Editing Johannes Kepler (section)

=== ''Astronomiae Pars Optica'' ===
[[File:Kepler Optica.jpg|thumb|upright=.8|A plate from ''Astronomiae Pars Optica'', illustrating the structure of [[eye]]s of various species]]
As Kepler slowly continued analyzing Tycho's Mars observations—now available to him in their entirety—and began the slow process of tabulating the ''[[Rudolphine Tables]]'', Kepler also picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and [[solar eclipse]]s presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of [[atmospheric refraction]] applied to ''all'' astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on 1 January 1604, was published as ''Astronomiae Pars Optica'' (The Optical Part of Astronomy). In it, Kepler described the [[inverse-square law]] governing the intensity of light, reflection by flat and curved mirrors, and principles of [[pinhole camera]]s, as well as the astronomical implications of optics such as [[parallax]] and the apparent sizes of heavenly bodies. He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the [[Lens (anatomy)|eye's lens]] onto the [[retina]]. The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul."<ref>Finger, "Origins of Neuroscience," p. 74. [[Oxford University Press]], 2001.</ref>

Today, ''Astronomiae Pars Optica'' is generally recognized as the foundation of modern optics (though the [[law of refraction]] is conspicuously absent).<ref>Caspar, ''Kepler'', pp. 142–146</ref> With respect to the beginnings of [[projective geometry]], Kepler introduced the idea of continuous change of a mathematical entity in this work. He argued that if a [[Focus (geometry)|focus]] of a [[conic section]] were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an [[ellipse]] becomes a [[parabola]] when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed. As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines. He also assumed that if a straight line is extended to infinity it will meet itself at a single [[point at infinity]], thus having the properties of a large circle.<ref>[[Morris Kline]], ''Mathematical Thought from Ancient to Modern Times'', p. 299. [[Oxford University Press]], 1972.</ref>