Chapter 2 1653 — ‘Tractatus’

The mathematical understanding of telescopes
Part of the Archimedes book series (ARIM, volume 9)


Solar Eclipse Focal Distance Spherical Aberration Spherical Lens Convex Lens 
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  1. 1.
    OC 1, 215. “Nunc autem in dioptricis totus sum...”Google Scholar
  2. 2.
    Berkel, “Illusies”, 83–84. In the 1660s Huygens would start to seek patronage abroad, first in Florence and then, successfully in Paris.Google Scholar
  3. 3.
    The most thorough-going account still are the ‘avertissements’ by the editors of the Oeuvres Complètes. Southall, “Some of Huygens’ contributions” reported on Huygens’ dioptrics after the publication of volume 13. Harting, Christiaan Huygens had earlier discussed it briefly. In relationship with his astronomical work and his practical dioptrics, Albert van Helden, “Development” and Anne van Helden/Van Gent, The Huygens collection and “Lens production” discuss some topics. In the context of the history of seventeenth-century geometrical optics — which in its own right has little been studied — Shapiro, “‘Optical Lectures’” mention Huygens’ contributions. They are remarkably absent from the Malet, “Isaac Barrow” and “Kepler and the telescope”. Hashimoto, “Huygens, dioptrics” is the only effort to discuss Huygens’ dioptrics in the context of his broader oeuvre.Google Scholar
  4. 4.
    OC 13, 1–271. The editors of the Oeuvres Complétes have labeled it Dioptrica, Pars I. Tractatus de refractione et telescopiis. Its content stems from the 1650s. The original version of Tractatus does not exist anymore. A copy was made in Paris by Niquet — probably in 1666 or 1667, at the beginning of Huygens’ stay in Paris — on which the text of the Oeuvres Complètes is based. The editors assume Niquet’s copy of Tractatus is largely identical with the original 1653 manuscript; “Avertissement”, XXX.Google Scholar
  5. 6.
    OC 1, 305–305.Google Scholar
  6. 7.
    Descartes, Geometrie, 352 (AT6, 424). “Au reste affin que vous sçachiées que la consideration des lignes courbes icy proposée n’est pas sans usage, & qu’elles ont diverses proprietés, qui ne cedent en rien a celles des sections coniques, ie veux encore adiouster icy lľexplication de certaines Ovales, que vous verrés estres tres utiles pour la Theorie de la Catoptrique, & de la Dioptrique.”Google Scholar
  7. 8.
    Descartes, Geometrie, 358–359 (AT6, 430–431). The left part 2A2 is a mirror that reflects rays intersecting in G so that they (virtually) intersect in F, provided that it diminishes the ‘tendency’ of the rays to a given degree.Google Scholar
  8. 9.
    Descartes, Geometrie, 353–354 (AT6, 424–426). The curve satisfies the equation F2 − FA = n(G2 − GA).Google Scholar
  9. 10.
    OC 1, 305. See note 9: the equation becomes AF = nAG.Google Scholar
  10. 11.
    Reproduced in OC 14, 419.Google Scholar
  11. 12.
    In Tractatus, he merely mentioned that a spherical surface is aplanatic for certain points: OC13, 64–67.Google Scholar
  12. 13.
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  13. 14.
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  14. 15.
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  15. 16.
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  16. 17.
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  17. 18.
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  20. 23.
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  21. 24.
    OC13, 70–73.Google Scholar
  22. 25.
    OC13, 42–47.Google Scholar
  23. 26.
    OC13, 88–89. Equivalent to the modern formula 1/f=(n−1)(1/R1+1/R2)Google Scholar
  24. 27.
    OC13, 98–109.Google Scholar
  25. 28.
    OC13, 122–125.Google Scholar
  26. 29.
    OC13, 118–123. In modern terms, L is the optical center.Google Scholar
  27. 30.
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  28. 32.
    OC13, 176n1.Google Scholar
  29. 33.
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  30. 34.
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  31. 35.
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  32. 36.
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  33. 37.
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  34. 38.
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  35. 39.
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  36. 40.
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  38. 43.
    OC1, 280; 301–303; 321–322. Huygens did not pin much faith in Van Schooten’s proposal.Google Scholar
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  40. 46.
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  43. 49.
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  44. 50.
