The Positive Sciences of the Ancient Hindus c5.s7: Section 7. Notion of Three Axes
The Positive Sciences of the Ancient Hindus c5.s7
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Section 7. Notion of Three Axes
c5.s7.2
Motion, we have seen, was defined as the change of position of a particle in space. To conceive position in space, Vâchaspati takes three axes, and the position in space of one particle relatively to another may be indicated by distances measured along these three axes. This remarkable analysis (*circa* 842 A.D. : वस्वङ्कवसुवत्सरे, Vâchaspati, Nyâyasûchînibandha) anticipates in a rudimentary manner the foundations of solid (co-ordinate) geometry, eight centuries before Descartes (*vide* p. 118, *supra*).
c5.s7.3
*The Principle of the Differential Calculus applied to the Computation of Motion (Variable Motion).*
c5.s7.4
Bhâskara (1150 A.D.), in computing what he calls the “instantaneous” motion (तात्कालिकी गति) of a planet, compares its successive positions in two successive instants, and regards the motion as constant during the interval, which he conceives to be indefinitely small (त्रुटिकाल). This is equivalent to the determination of the differential of the planet’s longitude, and the process bears “a strong analogy” (to quote the words of Mr. Spottiswoode, the Astronomer Royal) “to the corresponding process in modern mathematical astronomy.” I have elsewhere shown that Bhâskara’s process was not merely analogous to, but virtually identical with, that of the Differential Calculus, Mr. Spottiswoode’s cautious reservation having been due to his want of acquaintance with the original and the insufficiency of the materials placed before him (*vide* pp. 78–79 *supra*).