Ja (Indic)

Ja is the eighth consonant of Indic abugidas. In modern Indic scripts, ja is derived from the early "Ashoka" Brahmi letter after having gone through the Gupta letter .

← Cha		Ja			Jha →
Devanagari	Ashoka Brahmi		Tibetan	Bengali		Tamil
091C	1101A		/ ཛ 0F47 / 0F5B	099C		ஜ 0B9C
Gurmukhi	Thai		Baybayin	Malayalam		Sinhala
ਜ 0A1C	ช/ ซ 0E0A / 0E0B		- --	ജ 0D1C		ජ/ 𑋃 0DA2 / 112C3
Ancient scripts Ashoka Brahmi Kushana Brahmi Gupta Brahmi Tocharian 1101A 𑀚 1101A 1101A -- Kharoṣṭhī Siddhaṃ Sharada Grantha 𐨗 10A17 11595 𑆘 11198 𑌜 1131C
Bangla and Tibetan scripts Ashoka Brahmi Gupta Brahmi Tibetan Bengali 1101A 1101A / ཛ 0F47 / 0F5B 099C 'Phags-pa Oriya Limbu Lepcha Marchen ꡆ/ ꡒ A846 / A852 ଜ 0B1C ᤈ 1908 ᰈ 1C08 𑱸 11C78 Siddhaṃ Pracalit Tirhuta Zanabazar Square 11595 𑐖 11416 𑒖 11496 𑨒 11A12 Note: Korean Hangul is an alphabet, not an Indic abugida, but appears to ultimately have some derivation from 'Phags-pa.
Sharada-based scripts Sharada Ashoka Brahmi Gupta Brahmi Takri Dogra 𑆘 11198 1101A 1101A 𑚑 11691 𑠑 11811 Gurmukhi Khudawadi Mahajani Khojki Multani ਜ 0A1C 𑋂 112C2 𑅛 1115B 𑈐/ 𑈑 11210 / 11211 𑊌 1128C
Nagaris and other Gupta-based scripts Ashoka Brahmi Gupta Brahmi Devanagari 1101A 1101A 091C Gujarati Kaithi Syloti Nagari Modi જ 0A9C 𑂔 11094 ꠎ A80E 𑘕 11615 Nandinagari Gunjala Gondi Soyombo Bhaiksuki 𑦵 119B5 𑩣 11A63 𑶀 11D80 𑰕 11C15
Kawi scripts Grantha Baybayin Tagbanwa Hanunó'o Buhid 𑌜 1131C - -- - -- - -- - -- Balinese Javanese Batak Lontara Rejang ᬚ 1B1A ꦗ A997 ᯐ 1BD0 ᨍ 1A0D ꤺ A93A Ashoka Brahmi Sundanese Makasar Chakma 1101A ᮏ 1B8F 𑻪 11EEA 𑻪 11EEA
Tai and Khmer scripts Ashoka Brahmi Grantha Khmer Lao 1101A 𑌜 1131C ជ 1787 ຊ 0E8A Thai Tai Tham Tai Viet Tai Le New Tai Lü ช/ ซ 0E0A / 0E0B ᨩ/ ᨪ 1A29 / 1A2A - -- ᥗ 1957 ᦋ/ ᦌ 198B / 198C
Other Grantha-based scripts Ashoka Brahmi Grantha Ahom Dives Akuru 1101A 𑌜 1131C 𑜊 1170A 𑤓 11913 Malayalam Saurashtra Cham Burmese Kayah Li ജ 0D1C ꢙ A899 ꨎ AA0E ဇ 1007 - --
Other Brahmic scripts Ashoka Brahmi Masaram Gondi Meetei Mayek 1101A 𑴓 11D13 ꯖ ABD6 Tamil Kannada Sinhala Telugu ஜ 0B9C ජ 0DA2 జ/ 𑋃 0C1C / 112C3 ಜ 0C9C
Phonemic representation:				/d͡ʒ/
IAST transliteration:				ja Ja
ISCII code point:				BA (186)

Āryabhaṭa numeration

Further information: Āryabhaṭa numeration

Aryabhata used Devanagari letters for numbers, very similar to the Greek numerals, even after the invention of Indian numerals. The values of the different forms of ज are:[1]

