Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical Optics

Journal of the History of Ideas

Volumn 58, Issue 2, 1997, Pages 265-286

  Malet, Antoni ^a  

^a NONE

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EID: 0007227969     PISSN: 00225037     EISSN: None     Source Type: Journal    
DOI: 10.2307/3653869     Document Type: Article

References (151)

1. See the "Life" which prefaces The Works of Isaac Barrow (4 vols.; London, 1683-87), and A. Hill, "Some Account of the Life of Dr. Isaac Barrow," in The Theological Works of Isaac Barrow, ed. A. Napier (9 vols.; Cambridge, 1859), 1, xxxvii-liv. For recent biographical studies, see M. Feingold and J. Gascoine in Before Newton: The life and times of Isaac Barrow, ed. M. Feingold (Cambridge, 1990).
2. See the "Life" which prefaces The Works of Isaac Barrow (4 vols.; London, 1683-87), and A. Hill, "Some Account of the Life of Dr. Isaac Barrow," in The Theological Works of Isaac Barrow, ed. A. Napier (9 vols.; Cambridge, 1859), 1, xxxvii-liv. For recent biographical studies, see M. Feingold and J. Gascoine in Before Newton: The life and times of Isaac Barrow, ed. M. Feingold (Cambridge, 1990).
3. See the "Life" which prefaces The Works of Isaac Barrow (4 vols.; London, 1683-87), and A. Hill, "Some Account of the Life of Dr. Isaac Barrow," in The Theological Works of Isaac Barrow, ed. A. Napier (9 vols.; Cambridge, 1859), 1, xxxvii-liv. For recent biographical studies, see M. Feingold and J. Gascoine in Before Newton: The life and times of Isaac Barrow, ed. M. Feingold (Cambridge, 1990).
4. J. Gascoigne, "Isaac Barrow's academic milieu: Interregnum and Restoration Cambridge," in Before Newton, 279-81.
5. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
6. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
7. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
8. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
9. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
10. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
11. Barrow's three main scientific works, written between 1664 and 1669, are Mathematical Lectures (1683), Optical Lectures (1669), and Geometrical Lectures (1670); quotations are from The Mathematical Works of Isaac Barrow, ed. W. Whewell (Cambridge, 1860). Unless otherwise stated, English quotations from Mathematical Lectures will come from John Kirkby's translation, The Usefulness of Mathematical Learning explained and demonstrated (London, 1734), and Optical Lectures from Isaac Barrow's Optical Lectures, eds. A. G. Bennett, D. F. Edgar, tr. H. C. Fay (London, 1987).
12. See F. Oakley, Omnipotence, Covenant, and Order: An Excursion in the History of Ideas from Abelard to Leibniz (London, etc., 1984); and "Christian Theology and the Newtonian Science: The Rise of the Concept of the Laws of Nature," Church History, 30 (1961), 433-57; K. Hutchison, "Supernaturalism and the Mechanical Philosophy," History of Science, 21 (1983), 297-333; E. B. Davis, "The uses of voluntarist theology in 17th-century science," Proceedings of the International Conference on Science and Belief (Pascal Centre for Advanced Studies in Faith and Science, Lancaster, August 1992, forthcoming), quotation comes from p. 3.
13. See F. Oakley, Omnipotence, Covenant, and Order: An Excursion in the History of Ideas from Abelard to Leibniz (London, etc., 1984); and "Christian Theology and the Newtonian Science: The Rise of the Concept of the Laws of Nature," Church History, 30 (1961), 433-57; K. Hutchison, "Supernaturalism and the Mechanical Philosophy," History of Science, 21 (1983), 297-333; E. B. Davis, "The uses of voluntarist theology in 17th-century science," Proceedings of the International Conference on Science and Belief (Pascal Centre for Advanced Studies in Faith and Science, Lancaster, August 1992, forthcoming), quotation comes from p. 3.
14. See F. Oakley, Omnipotence, Covenant, and Order: An Excursion in the History of Ideas from Abelard to Leibniz (London, etc., 1984); and "Christian Theology and the Newtonian Science: The Rise of the Concept of the Laws of Nature," Church History, 30 (1961), 433-57; K. Hutchison, "Supernaturalism and the Mechanical Philosophy," History of Science, 21 (1983), 297-333; E. B. Davis, "The uses of voluntarist theology in 17th-century science," Proceedings of the International Conference on Science and Belief (Pascal Centre for Advanced Studies in Faith and Science, Lancaster, August 1992, forthcoming), quotation comes from p. 3.
15. See F. Oakley, Omnipotence, Covenant, and Order: An Excursion in the History of Ideas from Abelard to Leibniz (London, etc., 1984); and "Christian Theology and the Newtonian Science: The Rise of the Concept of the Laws of Nature," Church History, 30 (1961), 433-57; K. Hutchison, "Supernaturalism and the Mechanical Philosophy," History of Science, 21 (1983), 297-333; E. B. Davis, "The uses of voluntarist theology in 17th-century science," Proceedings of the International Conference on Science and Belief (Pascal Centre for Advanced Studies in Faith and Science, Lancaster, August 1992, forthcoming), quotation comes from p. 3.
16. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
17. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
18. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
19. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
20. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
21. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
22. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
23. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
24. J. E. McGuire, "Boyle's Conception of Nature," JHI, 33 (1972), 523-42; J. Henry, "Henry More versus Robert Boyle: The Spirit of Nature and the Nature of Providence," in Henry More (1614-1687), ed. S. Hutton (Dordrecht, 1990), 55-76; S. Shapin, "Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice," Science in Context, 2 (1988), 32-58; M. Osier, "The Intellectual Sources of Robert Boyle's Philosophy of Nature: Gassendi's Voluntarism and Boyle's Physicotheological Project," in Philosophy, Science and Religion in England 1640-1700, eds. R. Kroll, et al. (Cambridge, 1992), 178-98; "Providence and Divine Will: Gassendi's Views on Scientific Knowledge," JHI, 44 (1983), 549-60; "Fortune, Fate, and Divination: Gassendi's Voluntarist Theology and the Baptism of Epicureanism," in Atoms, Pneuma, and Tranquillity, ed. M. J. Osler (Cambridge, 1991), 155-74; "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes's Philosophy of Nature," JHI, 46 (1985), 349-62; J. E. Force, R. H. Popkin, Essays on the Context, Nature and Influence of Isaac Newton's Theology (Dordrecht, 1990); D. Kubrin, "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy," JHI, 28 (1967), 325-46.
25. F. E. Manuel, The Religion of Isaac Newton (Oxford, 1974), 42.
26. Usefulness of Mathematical Learning, 88-89.
27. Ibid., 89-90.
28. Ibid., 90.
29. Ibid., 74. Newton will secularize this idea in his famous remark about nature being "wont to be simple and always consonant to itself"; cf. E. McMullin, Newton on Matter and Activity (Notre Dame, 1978), 13-20.
30. Ibid., 74. Newton will secularize this idea in his famous remark about nature being "wont to be simple and always consonant to itself"; cf. E. McMullin, Newton on Matter and Activity (Notre Dame, 1978), 13-20.
31. "The Being of God Proved from the Frame of Human Nature," Works, II, 105. Newton set forth the notion that God can move bodies in infinite space as souls move human bodies in his De gravitatione; see, Unpublished Scientific Papers of Isaac Newton, eds. A. R. Hall and M. B. Hall (Cambridge, 1962), 141-43. E. B. Davis, "Newton's Rejection of the 'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy," Science and Christian Belief, 3 (1991), 103-17, shows that the metaphor reappears in many places in Newton's papers.
32. "The Being of God Proved from the Frame of Human Nature," Works, II, 105. Newton set forth the notion that God can move bodies in infinite space as souls move human bodies in his De gravitatione; see, Unpublished Scientific Papers of Isaac Newton, eds. A. R. Hall and M. B. Hall (Cambridge, 1962), 141-43. E. B. Davis, "Newton's Rejection of the 'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy," Science and Christian Belief, 3 (1991), 103-17, shows that the metaphor reappears in many places in Newton's papers.
33. "The Being of God Proved from the Frame of Human Nature," Works, II, 105. Newton set forth the notion that God can move bodies in infinite space as souls move human bodies in his De gravitatione; see, Unpublished Scientific Papers of Isaac Newton, eds. A. R. Hall and M. B. Hall (Cambridge, 1962), 141-43. E. B. Davis, "Newton's Rejection of the 'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy," Science and Christian Belief, 3 (1991), 103-17, shows that the metaphor reappears in many places in Newton's papers.
34. "A Sermon on the Gunpowder Treason," Works, I, 144. See Essays on Newton's Theology, 144-49.
35. "A Sermon on the Gunpowder Treason," Works, I, 144. See Essays on Newton's Theology, 144-49.
36. "The unsearchableness of God's Judgments," Works, III, 263. See also "The Being of God Proved from Supernatural Effects," ibid., II, 128-29.
37. "The unsearchableness of God's Judgments," Works, III, 263. See also "The Being of God Proved from Supernatural Effects," ibid., II, 128-29.
38. Ibid., II, 130.
39. "The Being of God Proved from the Frame of Human Nature," ibid., II, 105.
40. "Maker of Heaven and Earth," ibid., II, 178-79. Barrow insists on this notion on page 184. Compare with Newton, Unpublished Scientific Papers, 138-41. For instance: "it must be agreed that God, by the sole action of thinking and willing, can prevent a body from penetrating any space defined by Certain limits" (ibid., 139).
41. "Maker of Heaven and Earth," ibid., II, 178-79. Barrow insists on this notion on page 184. Compare with Newton, Unpublished Scientific Papers, 138-41. For instance: "it must be agreed that God, by the sole action of thinking and willing, can prevent a body from penetrating any space defined by Certain limits" (ibid., 139).
42. "Maker of Heaven and Earth," ibid., II, 178-79. Barrow insists on this notion on page 184. Compare with Newton, Unpublished Scientific Papers, 138-41. For instance: "it must be agreed that God, by the sole action of thinking and willing, can prevent a body from penetrating any space defined by Certain limits" (ibid., 139).
43. See E. B. Davis's "Newton's Rejection of the 'Newtonian World View,'" 114-16. From a manuscript of Newton's kept at the Lehigh University library, Davis quotes the following fragment: "For Miracles are so called not because they are the works of God but because they happen seldom and for that reason create wonder...." See also, Sir Isaac Newton Theological Manuscripts, ed. H. McLachlan (Liverpool, 1950), 17-18; and H. Guerlac and M. C. Jacob, "Bentley, Newton, and Providence (The Boyle Lectures Once More)," JHI, 30 (1969), 307-18.
44. See E. B. Davis's "Newton's Rejection of the 'Newtonian World View,'" 114-16. From a manuscript of Newton's kept at the Lehigh University library, Davis quotes the following fragment: "For Miracles are so called not because they are the works of God but because they happen seldom and for that reason create wonder...." See also, Sir Isaac Newton Theological Manuscripts, ed. H. McLachlan (Liverpool, 1950), 17-18; and H. Guerlac and M. C. Jacob, "Bentley, Newton, and Providence (The Boyle Lectures Once More)," JHI, 30 (1969), 307-18.
