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1
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84914892171
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B. L. Add. Ms. 6788, f. 490.
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2
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84882194953
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The poem is also quoted, with variations due to the difficult handwriting by, Random House, New York, in her
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(1970)
Traces of Thomas Hariot
, pp. 256-257
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Rukeyser1
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9
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84914890691
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Miller Christy, W. Blackwood, London, Foxe's account, entitled North West Foxe, was first published in London in 1635
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(1894)
The Voyages of Foxes and James
, vol.88-89
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Wright1
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12
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84914946739
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B. L. Add. Ms. 6788, f. 490.
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14
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0039747058
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University of California Press, Berkeley, Greenblatt is, of course, known for locating competing discourses and inner tensions within the literary texts he analyzes. There are undoubtedly inner tensions in the mathematical texts I will analyze—most prominently between the requirements of the classical mathematical tradition and the cultural narrative of exploration. My focus here will be, however, not on these inner conflicts, but simply on placing a cultural narrative at the heart of a mathematical text.
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(1988)
Shakespearean Negotiations
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Greenblatt1
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18
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84914945436
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Taylor, The Mathematical Practitioners.
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20
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84914897785
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For both narratives see Haraway, Primate Visions, ch. 7, pp. 133–185.
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21
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84914914146
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Principal Navigations, vol. 7, p. 400.
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24
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0006207673
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John Gillies has also noted the emphasis on ‘straits’ in early modern geography, though he views it as a by-product of the cartographers' view that most of the surface of the globe is composed of land. In contrast, I would argue that ‘straits’ have a positive role in the narrative of exploration; hence their prominence in geographical accounts. See, Cambridge University Press, Cambridge
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(1994)
Shakespeare and the Geography of Difference
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Gillies1
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25
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79953509191
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Rhetorics of Property: Exploration, Inventory, Blazon
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There are, of course, obvious gendered overtones to this narrative, which I do not pursue here. For the sexual significance of division into parts in the English Renaissance. See, in her, Methuen, London and New York
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(1987)
Literary Fat Ladies
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Parker1
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27
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84968301300
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The Work of Gender in the Discourse of Discovery
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On the gendered content of exploration narratives see
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(1991)
Representations
, vol.33
, pp. 1-41
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Montrose1
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31
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84914927453
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The Roanoke Voyages 1584–1590
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For a few examples of this narrative see the participants' accounts of Frobisher's voyages in Richard Hakluyt, Kraus Reprint Limited, Nedeln/Liechtenstein, The Principal Navigations
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(1967)
Amadas' and Barlowe's reports on Virginia
, vol.7
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Quinn1
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34
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84914914391
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Silences and secrecy: The Hidden Agenda of Cartography in Early Modern Europe
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J. B. Harley argues that maps are ideological tools and symbols in
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(1989)
Imago Mundi
, vol.40
, pp. 58-76
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-
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35
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0001837244
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Meaning and Ambiguity in Tudor Cartography
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For an earlier form of Harley's argument see his, University of Chicago Press, London
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(1983)
English Map Making 1500–1650
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Tyacke1
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36
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84914903598
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Dennis Wood argues forcefully that maps serve interests by naturalizing power relationships. He identifies maps as Barthian ‘myths’, which transform an ideological position into a self evident, natural ‘truth’. See, University of Chicago Press, New York, especially ch. 5
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(1992)
The Power of Maps
, pp. 95-142
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Wood1
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37
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0002241413
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Myth Today
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in his, University of Chicago Press, New York
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(1972)
Mythologies
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Barthes1
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38
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0001854497
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Imperial Landscape
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For a related argument, about natural landscape painting as the ‘universal language’ of imperialism, see, W.J.T. Mitchell, University of Chicago Press, Chicago
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(1994)
Landscape and Power
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Mitchell1
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39
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84914904578
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Principal Navigations, vol. 7, p. 443.