• ज [d͡ʒə] = 8 (८)
• जि [d͡ʒɪ] = 800 (८००)
• जु [d͡ʒʊ] = 80,000 (८० ०००)
• जृ [d͡ʒri] = 8,000,000 (८० ०० ०००)
• जॢ [d͡ʒlə] = 8×10⁸ (८०^८)
• जे [d͡ʒe] = 8×10¹⁰ (८०^१०)
• जै [d͡ʒɛː] = 8×10¹² (८०^१२)
• जो [d͡ʒoː] = 8×10¹⁴ (८०^१४)
• जौ [d͡ʒɔː] = 8×10¹⁶ (८०^१६)

Historic Ja

There are three different general early historic scripts - Brahmi and its variants, Kharoṣṭhī, and Tocharian, the so-called slanting Brahmi. Ja as found in standard Brahmi, was a simple geometric shape, with variations toward more flowing forms by the Gupta . The Tocharian Ja did not have an alterante Fremdzeichen form. The third form of ja, in Kharoshthi () was probably derived from Aramaic separately from the Brahmi letter.

Brahmi Ja

The Brahmi letter , Ja, is probably derived from the Aramaic Zayin , and is thus related to the modern Latin Z and Greek Zeta. Several identifiable styles of writing the Brahmi Ja can be found, most associated with a specific set of inscriptions from an artifact or diverse records from an historic period.[2] As the earliest and most geometric style of Brahmi, the letters found on the Edicts of Ashoka and other records from around that time are normally the reference form for Brahmi letters, with vowel marks not attested until later forms of Brahmi back-formed to match the geometric writing style.

Brahmi Ja historic forms

Ashoka (3rd-1st c. BCE)	Girnar (~150 BCE)	Kushana (~150-250 CE)	Gujarat (~250 CE)	Gupta (~350 CE)

Tocharian Ja

The Tocharian letter is derived from the Brahmi , but does not have an alternate Fremdzeichen form.

Tocharian Ja with vowel marks

Ja	Jā	Ji	Jī	Ju	Jū	Jr	Jr̄	Je	Jai	Jo	Jau	Jä

Kharoṣṭhī Ja

The Kharoṣṭhī letter is generally accepted as being derived from the Aramaic Zayin , and is thus related to Z and Zeta, in addition to the Brahmi Ja.

Devanagari script

Ja (ज) is the eighth consonant of the Devanagari abugida. It ultimately arose from the Brahmi letter , after having gone through the Gupta letter . Letters that derive from it are the Gujarati letter જ and Modi letter 𑘕.

Devanagari Jja

Jja (ॼ) is the character ज with an underbar to represent the voiced palatal implosive [ʄ] that occurs in Sindhi. This underbar is distinct from the Devanagari stress sign anudātta. The underbar is fused to the stem of the letter while the anudātta is a stress accent applied to the entire syllable. This underbar used for Sindhi implosives does not exist as a separate character in Unicode. When the ु or ू vowel sign is applied to jja (ॼ), the ु and ू vowel signs are drawn beneath jja. When the उ ( ु) vowel sign or ऊ ( ू) vowel sign is applied to ja with an anudātta (ज॒), the उ ( ु) vowel sign or ऊ ( ू) vowel sign is first placed under ja (ज) and then the anudātta is placed underneath the उ ( ु) vowel sign or ऊ ( ू) vowel sign.[3]

Character Name	उ ( ु) vowel sign	ऊ ( ू) vowel sign
ॼ (Implosive ja)	ॼु	ॼू
ज॒ (Ja with anudātta)	जु॒	जू॒

An example of a Sindhi word that uses jja (ॼ) is ॼाण (ڄاڻَ), which is of the feminine grammatical gender and means information or knowledge.[4]

Devanagari Za

Za (ज़) is the character ज with a single dot underneath. It is used in Devanagari transcriptions of Urdu, English, and other languages to denote the voiced alveolar sibilant [z]. Za (ज़) should not be confused with ža (झ़), which is the character jha (झ) combined with a nuqta, and is used to transcribe the voiced post-alveolar fricative [ʒ] from Urdu (ژ) and English. Za (ज़) should also not be confused zha (ॹ), which is used in Devanagari transcriptions of the Avestan letter zhe (𐬲) to denote the voiced post-alveolar fricative [ʒ].

Devanagari Zha

Zha (ॹ) is the character ज with three dots underneath. It is used in Devanagari transcriptions of the Avestan letter zhe (𐬲) to denote the voiced patalal fricative [ʒ]. An example of its usage is in Kavasji Edulji Kanga's Avesta, yazna 41.3 to write ईॹीम्.[5] Zha (ॹ) should not be confused with za (ज़), which is used to denote the voiced alveolar sibilant [z] from Urdu, English, and other languages. Zha (ॹ) should also not be confused with ža (झ़), which is the character jha (झ) combined with a nuqta, and is used to transcribe the voiced post-alveolar fricative [ʒ] from Urdu (ژ) and English.