45. See E. B. Davis's "Newton's Rejection of the 'Newtonian World View,'" 114-16. From a manuscript of Newton's kept at the Lehigh University library, Davis quotes the following fragment: "For Miracles are so called not because they are the works of God but because they happen seldom and for that reason create wonder...." See also, Sir Isaac Newton Theological Manuscripts, ed. H. McLachlan (Liverpool, 1950), 17-18; and H. Guerlac and M. C. Jacob, "Bentley, Newton, and Providence (The Boyle Lectures Once More)," JHI, 30 (1969), 307-18.
46. "The Father Almighty," Works, II, 157.
47. "Maker of Heaven and Earth," ibid., II, 175-76 (Barrow's emphasis).
48. "The Being of God Proved from the Frame of Human Nature," ibid., II, 103.
49. Ibid.
50. Ibid., 178.
51. Ibid.
52. "The Unserchableness of God's Judgments," ibid., III, 263.
53. According to M. Nicholson, "The Early Stage of Cartesianism in England," Studies in Philology, 26 (1929), 362-64, More was teaching Descartes's Dioptrics and Meteors in the 1670s; see also A. Gabbey, "Philosophia Cartesiana Triumphata: Henry More (1646-1671)," Problems of Cartesianism, eds. T. M. Lennon, J. M. Nicholas, J. W. Davis (Kingston, 1982), 171-250; "Henry More and the Limits of Mechanism," Henry More, 19-35; C. Webster, "Henry More and Descartes: Some New Sources," British Journal for the History of Science, 4 (1969), 359-77. On More's "antidote" to mechanicism, see the More-Worthington correspondence, as quoted in A. R. Hall, Henry More: Magic, Religion and Experiment (Oxford, 1990), 158.
54. According to M. Nicholson, "The Early Stage of Cartesianism in England," Studies in Philology, 26 (1929), 362-64, More was teaching Descartes's Dioptrics and Meteors in the 1670s; see also A. Gabbey, "Philosophia Cartesiana Triumphata: Henry More (1646-1671)," Problems of Cartesianism, eds. T. M. Lennon, J. M. Nicholas, J. W. Davis (Kingston, 1982), 171-250; "Henry More and the Limits of Mechanism," Henry More, 19-35; C. Webster, "Henry More and Descartes: Some New Sources," British Journal for the History of Science, 4 (1969), 359-77. On More's "antidote" to mechanicism, see the More-Worthington correspondence, as quoted in A. R. Hall, Henry More: Magic, Religion and Experiment (Oxford, 1990), 158.
55. According to M. Nicholson, "The Early Stage of Cartesianism in England," Studies in Philology, 26 (1929), 362-64, More was teaching Descartes's Dioptrics and Meteors in the 1670s; see also A. Gabbey, "Philosophia Cartesiana Triumphata: Henry More (1646-1671)," Problems of Cartesianism, eds. T. M. Lennon, J. M. Nicholas, J. W. Davis (Kingston, 1982), 171-250; "Henry More and the Limits of Mechanism," Henry More, 19-35; C. Webster, "Henry More and Descartes: Some New Sources," British Journal for the History of Science, 4 (1969), 359-77. On More's "antidote" to mechanicism, see the More-Worthington correspondence, as quoted in A. R. Hall, Henry More: Magic, Religion and Experiment (Oxford, 1990), 158.
56. According to M. Nicholson, "The Early Stage of Cartesianism in England," Studies in Philology, 26 (1929), 362-64, More was teaching Descartes's Dioptrics and Meteors in the 1670s; see also A. Gabbey, "Philosophia Cartesiana Triumphata: Henry More (1646-1671)," Problems of Cartesianism, eds. T. M. Lennon, J. M. Nicholas, J. W. Davis (Kingston, 1982), 171-250; "Henry More and the Limits of Mechanism," Henry More, 19-35; C. Webster, "Henry More and Descartes: Some New Sources," British Journal for the History of Science, 4 (1969), 359-77. On More's "antidote" to mechanicism, see the More-Worthington correspondence, as quoted in A. R. Hall, Henry More: Magic, Religion and Experiment (Oxford, 1990), 158.
57. According to M. Nicholson, "The Early Stage of Cartesianism in England," Studies in Philology, 26 (1929), 362-64, More was teaching Descartes's Dioptrics and Meteors in the 1670s; see also A. Gabbey, "Philosophia Cartesiana Triumphata: Henry More (1646-1671)," Problems of Cartesianism, eds. T. M. Lennon, J. M. Nicholas, J. W. Davis (Kingston, 1982), 171-250; "Henry More and the Limits of Mechanism," Henry More, 19-35; C. Webster, "Henry More and Descartes: Some New Sources," British Journal for the History of Science, 4 (1969), 359-77. On More's "antidote" to mechanicism, see the More-Worthington correspondence, as quoted in A. R. Hall, Henry More: Magic, Religion and Experiment (Oxford, 1990), 158.
58. John Henry, "A Cambridge Platonist's materialism: Henry More and the Concept of Soul," Journal of the Warburg and Courtauld Institutes, 49 (1986), 172-95; "Medicine and Pneumatology: Henry More, Richard Baxter, and Francis Glisson's Treatise on the Energetic Nature of Substance," Medical History, 31 (1987), 15-40; "Occult Qualities and the Experimental Philosophy: Active Principles in Pre-Newtonian Matter Theory," History of Science, 24 (1986), 335-81; and "Matter in Motion: The Problem of Activity in Seventeenth-century English Matter Theory" (Ph.D. diss., The Open University, 1983).
