A History of Hindu Chemistry from the Earliest Times to the Middle of the Sixteenth Century A.D. v2.c34.340

v2.c34.340

To conceive position in space, Váchaspati takes three axes, one proceeding from the point of sunrise in the horizon to that of sunset on any particular day ), ( roughly speaking, from the East to the West);—a second bisecting this line at right angles on the horizontal plane, ( roughly speaking, from the North to the South ), and the third proceeding from the point of their section up to the meridian position of the sun on that day, ( roughly speaking, up and down ). The position of any point in Space, relatively to another point, may now be given by measuring distances along these three directions, *i. e.* by arranging in a numerical series the intervening points of contact, the less magnitude or distance being that which comes earlier in this series, and the greater that which comes later. The position of any single atom in Space with reference to another may be indicated in this way with reference to the three axes. But this gives only a geometrical analysis of the conception of three-dimensioned Space, though it must be admitted in all fairness that by dint of clear thinking it anticipates in a rudimentary manner not only the foundations of solid (co-ordinate) geometry, but also of the geometry of position, and especially the conception of Space as a Manifold, which alone can serve as the basis of a generalisation comprehending all different possible kinds of geometry, Euclidean and non-Euclidean. (एकत्वेऽपि दिशः आदित्योदयदेशप्रत्यासन्नदेशसंयुक्तो यः स इतरस्माद्विप्रकृष्टदेशसंयोगात् परमाणोः पूर्वः एवमादित्यास्तमयदेशप्रत्यासन्नदेशसंयुक्तो यः स इतरस्माद्विप्रकृष्टदेशसंयोगात् परमाणोः पश्चिमः तौ च पूर्वपश्चिमौ परमाणू अपेक्ष्य यः सूर्योदयास्तमयदेशविप्रकृष्टदेशसंयोगः स मध्यवर्ती। एवमेतयोस्तौ तिर्यग्देशसम्बन्धिनौ मध्यस्य आर्जवेन व्यवस्थितौ पार्श्ववर्त्तिनौ तौ दक्षिणोत्तरौ परमाणू। एवं मध्यन्दिनवर्त्तिसूर्यसन्निकर्षाविप्रकर्षौ अपेक्ष्य उपर्यधोभावो द्रष्टव्यः। संयुक्तसंयोगात्पत्वभूयस्त्वे च सन्निकर्षविप्रकर्षौ पूर्व-संख्यावच्छिन्नत्वं च अल्पत्वं परसंख्यावच्छिन्नत्वं च भूयस्त्वम्। Váchaspati, Tátparyatíká, Chap. IV. A'hnika 2, Sútra 25.