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The point P moves in a circle of radius r, and its path equation is given by x2 + y2 = r2.
According to Hankel, H., "The analytical geometry, as Descartes' method was called, soon led to an abundance of new theorems and principles, which far transcended everything that ever could have been reached upon the path pursued by the ancients.":48
In the Jaina school, the concept of eight central space-points of the loka, as well as the movement of matter and souls along world-lines subject to instantaneous conditions define a coordinate frame of the universe, full of space-points or time-points as already described. The deciding verses are : 49
2.25, In transit from one body to another, (there is) vibration of the karmic
body only. 2.26. Transit (takes place) in rows (straight lines) in space. 2:27. The movement of a (liberated) soul is without a bend. 48. Moritz, R. E., On Mathematics and Mathematicians, Dover, 1942,
New York, p. 152, 49. 2:25 Vigrahagatau karmayogāḥ
2:26 Anuśreņi gatiḥ 2.27 Avigrahā jivasya 2.28 Vigrahavati ca samsāriņah prākcaturbhyah 2.29 Ekasamayā avigrahā 2:30 Eka m dvau trinvā anāhārakah
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