59. John Henry, "A Cambridge Platonist's materialism: Henry More and the Concept of Soul," Journal of the Warburg and Courtauld Institutes, 49 (1986), 172-95; "Medicine and Pneumatology: Henry More, Richard Baxter, and Francis Glisson's Treatise on the Energetic Nature of Substance," Medical History, 31 (1987), 15-40; "Occult Qualities and the Experimental Philosophy: Active Principles in Pre-Newtonian Matter Theory," History of Science, 24 (1986), 335-81; and "Matter in Motion: The Problem of Activity in Seventeenth-century English Matter Theory" (Ph.D. diss., The Open University, 1983).
60. John Henry, "A Cambridge Platonist's materialism: Henry More and the Concept of Soul," Journal of the Warburg and Courtauld Institutes, 49 (1986), 172-95; "Medicine and Pneumatology: Henry More, Richard Baxter, and Francis Glisson's Treatise on the Energetic Nature of Substance," Medical History, 31 (1987), 15-40; "Occult Qualities and the Experimental Philosophy: Active Principles in Pre-Newtonian Matter Theory," History of Science, 24 (1986), 335-81; and "Matter in Motion: The Problem of Activity in Seventeenth-century English Matter Theory" (Ph.D. diss., The Open University, 1983).
61. John Henry, "A Cambridge Platonist's materialism: Henry More and the Concept of Soul," Journal of the Warburg and Courtauld Institutes, 49 (1986), 172-95; "Medicine and Pneumatology: Henry More, Richard Baxter, and Francis Glisson's Treatise on the Energetic Nature of Substance," Medical History, 31 (1987), 15-40; "Occult Qualities and the Experimental Philosophy: Active Principles in Pre-Newtonian Matter Theory," History of Science, 24 (1986), 335-81; and "Matter in Motion: The Problem of Activity in Seventeenth-century English Matter Theory" (Ph.D. diss., The Open University, 1983).
62. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
63. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
64. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
65. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
66. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
67. M. Hunter, "Science and Heterodoxy: An early modern problem reconsidered," Reappraisals of the Scientific Revolution, eds. D. C. Lindberg and R. S. Westman (Cambridge, 1990), 437-60; "'Aikenhead the Atheist': The Context and Consequences of Articulate Irreligion in the Late Seventeenth Century," Atheism from the Reformation to the Enlightenment, eds. M. Hunter and D. Wootton (Oxford, 1992), 221-54. See also S. I. Mintz, The Hunting of Leviathan: Seventeenth-Century Reactions to the Materialism and Moral Philosophy of Thomas Hobbes (Cambridge, 1970), 69-88; R. L. Colie, Light and Enlightenment: A Study of the Cambridge Platonists and the Dutch Arminians (Cambridge, 1957); J. Redwood, Reason, Ridicule and Religion: The Age of the Enlightenment in England 1660-1750 (London, 1976); and O. Mayr, Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore, 1986).
68. Antidote Against Atheism (1712), 141, quoted in Mintz, Hunting of Leviathan, 88.
69. Antidote Against Atheism (1712), 141, quoted in Mintz, Hunting of Leviathan, 88.
70. See J. G. Lennox, "Aristotle, Galileo, and 'Mixed Sciences,'" Reinterpreting Galileo, ed. W. A. Wallace (Washington, D.C., 1986), 29-51; R. D. McKirahan Jr., "Aristotle's Subordinate Sciences," British Journal for the History of Science, 11 (1978), 197-220; W. A. Wallace, "Aristotelian Influences on Galileo's Thought," Aristotelismo veneto e scienza moderna, ed. L. Olivieri (2 vols.; Padua, 1983), I, 349-78; S. J. Livesey, "William of Ockham, the Subalternate Sciences, and Aristotle's Prohibition of Meta-basis," British Journal for the History of Science, 18 (1985), 127-45. The mixed mathematical sciences of the late seventeenth century have received little attention, but see J. A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy," History of Science, 24 (1986), 1-28
71. See J. G. Lennox, "Aristotle, Galileo, and 'Mixed Sciences,'" Reinterpreting Galileo, ed. W. A. Wallace (Washington, D.C., 1986), 29-51; R. D. McKirahan Jr., "Aristotle's Subordinate Sciences," British Journal for the History of Science, 11 (1978), 197-220; W. A. Wallace, "Aristotelian Influences on Galileo's Thought," Aristotelismo veneto e scienza moderna, ed. L. Olivieri (2 vols.; Padua, 1983), I, 349-78; S. J. Livesey, "William of Ockham, the Subalternate Sciences, and Aristotle's Prohibition of Meta-basis," British Journal for the History of Science, 18 (1985), 127-45. The mixed mathematical sciences of the late seventeenth century have received little attention, but see J. A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy," History of Science, 24 (1986), 1-28
72. See J. G. Lennox, "Aristotle, Galileo, and 'Mixed Sciences,'" Reinterpreting Galileo, ed. W. A. Wallace (Washington, D.C., 1986), 29-51; R. D. McKirahan Jr., "Aristotle's Subordinate Sciences," British Journal for the History of Science, 11 (1978), 197-220; W. A. Wallace, "Aristotelian Influences on Galileo's Thought," Aristotelismo veneto e scienza moderna, ed. L. Olivieri (2 vols.; Padua, 1983), I, 349-78; S. J. Livesey, "William of Ockham, the Subalternate Sciences, and Aristotle's Prohibition of Meta-basis," British Journal for the History of Science, 18 (1985), 127-45. The mixed mathematical sciences of the late seventeenth century have received little attention, but see J. A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy," History of Science, 24 (1986), 1-28
73. See J. G. Lennox, "Aristotle, Galileo, and 'Mixed Sciences,'" Reinterpreting Galileo, ed. W. A. Wallace (Washington, D.C., 1986), 29-51; R. D. McKirahan Jr., "Aristotle's Subordinate Sciences," British Journal for the History of Science, 11 (1978), 197-220; W. A. Wallace, "Aristotelian Influences on Galileo's Thought," Aristotelismo veneto e scienza moderna, ed. L. Olivieri (2 vols.; Padua, 1983), I, 349-78; S. J. Livesey, "William of Ockham, the Subalternate Sciences, and Aristotle's Prohibition of Meta-basis," British Journal for the History of Science, 18 (1985), 127-45. The mixed mathematical sciences of the late seventeenth century have received little attention, but see J. A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy," History of Science, 24 (1986), 1-28
74. See J. G. Lennox, "Aristotle, Galileo, and 'Mixed Sciences,'" Reinterpreting Galileo, ed. W. A. Wallace (Washington, D.C., 1986), 29-51; R. D. McKirahan Jr., "Aristotle's Subordinate Sciences," British Journal for the History of Science, 11 (1978), 197-220; W. A. Wallace, "Aristotelian Influences on Galileo's Thought," Aristotelismo veneto e scienza moderna, ed. L. Olivieri (2 vols.; Padua, 1983), I, 349-78; S. J. Livesey, "William of Ockham, the Subalternate Sciences, and Aristotle's Prohibition of Meta-basis," British Journal for the History of Science, 18 (1985), 127-45. The mixed mathematical sciences of the late seventeenth century have received little attention, but see J. A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy," History of Science, 24 (1986), 1-28