Devanagari-using Languages

In many languages, ज is pronounced as [d͡ʒə] or [d͡ʒ] when appropriate. In Marathi, ज is sometimes pronounced as [d͡zə] or [d͡z] in addition to [d͡ʒə] or [d͡ʒ]. Like all Indic scripts, Devanagari uses vowel marks attached to the base consonant to override the inherent /ə/ vowel:

Devanagari ज with vowel marks

Ja	Jā	Ji	Jī	Ju	Jū	Jr	Jr̄	Jl	Jl̄	Je	Jai	Jo	Jau	J
ज	जा	जि	जी	जु	जू	जृ	जॄ	जॢ	जॣ	जे	जै	जो	जौ	ज्

Conjuncts with ज

Half form of Ja.

Devanagari exhibits conjunct ligatures, as is common in Indic scripts. In modern Devanagari texts, most conjuncts are formed by reducing the letter shape to fit tightly to the following letter, usually by dropping a character's vertical stem, sometimes referred to as a "half form". Some conjunct clusters are always represented by a true ligature, instead of a shape that can be broken into constituent independent letters. Vertically stacked conjuncts are ubiquitous in older texts, while only a few are still used routinely in modern Devanagari texts. The use of ligatures and vertical conjuncts may vary across languages using the Devanagari script, with Marathi in particular preferring the use of half forms where texts in other languages would show ligatures and vertical stacks.[6]

Ligature conjuncts of ज

Jja half form

True ligatures are quite rare in Indic scripts. The most common ligated conjuncts in Devanagari are in the form of a slight mutation to fit in context or as a consistent variant form appended to the adjacent characters. Those variants include Na and the Repha and Rakar forms of Ra. Nepali and Marathi texts use the "eyelash" Ra half form for an initial "R" instead of repha. The conjunct jja also has a unique half form that differs from the regular conjunct.

• र্ (r) + ज (ja) gives us the ligature rja:

• ज্ (j) + र (ra) gives us the ligature jra:

• ज্ (j) + न (na) gives us the ligature jna:

• ज্ (j) + ज (ja) gives us the ligature jja:

• ज্ (j) + ज্ (j) + व (va) gives us the ligature jjva:

• ज্ (j) + ज্ (j) + य (ya) gives us the ligature jjya:

Devanagari Jña

Jña half form

One of the most common true ligatures in Devanagari is the conjunct jña ज्ञ. This ligature is a required form for most Devanagari languages, and the conjunct even has its own half form that freely joins other letters in horizontal conjuncts. ज्ञ্‍

• ज্ (j) + ञ (ña) gives us the ligature jña:

• र্ (r) + ज্ (j) + ञ (ña) gives us the ligature rjña:

• भ্ (bʰ) + ज্ (j) + ञ (ña) gives us the ligature bʰjña:

• ब্ (b) + ज্ (j) + ञ (ña) gives us the ligature bjña:

• छ্ (cʰ) + ज্ (j) + ञ (ña) gives us the ligature cʰjña:

• च্ (c) + ज্ (j) + ञ (ña) gives us the ligature cjña:

• ढ্ (ḍʱ) + ज্ (j) + ञ (ña) gives us the ligature ḍʱjña:

• ड্ (ḍ) + ज্ (j) + ञ (ña) gives us the ligature ḍjña:

• द্ (d) + ज্ (j) + ञ (ña) gives us the ligature djña:

• घ্ (ɡʱ) + ज্ (j) + ञ (ña) gives us the ligature ɡʱjña:

• ग্ (g) + ज্ (j) + ञ (ña) gives us the ligature gjña:

• ह্ (h) + ज্ (j) + ञ (ña) gives us the ligature hjña:

• ज্ (j) + ज্ (j) + ञ (ña) gives us the ligature jjña:

• झ্ (jʰ) + ज্ (j) + ञ (ña) gives us the ligature jʰjña:

• ख্ (kʰ) + ज্ (j) + ञ (ña) gives us the ligature kʰjña:

• क্ (k) + ज্ (j) + ञ (ña) gives us the ligature kjña:

• ल্ (l) + ज্ (j) + ञ (ña) gives us the ligature ljña:

• म্ (m) + ज্ (j) + ञ (ña) gives us the ligature mjña:

