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________________ On Geometry of Jambudvipa Dr. S. S. Lishk Jainas thought that the earth was made up of a series of concentric rings of land masse surrounded by concentric ocean rings. The central island of the earth was Jambudvipa. 1 The mount Meru is placed at the centre of Jambudvipa. According to Tiloya Pannattia (gatba 4, 1780 et. seq.), Meru is made up of frustrum of cones. A mathematical analysis 8 of the dimensions of the mount Meru shows that the concept of Meru implies the notion of obliquity of ecliptic. Earth's true axis passes along the hypotenuse of an approximate cone of Meru and not along the axis of Meru. So true radius of Jambudvipa is equal to apparent radius of Jambudvipa less radius of Meru's base on earth, i. e., 50000_-5000=45000 yojanas. With this concept the circumference of Jambudvipa coincides with the parallel of maximum declination of the Sun, i. e., 230.5 North. Now as regards the concept of samatala bhumi, Surya Prajnapti. 18, the seventh upanga (sub-limb) of Jaina canonical literature, states-that "From the samatala bhumi, the Sun moves at a height of 800 Yojanas." A mathematical analysis of these data shows that samatala bbumi represents the plane parallel to the plane of ecliptic and bounded by the Parallel of celestial latitude of 730.7. The centre of samatala bhumi is coincident with the projection (on earth) of pole of ecliptic. Radius of samatala bhumi is equal to 900 minus 730.7, i. e., 160.3. Obviously with this concept of samatala bhumi, the Jaina notion that the Moon is 89 Yojanas higher than the Sun, becomes easily discernible. A notion of celestial latitude of the Moon is implied therein.5 Besides it may be noted that the radius of Meru is equal to height of the Moon over that of the Sun above samatala bhumi because. Height of the Moon above that of the Sun=80 Yojanas = 5000 yojanas (... 1 yojana=500 Yojanas) =Radius of Meru's base on flat earth Besides it may be remarked that the only characteristic for samatala bhqmi as referred to in the text is that the Sun remains above it always at a height (celestial co-latitudinal distance as implied in Jaina texts) of 800 EIJH1 dai saMsAra samudra meM dharma hI dIpa www.jamenbray.org
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________________ caturtha khaNDa / 376 Yojanas. on the other hand the Sun covers 510 Yojanas on its southward Journey from sarvabhyantara mandala to sarvabahya mandala and vice-versa. The consistency of figures 800 Yojanas and 510 Yojanas support our view? regarding the concept of Meru and the concept of samatala bhumi. Even in the case of Meru, consistency of figures tbroughout gives a good criterion: It is also worth mentioning that although the apparent geometry confirms the Jainian notion about the shape of flat earth, yet the actual observation and determinations do fit the real geometry of earth. Now it may be worth noticing that the actual distances were measured both in time degrees 8 and in earth distances'. Thus the Sun's southward journey from the sarvabhyantara mandala (innermost mandala, i. e.. Sun's diurnal path on summer solstice day) and vice versa was measured into earth distances of 510 Yojanas. In Jambudvipa Prajnapti 7.2, it is stated 10 there are 65 solar mandalas stretched over 180 Yojanas of Jambudvipa apd then the area of lavana samudra (salt ocean) begins therefrom. Now since 510 Yojanas are equated with 47deg, double the maximum declination of the Sun, this leads to conclude that 180 Yojanas = 160.6 = 230.5--60.9 This suggests that north-south stretch of mandalas in Jambudvipa is extended southward from Sun's extreme north position 230.5 upto 60.9 in the northern hemisphere as we understand it these days, verisimilarly coinciding with the southern limit of ancient India including modern Sri Lanka. It seems convincing that verisimilarly the southward journey of the Sun was measured in Yojanas starting from a station on earth where the noon-shadow length of gnomon was zero on the summer solstice day, i. e., starting from a station situated in the neighbourhood of terrestrial latitude of 230.5 north (which is incidently very close to the latitude of Ujjain, a renowned seat of ancient Indian culture) upto the station situated at about the extreme southern limit of ancient India where again the noon-shadow length was observed to be zero after 65 