75. McKirahan, "Aristotle's Subordinate Sciences," 201.
76. See Theology and Science in the Fourteenth Century: The Questions on the Unity and Subalternation of the Sciences from John of Reading 's Commentary on the Sentences, ed. S. J. Livesey (Leiden, 1989), 22-53; and N. Jardine, "Epistemology of the Sciences," and W. A. Wallace, "Traditional Natural Philosophy," Cambridge History of Renaissance Philosophy, eds. C. B. Schmitt et al. (Cambridge, 1988), 685-711 and 201-35.
77. See Theology and Science in the Fourteenth Century: The Questions on the Unity and Subalternation of the Sciences from John of Reading 's Commentary on the Sentences, ed. S. J. Livesey (Leiden, 1989), 22-53; and N. Jardine, "Epistemology of the Sciences," and W. A. Wallace, "Traditional Natural Philosophy," Cambridge History of Renaissance Philosophy, eds. C. B. Schmitt et al. (Cambridge, 1988), 685-711 and 201-35.
78. See Theology and Science in the Fourteenth Century: The Questions on the Unity and Subalternation of the Sciences from John of Reading 's Commentary on the Sentences, ed. S. J. Livesey (Leiden, 1989), 22-53; and N. Jardine, "Epistemology of the Sciences," and W. A. Wallace, "Traditional Natural Philosophy," Cambridge History of Renaissance Philosophy, eds. C. B. Schmitt et al. (Cambridge, 1988), 685-711 and 201-35.
79. McKirahan, "Aristotle's Subordinate Sciences," 199-201; A. Lejeune, Euclide et Ptolémée, deux stades de l'optique géométrique grecque (Louvaine, 1948).
80. McKirahan, "Aristotle's Subordinate Sciences," 199-201; A. Lejeune, Euclide et Ptolémée, deux stades de l'optique géométrique grecque (Louvaine, 1948).
81. Euclide, L'optique et la catoptrique, ed. P. Ver Eecke (Paris, 1959), determination IV, 1. P. Dear, "Jesuit Mathematical Science and the Reconstitution of Experience in the Early Seventeenth Century," Studies in History and Philosophy of Science, 18 (1987), 133-75.
82. Euclide, L'optique et la catoptrique, ed. P. Ver Eecke (Paris, 1959), determination IV, 1. P. Dear, "Jesuit Mathematical Science and the Reconstitution of Experience in the Early Seventeenth Century," Studies in History and Philosophy of Science, 18 (1987), 133-75.
83. See P. Dear, Mersenne and the Learning of the Schools (Ithaca, N.Y., 1988), 62-66. See A. Malet, "Mathematics and Mathematization in the Seventeenth Century," Studies in the History and Philosophy of Science, 22 (1991), 673-78.
84. See P. Dear, Mersenne and the Learning of the Schools (Ithaca, N.Y., 1988), 62-66. See A. Malet, "Mathematics and Mathematization in the Seventeenth Century," Studies in the History and Philosophy of Science, 22 (1991), 673-78.
85. N. Jardine, "Epistemology of the Sciences," 709-10.
86. On Hobbes and definition, see Mintz, Hunting of Leviathan, 24-25; S. Shapin, S. Schaffer, Leviathan and the Air-Pump (Princeton, 1985), 100-101. See Roberval, "Avant-propos sur les mathématiques," published in V. Cousin, "Roberval philosophe," Fragments philosophiques pour servir à l'histoire de la philosophie (5 vols.; Paris, 1866), III, 229-58, especially 236.
87. On Hobbes and definition, see Mintz, Hunting of Leviathan, 24-25; S. Shapin, S. Schaffer, Leviathan and the Air-Pump (Princeton, 1985), 100-101. See Roberval, "Avant-propos sur les mathématiques," published in V. Cousin, "Roberval philosophe," Fragments philosophiques pour servir à l'histoire de la philosophie (5 vols.; Paris, 1866), III, 229-58, especially 236.
88. On Hobbes and definition, see Mintz, Hunting of Leviathan, 24-25; S. Shapin, S. Schaffer, Leviathan and the Air-Pump (Princeton, 1985), 100-101. See Roberval, "Avant-propos sur les mathématiques," published in V. Cousin, "Roberval philosophe," Fragments philosophiques pour servir à l'histoire de la philosophie (5 vols.; Paris, 1866), III, 229-58, especially 236.
