Archive for History of Exact Sciences

, Volume 72, Issue 5, pp 497–546 | Cite as

Binocular vision and image location before Kepler

  • Robert Goulding


Kepler’s 1604 Optics (Ad Vitellionem Paralipomena) proposed among many other things a new way of locating the place of the image under reflection or refraction. He rejected the “perspectivist” method that had been used through antiquity and the Middle Ages, whereby the image was located on the perpendicular between the object and the mirror (the “cathetus”). Kepler faulted the method for requiring a metaphysical commitment to the action of final causes in optics: the notion that the image was at that place because it was best or appropriate for it to be there, and for no other discernible reason. Kepler’s new theory relied on binocular vision and depth perception to determine the location of the image. No final causes were required, and he showed that the image would in general not be found on the cathetus. According to modern scholarship, Kepler’s theory was part of his revolutionary transformation of the science of optics, and his abandonment of perspectivist optics; as a consequence, the theory of binocular vision is also thought to be original with him. This article demonstrates that the very same theory of binocular image location was set out by Giovanni Battista Benedetti some twenty years earlier, and his writings on this subject may have been Kepler’s unacknowledged source for his own theory. Furthermore, another mathematician, Simon Stevin, developed much the same theory at the same time as Kepler and, it seems, independently of either Benedetti or Kepler. The discovery of these other binocular theories, especially Benedetti’s, requires us to recognize that Kepler’s revolution (if it can be called that) emerged out of a wider dissatisfaction with the foundations of perspectivist optics, which other lesser-known opticians resolved in much the same way that Kepler did.



The research on this paper was conducted while being a Member of the Institute of Advanced Study in Princeton, NJ, 2016–2017. I am very grateful for the support and resources of the Institute, for the suggestions and encouragement of other Members, and for the generosity of William D. Loughlin, whose gift supported my membership. I am also grateful to the reviewer for this journal, whose suggestions and criticisms greatly improved this article.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Authors and Affiliations

  1. 1.University of Notre DameNotre DameUSA

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