1Koestler, Arthur (1959). The Sleepwalkers, p. 314, Hutchinson, London. The Sleepwalkers includes a fascinating account of Kepler's long struggle to reconcile the orbits of Mars with circular motion. The reference to spheres turning on spheres relates to the point that while the observed orbits of the planets did not exhibit perfect uniform circular motion, for early renaissance astronomers (including Copernicus) philosophical considerations demanded that they did so. One duty of early astronomers had been to ‘save the phenomena’ by using a variety of mathematical devices, e.g. some involved postulating that the planet's orbits were composed of circles upon circles. In this way regressions could be explained. Kepler eventually saw that the anomalies in the orbit of Mars could be explained by proposing that its path was elliptical. Viewed in contemporary terms this was very radical thinking.Google Scholar

2Goodman, D. C. (1973). Descartes Principles of Philosophy 1644 Article XXXVI, reprinted in Science and Religious Belief, p. 54, Dorset Press.Google Scholar

3 1974. Towards a Mechanistic Philosophy, p. 24. Open University Press.Google Scholar

4 1974. Towards a Mechanistic Philosophy p. 23. Open University Press.Google Scholar

5Towards a Mechanistic Philosophy p. 63. Open University Press.Google Scholar

6Towards a Mechanistic Philosophy p. 73. Open University Press.Google Scholar

7Descartes, ed. Goodman, p. 56, op cit.Google Scholar

8Towards a Mechanistic Philosophy, p. 23, op cit.Google Scholar

9 1970. Whiteside, D. T.‘Before the Principia’, Journal for the History of Astronomy, 1, p. 10.Google Scholar

10 1970. Whiteside, D. T.‘Before the Principia’, Journal for the History of Astronomy, 1, p. 10.Google Scholar

11 1971. Westfall, R. S.Force in Newton's Physics, Macdonald, London.Google Scholar

12 1924. Burtt, E. A.The Metaphysical Foundations of Modern Science, p. 136, Kegan Paul, London.Google Scholar

13Reprinted letter, Science and Religious Belief, op. cit. ed. Goodman, p. 132.Google Scholar

14Westfall, R. S. op cit., p. 377. With orthodox mechanical philosophy an aether is essential for action to be transferred through a distance.Google Scholar

15Westfall, R. S. op. cit., p. 378.Google Scholar

16Whiteside, D. T. op cit., p. 5.Google Scholar

17Brooke, John Hedley (1974). God said let Newton be, Open University Press.Google Scholar

18Cohen, I. B. (1961). The Grand Design—A New Physics, Chapter 7, Heinemann. Before the standardization of length it was common to relate it to that of the length of a pendulum which would beat specified time periods at a given location (latitude). A yard was usually related to the beat of a second.Google Scholar

19There is in fact some controversy over the originality of the idea of universal gravitation. Robert Hooke made an explicit statement of the idea in his Cutlerian Lecture of 1676 (published in 1674)—also see ‘The rational basis of Kepler's laws’, Forbes, Brit. Astr. Assoc., 1971, pp. 373–377. Newton can only claim that he had the idea earlier. However, it is mathematical analyses which distinguishes Newton's theories from Hooke's intuition, and which makes Newton the main author of the theory of gravitational attraction.Google Scholar

20Thayer, H. S.Newton's Philosophy of Nature, third letter to Bentley 1692 quoted from selections from his writings, p. 54, Hafner Press.Google Scholar

21Newton's Optics, Query 28, reprinted op cit., Hafner, p. 156.Google Scholar

22Westfall, R. S. op. cit., Newton manuscript quoted, p. 397.Google Scholar

23Brooke John Hedley, op cit., p. 5.Google Scholar

24Brooke John Hedley, op cit., p. 5.Google Scholar

25Westfall, R. S. op cit., p. 395. The other considerations are quoted as being its elasticity and density which Newton had calculated by experiments concerned with the velocity of light.Google Scholar

26Newton's Optics, Query 31.Google Scholar

27Newton's Optics, Query 31.Google Scholar

28Newton's Optics, Query 31.Google Scholar