Abstract
In Chapters 6 through 8 of the Analyse, l’Hôpital studies various kinds of envelopes: curves that are tangent to all the members of some family of lines or curves. In Chapter 7, l’Hôpital studies caustics by refraction, or dicaustics. This problem derives from optics and is essentially the study of envelopes made by light rays refracted through a lens. L’Hôpital considers a variety of shapes of lenses and sources of light rays.
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- 1.
In L’Hôpital (1696) the term rompre is used, literally meaning “to break.” We consistently translate the term rayon rompu as “refracted ray.”
- 2.
In L’Hôpital (1696) the curved line was given as FHN, but corrected in the Errata.
- 3.
A caustic by refraction is sometimes called a “Dicaustic.”
- 4.
I.e., describe the involute in reserve order, see §110, Footnote 4.
- 5.
- 6.
In L’Hôpital (1696) the connective between BM(y) and ML was missing.
- 7.
In L’Hôpital (1696) the parentheses around \(\frac{by} {a}\) were missing.
- 8.
In L’Hôpital (1696) the parentheses following AH were omitted.
- 9.
I.e., the place of the general point M of the curved line GM.
- 10.
The Ovals of Descartes, or Cartesian Ovals, are a quartic curve (Lockwood 1971, p. 188).
- 11.
In L’Hôpital (1696), the indefinite article une was omitted, but this was corrected in the Errata.
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Bradley, R.E., Petrilli, S.J., Sandifer, C.E. (2015). Use of the Differential Calculus for Finding Caustics by Refraction. In: L’Hôpital's Analyse des infiniments petits. Science Networks. Historical Studies, vol 50. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-17115-9_7
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