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Chapter 2 1653 — ‘Tractatus’

The mathematical understanding of telescopes

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Lenses and Waves

Part of the book series: Archimedes ((ARIM,volume 9))

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References

  1. OC 1, 215. “Nunc autem in dioptricis totus sum...”

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  2. Berkel, “Illusies”, 83–84. In the 1660s Huygens would start to seek patronage abroad, first in Florence and then, successfully in Paris.

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  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.

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  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.

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  5. OC 1, 305–305.

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  6. 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.”

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  7. 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.

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  8. Descartes, Geometrie, 353–354 (AT6, 424–426). The curve satisfies the equation F2 − FA = n(G2 − GA).

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  9. OC 1, 305. See note 9: the equation becomes AF = nAG.

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  10. Reproduced in OC 14, 419.

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  52. 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.

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  53. See Lindberg, “Laying the foundations”, 14–29.

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  55. Dupré, Galileo, the telescope, 31.

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  56. 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.

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  61. Malet, “Kepler and the telescope” offers a detailed discussion of Dioptrice, without however presenting it as a part of the ‘optical part of astronomy’.

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  71. 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.

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  72. OC1, 6 (Stampioen’s list of recommended readings spans pages 5–10) and OC6, 215.

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  73. Della Porta’s account of refraction by spheres and lenses in De refractione is discussed in Lindberg, “Optics in 16th century Italy”, 143–146.

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  76. Compare Lindberg, “Optics in 16th century Italy”, 146–147.

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  84. Descartes, AT6, 147. “Des moyens de perfectionner la vision. Discours septiesme.”

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  85. Descartes, AT6, 155–160.

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  86. Descartes, AT6, 165. “Des figures que doivent avoir les corps transparens pour detourner les rayons par refraction en toutes les façons qui servent a la veuë”

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  87. Descartes, AT6, 82–83. Ribe, “Cartesian optics” offers an enlightening account of the artisanal roots of La Dioptrique.

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  88. Descartes, AT6, 82.

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  89. OC10, 402–403. “Mr. des Cartes n’a connu quel seroit ľeffet de ses Lunettes hyperboliques, et en a presumè incomparablement plus qu’il ne devoit. n’entendant pas assez cette Theorie de la dioptrique, ce qui paroit par sa demonstration très mal bastie des Telescopes.”

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  90. Stampioen, Wis-konstigh ende reden-maetigh bewys, 58. “... mijn Knecht Ondersoeck sal hem eens een beter Verre-kijcker sonder cirkeltjes daer toe weten te drayen:... Maer niettemin ť geen dese Mathematicien al over 6 Iaren belooft heeft te doen, blijft nog on-vol-daen.”

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  94. Compare Shapiro, “The Optical Lectures”, 130 & 133–134.

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  95. Compare Shapiro, “The Optical Lectures”, 150–151; and Malet, “Isaac Barrow”, 286.

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  98. Newton, Optical Papers 1, 427.

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  100. See: Albury, “Halley, Huygens, and Newton”, 455–457.

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  103. Beeckman, Journal, II, 209–211; 294–296. For lens grinding see down, page 57.

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  104. For the second idea see Beeckman, Journal, II, 367–368. For a later consideration see for example: III, 296.

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  105. Beeckman, Journal, II, 296; 357.

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  106. Beeckman, Journal, III, 109–110.

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  107. Van Helden, Measure, 118–119.

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  108. Compare Dear, Discipline and Experience, 210–216.

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  109. Van Helden, “Astronomical telescope”, 26–32. See also below section 3.1.1.

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  110. Rigaud, Correspondence, 46: “This is that admirable secret, which, as all other things, appeared when it pleased the All Disposer, at whose direction a spider’s line drawn in an opened case could first give me by its perfect apparition, when I was with two convexes trying experiments about the sun, the unexpected knowledge.”

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  111. McKeon, “Les débuts I”, 258–266.

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  112. Old Corr 3, 293: “... prendre les diametres du soleil, de la lune et des planetes par une methode que nous avons, Monsieur Picard et moy, que ie croy la meilleure de toutes celles que ľon a pratiquer Jusques a present,...”

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  114. 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.

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  115. OC21, 348–351.

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  116. Van Helden, Measure, 120–121.

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  118. McKeon, “Les débuts I”, 286; Van Helden, Measure, 118.

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  119. McKeon, “Renouvellement”, 122.

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  120. McKeon, “Renouvellement”, 126.

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  121. Flamsteed, Gresham lectures, 34–39 (Forbes’s introduction).

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  127. Flamsteed, Gresham lectures, 119 & 132. Flamsteed later deleted the part between brackets.

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  128. Flamsteed, Gresham lectures, 120–127.

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  129. Flamsteed, Gresham lectures, 136.

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  135. Flamsteed, Gresham lectures, 4–5 (Forbes’ introduction).

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  136. Molyneux, Dioptrica nova, (Admonition to the reader).

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  137. Molyneux mentioned Kepler, Cavalieri, Hérigone, Dechales, Fabri, Gregory and Barrow.

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(2005). Chapter 2 1653 — ‘Tractatus’. In: Lenses and Waves. Archimedes, vol 9. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2698-8_2

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