89. On Hobbes and definition, see Mintz, Hunting of Leviathan, 24-25; S. Shapin, S. Schaffer, Leviathan and the Air-Pump (Princeton, 1985), 100-101. See Roberval, "Avant-propos sur les mathématiques," published in V. Cousin, "Roberval philosophe," Fragments philosophiques pour servir à l'histoire de la philosophie (5 vols.; Paris, 1866), III, 229-58, especially 236.
90. Usefulness of Mathematical Learning, 120-21.
91. Usefulness of Mathematical Learning, 109.
92. Ibid., 110.
93. Ibid.
94. Mathematical Works, 112 (my translation).
95. "Maker of Heaven and Earth," Works, II, 183. The "many worlds" debate has been often boundup with theological discussions on God's omnipotence. Cf. S. J. Dick, Plurality of Worlds: The Origins of the Extraterrestrial Life Debate from Democritus to Kant (Cambridge, 1984), 23ff; A. Funkenstein, Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century (Princeton, 1986), 163ff.
96. "Maker of Heaven and Earth," Works, II, 183. The "many worlds" debate has been often boundup with theological discussions on God's omnipotence. Cf. S. J. Dick, Plurality of Worlds: The Origins of the Extraterrestrial Life Debate from Democritus to Kant (Cambridge, 1984), 23ff; A. Funkenstein, Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century (Princeton, 1986), 163ff.
97. "Maker of Heaven and Earth," Works, II, 183. The "many worlds" debate has been often boundup with theological discussions on God's omnipotence. Cf. S. J. Dick, Plurality of Worlds: The Origins of the Extraterrestrial Life Debate from Democritus to Kant (Cambridge, 1984), 23ff; A. Funkenstein, Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century (Princeton, 1986), 163ff.
98. Dobbs, Janus Faces of Genius, 114. As is well known, eventually Newton published it in Query 31 of the Opticks.
99. R. Boyle, Reconcileableness of Reason and Religion, in Works, IV, 159 (quoted by Oakley, Omnipotence, Covenant, and Order, 88). On Newton's articulation of the principle in the early 1670s, see Dobbs, Janus Faces of Genius, 113-14.
100. R. Boyle, Reconcileableness of Reason and Religion, in Works, IV, 159 (quoted by Oakley, Omnipotence, Covenant, and Order, 88). On Newton's articulation of the principle in the early 1670s, see Dobbs, Janus Faces of Genius, 113-14.
101. R. Boyle, Reconcileableness of Reason and Religion, in Works, IV, 159 (quoted by Oakley, Omnipotence, Covenant, and Order, 88). On Newton's articulation of the principle in the early 1670s, see Dobbs, Janus Faces of Genius, 113-14.
102. "Maker of Heaven and Earth," Works, II, 174-76; quotations come from page 176. Compare with Stillingfleet, Origines sacrae (London, 1662), 445, and 229-30, 367-68.
103. "Maker of Heaven and Earth," Works, II, 174-76; quotations come from page 176. Compare with Stillingfleet, Origines sacrae (London, 1662), 445, and 229-30, 367-68.
104. Usefulness of Mathematical Learning, 13, 16, 19; quotation comes from 19.
105. Barrow devoted the whole Lecture III to analyzing the relationship between arithmetic and geometry.
106. Usefulness of Mathematical Learning, 20-21; quotation comes from 21.
107. "E quibus autumo satis liquido constare (quod mihi propositum fuerat ostendere) Mathematicam, habitam dictamque vulgo, ipsi Physicae quasi coextendi et adaequari"; cf. Mathematical Works, 44 (I have modified Kirkby's translation).
108. Usefulness of Mathematical Learning, 24.
109. Ibid., 27.
110. Ibid.
111. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
112. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
113. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
114. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
115. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
116. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
117. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
118. A. C. Crombie, "Mathematics and Platonism in the sixteenth-century Italian Universities and in Jesuit Educational Policy," Prismata: Naturwissenschaftsgeschichtliche, eds. Y. Maeyama and W. G. Saltzer (Wiesbaden, 1977), 63-94; G. C. Giacobbe, "Il Commentarium de certitudine mathematicarum disciplinarum di Alessandro Piccolomini," Physis, 14 (1972), 162-93; "La riflessione metamatematica di Pietro Catena," Physis, 15, (1973), 178-96; "Epigoni del seicento della 'quaestio de certitudine mathematicarum': Giuseppe Biancani," Physis, 18 (1976), 5-40; "Un gesuita progresista nella 'Quaestio de certitudine mathematicarum' rinascimentale: Benito Pereyra," Physis, 19 (1977), 51-86; A. Carugo, "Giuseppe Moleto: Mathematics and the Aristotelian Theory of Science at Padua in the Second Half of the Sixteenth Century," Aristotelismo veneto e scienza moderna, 509-17; P. Mancosu, "Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of the Quaestio de Certitudine Mathematicarum," Stud. Hist. Phil. Sci., 23 (1992), 241-65; M. R. Davi Daniele, "Bernardino Tomitano e la quaestio de certitudine mathematicarum," Aristotelismo veneto e scienza moderna, 607-21.
119. "The Social Status of Italian Mathematicians, 1450-1600," Hist. Sci., 27 (1989), 41-95; "The Anthropology of Incommensurability," Studies in the History and Philosophy of Science, 21 (1990), 183-209. See also his "Galileo's System of Patronage," History of Science, 28 (1990), 1-62.
