1. Modes of creation of a technical vocabulary the case of Sanskrit mathematics Pierre-Sylvain Filliozat

2. 1a. Mathematical knowledge contained in the Sanskrit language. Names of numbers 1b. Manipulation of language. Acceptance and extensive use of synonymy 1c. Rhetorical manipulations. Use of metonymy 2. Pā ṇ ini’s concept of ordinal and fraction 3. Relation with practice: case of kara ṇ ī in the śrauta ritual 4. Freedom of invention: case of kara ṇ ī in bījaga ṇ ita 5. Role of writing, case of kapā ṭ asa ṃ dhi and tricaturbhuja 6. Conclusion

3. eka11 daśa10 śata10010 2 sahasr a 100010 3 ayuta10 00010 4 lakşa100 00010 5 niyuta1 000 00010 6 koţi10 000 000 10 7 arbuda100 000 000 10 8 vŗnda1 000 000 000 10 9 kharva10 000 000 000 10 1 0 nikharva100 000 000 000 10 1 1 śańkha1 000 000 000 000 10 1 2 padma10 000 000 000 000 10 1 3 sagara100 000 000 000 000 10 1 4 antya1000 000 000 000 000 10 1 5 madhya 10 000 000 000 000 000 10 1 6 parārdha100 000 000 000 000 000 10 1 7

4. gu ṇ o maurvyāmapradhāne rūpādau sūda indriye | tyāge śauryādisa ṃ dhyādisattvādyāv ṛ ttirajju ṣ u | śuklādāvapi va ṭ yā ṃ ca iti medinī Bowstring, secondary, property such as colour etc., cook, sense organ, generosity, quality such as valour etc., way of dealing with an enemy such as negotiation etc., substance of primordial matter such as sattva etc., repetition, cord gu ṇ a āmantra ṇ e, hana hi ṃ sāgatyo ḥ vadhādau viyat khasya kha ṃ khena ghāte khahāro bhavet khena bhaktaś ca rāśi ḥ || Bhāskara, Bīja 14 In multiplication (/murder) etc. of zero (/void) the result is zero (/sky), in multiplication (/blow) by zero (/void)zero (/void). A number (/heap) divided by zero (/void) will be number having a zero (/void) divisor.

5. sa ṃ vatsaré-sa ṃ vatsare ha vā 'syāgnihotrá ṃ mahátokthéna sá ṃ padyate “Every year, indeed, his libation in fire amounts to the grand litany.” (Śatapathabrāhma ṇ a 11.3.3.20) grand litany: recitation 3 times of 80 stanzas of three lines 2times a day = 720 = 2*360 in a year tāni sa ṃ vatsaré dáśa ca sahásrāņy astaú ca śatāni sám apadyata In the year they [the muhūrtas] amounted to ten thousand eight hundred. (Śatapathabrāhma ṇ a 10.4.2.20)

6. dak ṣ i ṇ ā gāyatrīsa ṃ pannā brāhma ṇ asya / jagatyā rājña ḥ / b ṛ hatī-sa ṃ pannā ḥ paśu-kāmasya / “The fee amounts to the gāyatrī for the Brahmin, to the jagatī for the nobleman, to the b ṛ hatī for the cattle- seeker.” (Kātyāyanaśrautasūtra 22.11.21-25) The gāyatrī is a stanza of 3 lines of 8 syllables. Its name refers here to the number 24. The jagatī is a stanza of 4 lines of 12 syllables = 48. The b ṛ hatī is a stanza of 2 lines of 8 syllables, 1 of 12 and 1 of 8 = 36.

7. dīrghasyāk ṣṇ ayārajju ḥ pārśvamānī tirya ṅ mānī ca yatp ṛ thagbhūte kurutastadubhaya ṃ karoti | (Āpastamba 1.4) “The diagonal cord of a rectangle produces both the squares that the flank cord and the transverse cord produce separately.”

8. pait ṛ kyā ṃ dvipuru ṣ a ṃ caturaśra ṃ k ṛ tvā kara ṇ īmadhye ṣ u śa ṅ kava ḥ sa samādhi ḥ |(Kātyāyana 2.6) “Regarding the pait ṛ kī, after making a square with a side of two puru ṣ as, pins are fixed in the middle of the producing cords.”

9. The square of a sum of square roots is : Technical names are given for: a + b called mahatī “large” and called laghu “light” The sum is the addition of these two elements, operated like the addition of two integers. Ka, abbreviation of kara ṇ ī, is used in writing. For the addition of ka8 and ka2: mahatī =8 + 2 = 10, laghu =, sum = ka18. This operation is possible only if the product of a and b is a square. The choice of the words mahatī and laghu is based on a mathematical fact: for all numbers a and b :

12. vinyasyādho gu ṇ ya ṃ kapā ṭ asa ṃ dhikrame ṇ a gu ṇ arāśe ḥ | gu ṇ ayed vilomagatyānulomamārge ṇ a vā kramaśa ḥ || utsāryotsārya tata ḥ kapā ṭ asa ṃ dhir bhaved ida ṃ kara ṇ am | “After placing the multiplicand below, in the manner of adjusting verandah panels one should multiply by the multiplier, sliding step by step in reverse movement or in direct course. Therefore this operation will be the adjustment of verandah panels.”

14. tribhujasya vadho bhujayordvigu ṇ italamboddh ṛ to h ṛ dayarajju ḥ | sā dvigu ṇ ā tricaturbhujako ṇ asp ṛ gv ṛ ttavi ṣ kambha ḥ || (Brahmasphu ṭ asiddhānta 12.27) “The product of two sides divided by twice the altitude is the circum-radius of the trilateral; twice that is the diameter of the circle touching the vertices of the triquadrilateral.”

15. sthūlaphala ṃ tricaturbhuja- bāhupratibāhuyogadalaghāta ḥ | bhujayogārdhacatu ṣṭ aya- bhujonaghātāt pada ṃ sūk ṣ mam || “The product of half the sides and counter sides of a tricaturbhuja is the gross area; the square root of the product of four sets of half the sum of the sides lessened by the sides is its exact [area].” s being the half perimeter of a tricaturbhuja of sides a, b, c, d, the area is: