wm.,75Smṛti,17Spain,64,65,100Spitta-Bey,5Sprenger,94Śrautasūtra,39Steffens, F.,116Steinschneider,5,57,65,66,98,126Stifel,62Subandhus,44Suetonius,80Suleimān,100Śūnya,43,53,57Suter,5,9,68,69,93,116,131Sūtras,13Sykes, P. M.,75Sylvester II,seeGerbertSymonds, J. A.,129

Sachau,6

Sacrobosco,3,58,133

Sacy, S. de,66,70

Sa‛dī,102

Śaka inscriptions,20

Samū'īl 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

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,seeGerbert

Symonds, J. A.,129


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