120. "The Social Status of Italian Mathematicians, 1450-1600," Hist. Sci., 27 (1989), 41-95; "The Anthropology of Incommensurability," Studies in the History and Philosophy of Science, 21 (1990), 183-209. See also his "Galileo's System of Patronage," History of Science, 28 (1990), 1-62.
121. "The Social Status of Italian Mathematicians, 1450-1600," Hist. Sci., 27 (1989), 41-95; "The Anthropology of Incommensurability," Studies in the History and Philosophy of Science, 21 (1990), 183-209. See also his "Galileo's System of Patronage," History of Science, 28 (1990), 1-62.
122. See M. R. Davi Daniele, "Bernardino Tomitano," 615ff; Mancosu, "Aristotelian Logic," 261.
123. See M. R. Davi Daniele, "Bernardino Tomitano," 615ff; Mancosu, "Aristotelian Logic," 261.
124. Barrow, Usefulness of Mathematical Learning, 85. Anachronistically speaking, a passio propria is a necessary and sufficient condition.
125. McKirahan, "Aristotle's Subordinate Sciences," 204.
126. Usefulness of Mathematical Learning, 86.
127. Ibid., 88.
128. Ibid., 99.
129. See A. I. Sabra, Theories of Light from Descartes to Newton (London, 1967); A. E. Shapiro, "Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century," Archive for the History of Exact Sciences, 11 (1973), 134-266; P. Duhem, "L'optique de Malebranche," Revue de métaphysique et de la morale, 23 (1916), 37-91. In Restoration England, Hooke was essentially alone in embracing an undulatory theory of light.
130. See A. I. Sabra, Theories of Light from Descartes to Newton (London, 1967); A. E. Shapiro, "Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century," Archive for the History of Exact Sciences, 11 (1973), 134-266; P. Duhem, "L'optique de Malebranche," Revue de métaphysique et de la morale, 23 (1916), 37-91. In Restoration England, Hooke was essentially alone in embracing an undulatory theory of light.
131. See A. I. Sabra, Theories of Light from Descartes to Newton (London, 1967); A. E. Shapiro, "Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century," Archive for the History of Exact Sciences, 11 (1973), 134-266; P. Duhem, "L'optique de Malebranche," Revue de métaphysique et de la morale, 23 (1916), 37-91. In Restoration England, Hooke was essentially alone in embracing an undulatory theory of light.
132. See R. Kargon, Atomism in England from Hariot to Newton (Oxford, 1966), 78-79 and 118-21; and A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
133. See R. Kargon, Atomism in England from Hariot to Newton (Oxford, 1966), 78-79 and 118-21; and A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
134. Mathematical Works, 18. There are many declarations to the same purpose in the first two lectures.
135. On Gregorie's optics, see A. Malet, "Studies on James Gregorie (1638-1675)" (Ph.D. Diss., Princeton University, 1989), 99-173; and "Gregorie, Descartes, Kepler, and the Law of Refraction," Archives Internationales d'Histoire des Sciences, 40 (1990), 278-304. On the Keplerian pre-history of the mathematics of focal points, see A. Malet, "Keplerian Illusions: Geometrical Pictures versus Optical Images in Kepler's Visual Theory," Studies in the History and Philosophy of Science, 21 (1990), 1-40. For a discussion of the technicalities of Barrow's Optical Lectures and its reception through the eighteenth century, see A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
136. On Gregorie's optics, see A. Malet, "Studies on James Gregorie (1638-1675)" (Ph.D. Diss., Princeton University, 1989), 99-173; and "Gregorie, Descartes, Kepler, and the Law of Refraction," Archives Internationales d'Histoire des Sciences, 40 (1990), 278-304. On the Keplerian pre-history of the mathematics of focal points, see A. Malet, "Keplerian Illusions: Geometrical Pictures versus Optical Images in Kepler's Visual Theory," Studies in the History and Philosophy of Science, 21 (1990), 1-40. For a discussion of the technicalities of Barrow's Optical Lectures and its reception through the eighteenth century, see A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
137. On Gregorie's optics, see A. Malet, "Studies on James Gregorie (1638-1675)" (Ph.D. Diss., Princeton University, 1989), 99-173; and "Gregorie, Descartes, Kepler, and the Law of Refraction," Archives Internationales d'Histoire des Sciences, 40 (1990), 278-304. On the Keplerian pre-history of the mathematics of focal points, see A. Malet, "Keplerian Illusions: Geometrical Pictures versus Optical Images in Kepler's Visual Theory," Studies in the History and Philosophy of Science, 21 (1990), 1-40. For a discussion of the technicalities of Barrow's Optical Lectures and its reception through the eighteenth century, see A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
138. On Gregorie's optics, see A. Malet, "Studies on James Gregorie (1638-1675)" (Ph.D. Diss., Princeton University, 1989), 99-173; and "Gregorie, Descartes, Kepler, and the Law of Refraction," Archives Internationales d'Histoire des Sciences, 40 (1990), 278-304. On the Keplerian pre-history of the mathematics of focal points, see A. Malet, "Keplerian Illusions: Geometrical Pictures versus Optical Images in Kepler's Visual Theory," Studies in the History and Philosophy of Science, 21 (1990), 1-40. For a discussion of the technicalities of Barrow's Optical Lectures and its reception through the eighteenth century, see A. E. Shapiro, "The Optical Lectures," in M. Feingold (ed.), Before Newton, 105-78.
139. See L. S. Joy, Gassendi the Atomist (Cambridge, 1987), 123-24; O. R. Bloch, La philosophie de Gassendi (La Haye, 1971), 15ff. J. Locke, Essay Concerning Human Understanding (2 vols.; Oxford, 1894), I, 219-25. R. Boyle, A Discourse of Things above Reason, in Works (London, 1772), IV, 406-69, p. 414. R. Descartes, La Dioptrique, in C. Adam, P. Tannery (eds.), Oeuvres de Descartes (12 vols.; Paris, 1897-1910), VI, 144. On Roberval and Huygens, see below.