• न্ (n) + ज্ (j) + ञ (ña) gives us the ligature njña:

• ञ্ (ñ) + ज্ (j) + ञ (ña) gives us the ligature ñjña:

• ङ্ (ŋ) + ज্ (j) + ञ (ña) gives us the ligature ŋjña:

• फ্ (pʰ) + ज্ (j) + ञ (ña) gives us the ligature pʰjña:

• प্ (p) + ज্ (j) + ञ (ña) gives us the ligature pjña:

• श্ (ʃ) + ज্ (j) + ञ (ña) gives us the ligature ʃjña:

• स্ (s) + ज্ (j) + ञ (ña) gives us the ligature sjña:

• ष্ (ṣ) + ज্ (j) + ञ (ña) gives us the ligature ṣjña:

• थ্ (tʰ) + ज্ (j) + ञ (ña) gives us the ligature tʰjña:

• त্ (t) + ज্ (j) + ञ (ña) gives us the ligature tjña:

• ठ্ (ṭʰ) + ज্ (j) + ञ (ña) gives us the ligature ṭʰjña:

• ट্ (ṭ) + ज্ (j) + ञ (ña) gives us the ligature ṭjña:

• व্ (v) + ज্ (j) + ञ (ña) gives us the ligature vjña:

• य্ (y) + ज্ (j) + ञ (ña) gives us the ligature yjña:

Stacked conjuncts of ज

Vertically stacked ligatures are the most common conjunct forms found in Devanagari text. Although the constituent characters may need to be stretched and moved slightly in order to stack neatly, stacked conjuncts can be broken down into recognizable base letters, or a letter and an otherwise standard ligature.

• भ্ (bʰ) + ज (ja) gives us the ligature bʰja:

• ब্ (b) + ज (ja) gives us the ligature bja:

• छ্ (cʰ) + ज (ja) gives us the ligature cʰja:

• च্ (c) + ज (ja) gives us the ligature cja:

• ढ্ (ḍʱ) + ज (ja) gives us the ligature ḍʱja:

• ड্ (ḍ) + ज (ja) gives us the ligature ḍja:

• ध্ (dʱ) + ज (ja) gives us the ligature dʱja:

• द্ (d) + ज (ja) gives us the ligature dja:

• घ্ (ɡʱ) + ज (ja) gives us the ligature ɡʱja:

• ग্ (g) + ज (ja) gives us the ligature gja:

• ह্ (h) + ज (ja) gives us the ligature hja:

• ज্ (j) + च (ca) gives us the ligature jca:

• ज্ (j) + ड (ḍa) gives us the ligature jḍa:

• झ্ (jʰ) + ज (ja) gives us the ligature jʰja:

• ज্ (j) + ल (la) gives us the ligature jla:

• ज্ (j) + ङ (ŋa) gives us the ligature jŋa:

• ज্ (j) + ञ (ña) gives us the ligature jña:

• ज্ (j) + श (ʃa) gives us the ligature jʃa:

• ख্ (kʰ) + ज (ja) gives us the ligature kʰja:

• क্ (k) + ज (ja) gives us the ligature kja:

• ल্ (l) + ज (ja) gives us the ligature lja:

• ळ্ (ḷ) + ज (ja) gives us the ligature ḷja:

• म্ (m) + ज (ja) gives us the ligature mja:

• ङ্ (ŋ) + ज (ja) gives us the ligature ŋja:

• न্ (n) + ज (ja) gives us the ligature nja:

• ञ্ (ñ) + ज (ja) gives us the ligature ñja:

• फ্ (pʰ) + ज (ja) gives us the ligature pʰja:

• प্ (p) + ज (ja) gives us the ligature pja:

• श্ (ʃ) + ज (ja) gives us the ligature ʃja:

• स্ (s) + ज (ja) gives us the ligature sja:

• ष্ (ṣ) + ज (ja) gives us the ligature ṣja:

• त্ (t) + ज (ja) gives us the ligature tja:

• ठ্ (ṭʰ) + ज (ja) gives us the ligature ṭʰja:

• ट্ (ṭ) + ज (ja) gives us the ligature ṭja:

• व্ (v) + ज (ja) gives us the ligature vja:

• य্ (y) + ज (ja) gives us the ligature yja:

Bengali script

The Bengali script জ is derived from the Siddhaṃ , and is marked by a similar horizontal head line, but less geometric shape, than its Devanagari counterpart, ज. The inherent vowel of Bengali consonant letters is /ɔ/, so the bare letter জ will sometimes be transliterated as "jo" instead of "ja". Adding okar, the "o" vowel mark, gives a reading of /d͡ʒo/.