days since summer solstice day. This leads us to conclude that the concept of solar mandalas implies that the outermost limit of Jambudvipa coincides with the parallel of terrestrial latitude of 60.9 wherefrom lavaga samudra starts. The dimensions of circumference of Jambudvipa have been already dealt with as to how they were generated mathematically11. A mathematical analysis of the consistent dimensions of the mount Meru coupled with the study of the concept of samatala bhumi shows that the outermost limit of Jambudvipa coincides with the parallel of terrestrial latitude of 230.5 North. This conclusion implies that the true radius of Jambudvipa with Meru at its centre, is 5000 yojanas (=80 Yojanas) less than its apparent radius. Probably later at some stage the apparent radius of Jambudvipa might have been taken for its true radius, as a result of which
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________________ On Geometry of Jambudvipa | 377 the outermost limit of Jambudvipa might have been shifted 80 Yojanas southward to the parallel of latitude of 230.5 North. But the development of the concept of magdala with the help of gnomonic experiments, the outermost limit of Jambudvipa had been shifted to 180 Yojanas southward to the parallel of 230.5 North. Probably to cover up the gap between the sequential shifts from 80 Yojanas to 180 or to account for any error in the gnomonic experiments the concept of Jagat might have been evolved which the author is yet investigating. Finally it may be envisaged that Jambudvipa as implied in the recent model of the concept of solar magdalas (Sun's diurnal paths) is stretched over northern hemisphere of the earth with its periphery coinciding almost with the parallel of terrestrial latitude of 60,9 North. This study opens many new vistas of research on certain physical theories in Hindu astronomy and the role of Jainacaryas will be further highlighted. References 1. See Lishk, S. S. and Sharma, S. D. (1976) Notion of Circular Flat Earth. in Jaina Cosmography. The Jaina Antiquary, Vol. 28, Nos. 1-2, pp 1-5. 2. Jain, L. C. (1958) Tiloya Pannatti ka Ganit (prefixed with Jambudva Pangatti Samgaho edited by A. N. Upadhye and Hira Lal Jain) pp. 62-64. 3. Lishk, S. S. and Sharma, S. D. (1978) Notion of Obliquity of Ecliptic implied in the Concept of Mount Meru in Jambudvipa Prajnapti. Jain Journal, Vol. 12, No. 3, pp. 79-92. 4. Ibid. 5. Lishk, S. S. and Sharma, S. D. (1975) Latitude of the Moon as Determined in Jaina Astronomy. Shramana, Vol. 27, No. 2, pp. 28-35. 6. Lishk, S. S. and Sharma, S D. (1979) Length Units in Jaina Astronomy. Jain Journal, Vol. 13, No. 4, pp. 143-154. See also Lishk, S. S. and Sharma, S. D. (1975) The Evolution of Measures in Jaina Astronomy. Tirthankar, Vol. 1, Nos. 7-12, pp. 83-92. 7. See ref. 3. 8. Lishk, S. S. and Sharma, S. D. (1979) Zodiacal Circumference as Graduated in Jaina Astronomy. Indian Journal of History of Science, Vol. 14, No. 4, pp. 1-15. 9. Lishk, S. S. and Sharma, S. D. (1977) Seasons Determination Through the Science of Sciatherics in Jaina School of Astronomy. Indian Journal of History of Science, Vol. 12, No. 1, pp. 37-44. See also Lishk, S. S. (1980) Certain peculiarities of Jaina School of Astronomy. Jaina Journal, Vol. 14, No. 3, pp. 81-88. See also Lishk, S. S. and Sharma, S D (1977) Role of pre-Aryabhata I Jaina School of Astronomy in the Development of Siddhantic Astronomy. Indian Jourual of History of Science, Vol. 11, No. 2, pp. 106-113. 10. Lishk, S. S. (1983) Notion of Declination implied in the Concept of
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________________ as aug / 265 Mandala (Diurnal Circle) in Jaina School of Astronomy. Jaina Journal, Voi. 18, No. 3, pp. 83-101. For more details, see Lishk, SS (1978) A Mathematical Analysis of PostVedanga Pre-Siddhantic Data io Jaina Astronomy. Ph. D. Thesis. Library of Panjabi University, Patiala. (Original texts have been quoted there in Prakrit version.) 11. Gupta, R. C. (1974) Circumference of Jambudvipa in Jajna Cosmography. Indian Journal of History of Science Vol. 10. No. 1, pp. 38.46. 12. Jain, L. C. On Certain Physical Theories in Hindu Astronomy. Prachya Pratibha, Vol. 5, No. 1, pp. 75 $6. See also Jain, Anupam. Survey of the Work Done on Jaina Mathematics. Manuscript. - Govt. In-Service Teacher Training Centre, Patiala -147001 (Punjab) ga dia saMsAra samuMda dharma hI dIpa