140. See L. S. Joy, Gassendi the Atomist (Cambridge, 1987), 123-24; O. R. Bloch, La philosophie de Gassendi (La Haye, 1971), 15ff. J. Locke, Essay Concerning Human Understanding (2 vols.; Oxford, 1894), I, 219-25. R. Boyle, A Discourse of Things above Reason, in Works (London, 1772), IV, 406-69, p. 414. R. Descartes, La Dioptrique, in C. Adam, P. Tannery (eds.), Oeuvres de Descartes (12 vols.; Paris, 1897-1910), VI, 144. On Roberval and Huygens, see below.
141. See L. S. Joy, Gassendi the Atomist (Cambridge, 1987), 123-24; O. R. Bloch, La philosophie de Gassendi (La Haye, 1971), 15ff. J. Locke, Essay Concerning Human Understanding (2 vols.; Oxford, 1894), I, 219-25. R. Boyle, A Discourse of Things above Reason, in Works (London, 1772), IV, 406-69, p. 414. R. Descartes, La Dioptrique, in C. Adam, P. Tannery (eds.), Oeuvres de Descartes (12 vols.; Paris, 1897-1910), VI, 144. On Roberval and Huygens, see below.
142. See L. S. Joy, Gassendi the Atomist (Cambridge, 1987), 123-24; O. R. Bloch, La philosophie de Gassendi (La Haye, 1971), 15ff. J. Locke, Essay Concerning Human Understanding (2 vols.; Oxford, 1894), I, 219-25. R. Boyle, A Discourse of Things above Reason, in Works (London, 1772), IV, 406-69, p. 414. R. Descartes, La Dioptrique, in C. Adam, P. Tannery (eds.), Oeuvres de Descartes (12 vols.; Paris, 1897-1910), VI, 144. On Roberval and Huygens, see below.
143. See L. S. Joy, Gassendi the Atomist (Cambridge, 1987), 123-24; O. R. Bloch, La philosophie de Gassendi (La Haye, 1971), 15ff. J. Locke, Essay Concerning Human Understanding (2 vols.; Oxford, 1894), I, 219-25. R. Boyle, A Discourse of Things above Reason, in Works (London, 1772), IV, 406-69, p. 414. R. Descartes, La Dioptrique, in C. Adam, P. Tannery (eds.), Oeuvres de Descartes (12 vols.; Paris, 1897-1910), VI, 144. On Roberval and Huygens, see below.
144. See, for instance, Mathematical Works, 118, where he corrects Galileo, and 101, where he explains a phenomenon "of substantial advantage in the making of telescopes." For instances of observations and experiments adduced as corroboration of his theory, see Mathematical Works, Lecture IV, §21, 53; V, §20, 61; V, §22, 63-64; VI, §19, 69; VII, §21, 76; X, §26, 93-94; XV, appendix, 133-36; XVI, §14, 140-41. Barrow's handling of observations and experiments ranges from the trivial to the sophisticated. I have analyzed in full and technical detail this facet of Barrow's optics in "Studies on James Gregorie (1638-1675)," 158-62, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
145. See, for instance, Mathematical Works, 118, where he corrects Galileo, and 101, where he explains a phenomenon "of substantial advantage in the making of telescopes." For instances of observations and experiments adduced as corroboration of his theory, see Mathematical Works, Lecture IV, §21, 53; V, §20, 61; V, §22, 63-64; VI, §19, 69; VII, §21, 76; X, §26, 93-94; XV, appendix, 133-36; XVI, §14, 140-41. Barrow's handling of observations and experiments ranges from the trivial to the sophisticated. I have analyzed in full and technical detail this facet of Barrow's optics in "Studies on James Gregorie (1638-1675)," 158-62, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
146. See, for instance, Mathematical Works, 118, where he corrects Galileo, and 101, where he explains a phenomenon "of substantial advantage in the making of telescopes." For instances of observations and experiments adduced as corroboration of his theory, see Mathematical Works, Lecture IV, §21, 53; V, §20, 61; V, §22, 63-64; VI, §19, 69; VII, §21, 76; X, §26, 93-94; XV, appendix, 133-36; XVI, §14, 140-41. Barrow's handling of observations and experiments ranges from the trivial to the sophisticated. I have analyzed in full and technical detail this facet of Barrow's optics in "Studies on James Gregorie (1638-1675)," 158-62, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
147. See, for instance, Mathematical Works, 118, where he corrects Galileo, and 101, where he explains a phenomenon "of substantial advantage in the making of telescopes." For instances of observations and experiments adduced as corroboration of his theory, see Mathematical Works, Lecture IV, §21, 53; V, §20, 61; V, §22, 63-64; VI, §19, 69; VII, §21, 76; X, §26, 93-94; XV, appendix, 133-36; XVI, §14, 140-41. Barrow's handling of observations and experiments ranges from the trivial to the sophisticated. I have analyzed in full and technical detail this facet of Barrow's optics in "Studies on James Gregorie (1638-1675)," 158-62, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
148. Mathematical Works, 152-53. See "Studies on James Gregorie (1638-1675)," 162-63, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
149. Mathematical Works, 152-53. See "Studies on James Gregorie (1638-1675)," 162-63, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
150. Mathematical Works, 152-53. See "Studies on James Gregorie (1638-1675)," 162-63, to appear in "The Seventeenth-Century Mathematization of Optical Images," forthcoming.
151. M. Atherton, Berkeley's Revolution in Vision (Ithaca, 1990), 77-86, and passim.