Like all Indic consonants, জ can be modified by marks to indicate another (or no) vowel than its inherent "a".

Bengali জ with vowel marks

ja	jā	ji	jī	ju	jū	jr	jr̄	je	jai	jo	jau	j
জ	জা	জি	জী	জু	জূ	জৃ	জৄ	জে	জৈ	জো	জৌ	জ্

জ in Bengali-using languages

জ is used as a basic consonant character in all of the major Bengali script orthographies, including Bengali and Assamese.

Conjuncts with জ

Bengali জ exhibits conjunct ligatures, as is common in Indic scripts, with a tendency towards stacked ligatures.[7]

• ব্ (b) + জ (ja) gives us the ligature bja:

• জ্ (j) + জ (ja) gives us the ligature jja:

• জ্ (j) + ঝ (jʰa) gives us the ligature jjʰa:

• জ্ (j) + জ্ (j) + ব (va) gives us the ligature jjva, with the va phala suffix:

• জ্ (j) + ঞ (ña) gives us the ligature jña:

• জ্ (j) + র (ra) gives us the ligature jra, with the ra phala suffix:

• জ্ (j) + ব (va) gives us the ligature jva, with the va phala suffix:

• জ্ (j) + য (ya) gives us the ligature jya, with the ya phala suffix:

• ঞ (ñ) + জ (ja) gives us the ligature ñja:

• র্ (r) + জ (ja) gives us the ligature rja, with the repha prefix:

• র্ (r) + জ্ (j) + য (ya) gives us the ligature rjya, with the repha prefix and ya phala suffix:

Gujarati script

Ja (જ) is the eighth consonant of the Gujarati script. It is possibly derived from a variant of 16th century Devanagari letter ja (ज) with the top bar (shiro rekha) removed. Ja (જ) is visually similar to the corresponding Modi letter. When combined with certain vowels, the Gujarati Ja may assume unique forms (such as જા, જી, and જો):

J	Ja	Jā	Ji	Jii	Ju	Jū	Jr	Jr̄	Jl	Jl̄	Je	Jai	Jo	Jau
જ્(જ્‍ZWJ)	જ	જા	જિ	જી	જુ	જૂ	જૃ	જૄ	જૢ	જૣ	જે	જૈ	જો	જૌ

Gujarati Za

Za (જ઼) is the character ja (જ) with a single dot underneath. It corresponds to the Devanagari character Za (ज़). It is also used in Gujarati transcriptions of Avestan (𐬰),[8][9][10] Urdu (ژ), English, and other languages to denote the voiced alveolar sibilant [z].

Gujarati Zha

Zha (ૹ) is the character ja (જ) with three dots underneath. It is used in Gujarati transcriptions of the Avestan letter zhe (𐬲) to denote the voiced patalal fricative [ʒ] and is analogous to the Devanagari character zha (ॹ).[8][9] Zha (ૹ) was added to the Unicode Standard as a single character ljust like the Devanagari character zha (ॹ) with Unicode 8.0 on 17 June 2015.[10][11] An example of a word in the Gujarati script the uses zha (ૹ) is ચીૹ્દી.[12]

Gurmukhi script

Jajjaa [d͡ʒəd͡ʒːɑ] (ਜ) is the thirteenth letter of the Gurmukhi alphabet. Its name is [d͡ʒəd͡ʒːɑ] and is pronounced as /d͡ʒ/ when used in words. It is derived from the Laṇḍā letter ja, and ultimately from the Brahmi ja. Gurmukhi jajaa does not have a special pairin or addha (reduced) form for making conjuncts, and in modern Punjabi texts do not take a half form or halant to indicate the bare consonant /d͡ʒ/, although Gurmukhi Sanskrit texts may use an explicit halant.

Jajje vicc bindi

A dot added below Jajja (ਜ਼) denotes that it has to be pronounced as the voiced alveolar fricative /z/.

Thai script

Cho chang (ช) and so so (ซ) are the tenth and eleventh letters of the Thai script. They fall under the low class of Thai consonants. Unlike many Indic scripts, Thai consonants do not form conjunct ligatures, and use the pinthu—an explicit virama with a dot shape—to indicate bare consonants.

