________________
The formula (iii) viz. c= 4h(d-)) refers to the theorem on the geometrical properties of circles viz.,
"the square on the chord=the rectangle contained by the segments of the diameter perpendicular to the chord.”
The formula (iv) is obtained by solving the quadratic equation c=4d-4h". This clearly explains that the early Jainas knew how to solve quadratic equations.
8. JAINA VALUE OF F(=v10)
The formula (1.), viz. circumference of a circle=v 10 (diameter)?, gives V 10 as value of .. Surya Prajnapti? (500 B.C.), gives two values of - viz. =3 and = 10. The former value was given by the early writers and the later one was adopted through the early Jain literature. In the Uttaradhyayana-sutra? (300 B.C.), the circumference of the Jambudvipa is given to be little over three times its diameter. According to the Jivabhigama-sutra', corressponding to an increment of 100 in the diameter, the circumference increases by 316. This gives r=3.16. All the medieval Jaina works from 500 B.C. till the 15th century A.D. used ✓ 10 as the value of , althogh by that time more accurate value of had been discovered by the Indians It may be observed here that Professor Mikami's statement that the value of = v10 is found recorded in a Chinese work by Chong Heng (78-139 A.D.) before it appeared in any Indian work” is not correcto. 9. THEORY OF NUMBERS
Jaina works refer to a very large number of names giving the positions (sthana or place) in the numeral system. Mahavira' (850 A.D.) has stated twenty-four notational places, while all other Indian mathematicians have given names for only eighteen places. The twenty-four notational places, according to Mahavira, are given below. Here the value of each succeeding place is taken to be ten times the value of the immediately preceding place.
Eka (for 1), dasa(for 10), shata(102), sahasra (10%), dasa sahasra (10), laksa (10%), dasa laksa (10%), koti (107), dasa koti (108), sata koti (10"), arbuda (1010), nyarbuda (1011), kharva (1012), maha kharva (1013), padma (1014). maha padma (1014), ksoni (104), maha ksoni (101), sankha (1018), maha sankha (101), ksiti (1020), maha ksiti (102), ksobha (1022), and finally maha ksobha (for 1028).
Thus in the Jain literature, the terminology above the fourth denomination have been coined by a system of grouping and regrouping. We may note here the deviation from the vedic terminology. In vedas.
3.
1. Surya Prajnapti. Sutra 20. 2. Uttara-dhayana-sutra. Chap. XXXVI, p, 59.
Compare also Jambudvipa Prajnapti. Sutra 19. Trigunam Savisesam (a little over three times).
Jivabhigama-sutra. Sutra 112. 4. Jivabhigama-Sutra. Sutra 82, 109, 112, etc.
Jambudvipa Prajnapti. Sutra 3. Bhagwati-sutra. Sutra 91,
Tattavärtha Dhigama-Sutra-Bhashya. 5. See Laghu Ksetra Samasa Prakarma of Ratna Sekhasa Suri (1440 A. D.) included in the Prakarma
Ratnakara
Ed. by Bhimaseiha Maraka. Bombay 1881. Verse 187. 6. Mikami's Chinese Mathematics. p, 70. 7. See G. S. S. Chap. I. p. 63-68. 8. See Yajurveda Samhita. Chap. XVII. 2.
जैन प्राच्य विद्याएँ
..
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