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40
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84914916073
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The Latin original is in, My translation closely follows, though not in all details, the one given in Muriel Rukeyser, The Traces of Thomas Hariot. ‘Raleana’ was the name given by the English to the Orinoco., 1596
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A Relation of the Second Voyage to Guiana
, pp. A4v
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Keymis1
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41
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84900777253
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Hariot mentions that he is preparing a map of Guiana in a letter to Sir Robert Cecil, dated 11 July, 1596. The letter is preserved in Hatfield House as Hatfield MS CP 42/36, and is printed in, Clarendon Press, Oxford
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(1983)
Thomas Hariot: A Biography
, pp. 230-232
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Shirley1
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43
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84914937971
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Significantly, it is impossible to identify the separate rivers depicted by Le Moyne, and his coastal mapping seems to represent nothing but his conventionalized view of a coastline broken by passages. The body of water at the northern edge of the map probably represents the Sea of Verrazano—the legendary sea lying just inland of the North American coast. See Cumming, The Southeast in Early Maps, pp. 124–125.
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45
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84914892298
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Significantly, Foucault refers to overseas colonies as primary examples of heterotopias, and to the ship as the ‘heterotopia par excellence’. See p. 27.
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47
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84914886952
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The lists of the rivers and Keymis' confident assertion of their source can be found in his Second Voyage, ff. B2r and B4r + v.
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49
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84914898167
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Significantly, Foucault refers to overseas colonies as primary examples of heterotopias, and to the ship as the ‘heterotopia par excellence’. See p. 27.
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50
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84914893861
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Keymis, Second Voyage, p. E2v.
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54
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84914924864
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The Works of William Oughtred. Clavis Mathematica
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Quoted from the preface to the Clavis of 1631. The translation is from
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(1915)
The Monist
, vol.25
, pp. 443
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Cajori1
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56
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70749132364
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Modern Language Association of America, New York, The poem was published in 1598 as a dedication to Hariot of Chapman's translation of a fragment of the Iliad entitled ‘Achilles Shield’.
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(1941)
The Poems of George Chapman
, pp. 381-384
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Bartlett1
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60
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84914926901
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The actual passage from fog to light was indeed a regular theme in English reports on the search for the northwest passage. See the accounts by George Best and Dionise Settle of Frobisher's voyages to the Canadian Arctic, and in particular Principal Navigations, vol. 7, pp. 236–237 and 340.
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61
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84914918122
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This depiction of Hariot's theory of refraction is found in Torporley's critique of Hariot entitled ‘A Synopsis of the Controversie of Atoms’, B. L. Birch MS. 4458, ff. 6–8.
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63
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84914932960
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Bacon, ‘New Organon’, p. 81.
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64
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84914930730
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In his unpublished papers, Hariot offers several sketches describing the passage of a ray of light through matter. This, probably his most graphic depiction, is entitled ‘Transitus radiorum per medium’, and it shows two rays of light being bounced back and forth within the medium and finally joining together in the eye. See B. L. Add. MS. 6789, f. 328.
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65
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84914899083
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This depiction of Hariot's theory of refraction is found in Torporley's critique of Hariot entitled ‘A Synopsis of the Controversie of Atoms’, B. L. Birch MS. 4458, ff. 6–8.
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66
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84914947768
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Johannes Kepler Gesammelte Werke, vol. 15, p. 368. The translation is Jacquot, ‘Thomas Harriot's Reputation’.
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70
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0041051284
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Harriot's Calculalion of the Meridional Parts as Logarithmic Tangents
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Jon V. Pepper suggests that Hariot may have been a mathematical atomist, but remains noncommittal on the issue. The evidence presented here provides strong evidence that that was indeed the case. See
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(1967)
Archive for the History of Exact Sciences
, vol.4
, Issue.47 n.
, pp. 370
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Pepper1
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71
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45149142383
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An External Problem in Harriot's Mathematics
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For a reconstruction of Hariot's solution to a different problem through atomistic considerations see, See especially Fenton's discussion of ‘The Maximal Intercept, Second Version’
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(1989)
Historia Mathematica
, vol.16
, pp. 154-163
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Fenton1
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72
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84964115242
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Harriot's Unpublished Papers
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Jon V. Pepper provides an excellent account of Hariot's work on the problem in his ‘Harriot's Calculalion of the Meridional Parts’. A less detailed account by the same author can be found in, My account of the cartographic problem, and Hariot's solution to it, are based on Pepper's far more detailed account
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(1968)
History of Science
, vol.6
, pp. 17-40
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80
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84914942863
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Keymis, Second Voyage, f. E2v.