Cho chang

In IPA, cho chang is pronounced as [tɕʰ] at the beginning of a syllable and are pronounced as [t̚] at the end of a syllable. The previous letter of the alphabet, cho ching (ฉ), is also named cho, however, it falls under the middle class of Thai consonants. In the acrophony of the Thai script, chang (ช้าง) means ‘elephant’. Kho khai corresponds to the Sanskrit character ‘ज’.

So so

In IPA, so so is pronounced as [s] at the beginning of a syllable and are pronounced as [t̚] at the end of a syllable. In the acrophony of the Thai script, so (โซ่) means ‘chain’. Old Thai had the voiced retroflex affricate sound /dʐ/. When the Thai script was developed, cho ching was slightly modified to create distinct letter for /dʐ/, which is now known as so so. During the Old Thai period, this sound merged into the aspirated stop /tɕʰ/. This is similar to how ज is sometimes pronounced as [d͡z] in addition to [d͡ʒ] in Marathi. However, Marathi uses the same letter for both sounds while Thai split the corresponding two sounds into the separate letters cho chang and so so. In modern Thai, the voicing of /dʐ/ became lost and thus is now pronounced as [s] at the beginning of a syllable.

Javanese script

Main article: Ja (Javanese)

References

1. Ifrah, Georges (2000). The Universal History of Numbers. From Prehistory to the Invention of the Computer. New York: John Wiley & Sons. pp. 447–450. ISBN 0-471-39340-1.
2. Evolutionary chart, Journal of the Asiatic Society of Bengal Vol 7, 1838
3. Everson, Michael (30 March 2005). "Proposal to add four characters for Sindhi to the BMP of the UCS" (PDF). Unicode.org. Archived from the original (PDF) on 12 July 2014. Retrieved 4 March 2015.
4. Lekhwani, Kanhaiyalal. 1987 (1909). An intensive course in Sindhi. Mysore: Central Institute of Indian Languages; [New York]: Hippocrene Books. OCLC 18986594
5. "Proposal to encode 55 characters for Vedic Sanskrit in the BMP of the UCS" (PDF). Unicode.org. 18 October 2007. Archived from the original (PDF) on 19 June 2012. Retrieved 4 March 2015.
6. Pall, Peeter. "Microsoft Word - kblhi2" (PDF). Eesti Keele Instituudi kohanimeandmed. Eesti Keele Instituudi kohanimeandmed. Retrieved 19 June 2020.
7. "The Bengali Alphabet" (PDF). Archived from the original (PDF) on 2013-09-28.
8. Rajan, Vinod (16 July 2013). "Proposal to encode Gujarati Letter ZHA" (PDF). Unicode.org. Archived from the original (PDF) on 13 July 2014. Retrieved 4 March 2015.
9. Rajan, Vinodh (15 April 2013). "Proposal to encode Gujarati Sign Triple Nukta" (PDF). Archived from the original (PDF) on 13 July 2014. Retrieved 4 March 2015.
10. Rajan, Vinodh (26 April 2013). "Recommendations to UTC on Script Proposals" (PDF). Unicode.org. Archived from the original (PDF) on 13 July 2014. Retrieved 4 March 2015.
11. West, Andrew (1 April 2015). "What's new in Unicode 8.0 ?". BabelStone. BabelStone. Archived from the original on 16 September 2016. Retrieved 2 November 2016.
12. Kanga, Ervad Kavasji Edalji (1936). Kanga, Navroji Pestonji Kavasji (ed.). Khordeh Avestâ (PDF). Bombay: Nirnaya Sagar Press. p. 5. Archived from the original (PDF) on 18 October 2016 – via www.avesta.org.

• Kurt Elfering: Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar. Wilhelm Fink Verlag, München, 1975, ISBN 3-7705-1326-6
• Georges Ifrah: The Universal History of Numbers. From Prehistory to the Invention of the Computer. John Wiley & Sons, New York, 2000, ISBN 0-471-39340-1.
• B. L. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkhäuser-Verlag, Basel Stuttgart, 1966, ISBN 3-7643-0399-9
• Fleet, J. F. (January 1911). "Aryabhata's System of Expressing Numbers". Journal of the Royal Asiatic Society of Great Britain and Ireland: 109–126. ISSN 0035-869X. JSTOR 25189823.
• Fleet, J. F. (1911). "Aryabhata's System of Expressing Numbers". The Journal of the Royal Asiatic Society of Great Britain and Ireland. Royal Asiatic Society of Great Britain and Ireland. 43: 109–126. doi:10.1017/S0035869X00040995. JSTOR 25189823.