    Van Helden, “Galileo and the telescope”, 153–157.Google Scholar
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  46. 52.
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  48. 54.
    Kepler, Dioptrice, dedication (KGW4, 331). “... circaque eam alij de palma primae inventionis certarent, alij de perfectione instrumenti sese jactarent amplius, quod ibi casus potissimum insit, hic Ratio dominetur: GALILAEUS vero super usu patefacto in perquirendis arcanis Astronomicis speciosissimum triumphum ageret; ut cui consilium suppeditaverat industria, nec successum negaverat fortuna: Ego doctus honesta quadam aemulatione novum Mathematicis campum aperui exerendi vim ingenij, hoc est causarum lege geometrica demonstrandarum, quibus tam exoptati, tam jucunda varietate multiplices effectus inniterentur.”Google Scholar
  49. 55.
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  50. 56.
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  52. 59.
    Dupré points out Risner’s programmatic discussion of the science of optics in the preface to the edition which constitute an important, yet still little studied, agenda for seventeenth-century optics. Dupré, Galileo, the Telescope, 54.Google Scholar
  53. 60.
    See Lindberg, “Laying the foundations”, 14–29.Google Scholar
  54. 61.
    Alhacen, Optics I, 68 (book 1, section 17) and 77 (book 1, section 46).Google Scholar
  55. 63.
    Dupré, Galileo, the telescope, 31.Google Scholar
  56. 64.
    Kepler, Paralipomena, 4 (KGW2, 16). “⋯ hae tenebrae sint Astronomorum oculi, hi defectus doctrinae sint abundantia, hi naevi mentes mortalium preciosissimis pictu ris illustrent.” Translation Donahue, Optics, 16.Google Scholar
  57. 65.
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  58. 66.
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    Lindberg, “Optics in 16th century Italy” 136–141. Maurolyco had preceded Kepler in his analysis of the pinhole image: Lindberg, “Optics in 16th century Italy”, 132–135; Lindberg, “Laying the foundations”.Google Scholar
  60. 68.
    Kepler, Paralipomena, 200–202 (KGW2, 181–183).Google Scholar
  61. 69.
    Malet, “Kepler and the telescope” offers a detailed discussion of Dioptrice, without however presenting it as a part of the ‘optical part of astronomy’.Google Scholar
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    Kepler, Dioptrice, dedication (KGW4, 331).Google Scholar
  63. 71.
    Kepler, Dioptrice, 11 (KGW4, 363).Google Scholar
  64. 72.
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  65. 73.
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  66. 74.
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  67. 75.
    Kepler, Dioptrice, dedication (KGW4, 335).Google Scholar
  68. 76.
    Kepler, Dioptrice, 21–24 (KGW4, 371–372).Google Scholar
  69. 77.
    Kepler, Dioptrice, 35–42 (KGW4, 381–387).Google Scholar
  70. 78.
    Kepler, Dioptrice, 42–43 (KGW4, 387–388).Google Scholar
  71. 79.
    A possible source of inspiration may have come from the analogous configuration of the eye and a convex spectacle glass, as the eye acts as a convex lens does. See also Malet, “Kepler and the telescope”, 119–120.Google Scholar
  72. 80.
    OC1, 6 (Stampioen’s list of recommended readings spans pages 5–10) and OC6, 215.Google Scholar
  73. 81.
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  74. 82.
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  75. 83.
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  76. 84.
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  77. 85.
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    McKeon, “Les débuts I”, 266–269.Google Scholar
  114. 126.
    McKeon, “Les débuts I”, 286. In Micrographia (1665) Hooke had suggested that a scale may be inserted into the focal plane of telescopes. Hooke, Micrographia, 237.Google Scholar
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    Flamsteed, Gresham lectures, 120–127.Google Scholar
  129. 141.
    Flamsteed, Gresham lectures, 136.Google Scholar
  130. 142.
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  131. 143.
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    Flamsteed, Gresham lectures, 8–9; 40 (Forbes’ introduction).Google Scholar
  133. 145.
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    Molyneux, Dioptrica nova, (Admonition to the reader).Google Scholar
  139. 151.
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  142. 154.
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  143. 155.
    Molyneux, Dioptrica nova, 24. From the preceding it will be clear, that following Molyneux’s line of thought this distance should be zero, for both points are by definition the same.Google Scholar
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