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82
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84914897154
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Keymis, Second Vovage, f. A4v. The poem describes Guiana in terms of the familiar narrative: it possesses ‘gold and gems the color of grass’, it is surrounded by mountains ‘like walls’, but nonetheless ‘has deep bounteous entrances’. A translation of the poem can be found in Muriel Rukeyser, The Traces of Thomas Hariot, p. 140.
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83
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84914922736
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B. L. Add. MS. 6782, f. 363.
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85
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84914941558
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Wright, Errors, f. Dlr.
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86
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84914893990
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Θ. The rest of the discussion is predicated on the proof of conformality. See Pepper, ‘Harriot's Calculation’.
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87
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84914904878
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Hariot's tables were based on the fact that the radii of the curve at regular angular intervals bear a constant ratio to each other. For a complete account of Hariot's method, see Pepper, ‘Harriot's Calculation’.
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88
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0007109581
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‘De Infinitis’ is acomplex tract which has been interpreted in various ways over the years. Jean Jacquot, in ‘Harriot's Reputation’, discusses both the paradoxes in the treatise and the general statements, and arrives at the conclusion that Hariot indeed conceived of the continuum as composed of mathematical atoms. Robert Kargon follows Jacquot, and states that Hario, Clarendon Press, Oxford
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(1966)
Atomism in England from Harriot to Newton
, pp. 36
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89
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84970305688
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Thomas Harriot and Atomism: A Reappraisal
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John Henry strongly criticizes this position in, In discussing Francesco Patrizi's assertion that the continuum is composed of a finite number of indivisibles, he argues that Hariot was far too good a mathematician to so boldly disregard ‘the logical coherence of geometry and mathematics’ (p. 285). Henry therefore concludes that Hariot's mathematical atomism must have faded in the face off the logical difficulties (p. 288.). While Henry's scholarship is impressive, I have several problems with his argument. Most importantly, Henry completely disregards Hariot's actual depiction of the continuum as composed of distinct indivisibles (see Fig. 10), and his statement that a ‘continuum is composed primarily of indivisibles in contact’ (B. L. Add. MS. 6782 f. 374v.)
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(1982)
History of Science
, vol.20
, pp. 267-296
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90
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0007028828
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Despite the logical difficulties of his position, Hariot is so far from dismissing mathematical atomism that he offers a model of the continuum based on it. My own interpretation is probably closest to, Clarendon Press, London, Gatti places the ‘De Infinitis’ in the context of what she refers to as ‘Giordano Bruno's drama of knowledge’. I am not sure about the Hariot-Bruno connection, which is severely criticized by Henry. There is no doubt, however, that Gatti's ‘drama’, quoted from Bruno's Cena delta Ceneri on page 32, bears a strong resemblance to the Elizabethan imperialist narrative
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(1989)
The Renaissance Drama of Knowledge
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Gatti1
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91
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84914905213
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B. L. Add. MS 6786, f. 349v.
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92
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84914900352
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‘The Gordian Knot, The Labyrinth of Daedalus, The Club of Hercules—Democritus his reason for atoms, Achilles—Zeno's reason’. All quotes are from B. L. Add. MS. 6786, f. 349v.
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93
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84914901974
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The tract is in B. L. Add. MS. 6782, ff. 362–374v. The title ‘Clava Herculis’ is on f. 372, and the ‘Achilles’ discussion is on ff. 367–368. The ‘Clava’ section was apparently intended to solve the difficulties by an appeal to Democritean atomism. It is a measure of Hariot's difficulties with the subject that this is the only page in the entire tract that remained completely empty.
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94
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84914911155
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B. L. Add. MS. 6782 f. 368.
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95
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84914914877
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B. L. Add. MS. 6782 f. 363.
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