Hobbes’s Geometrical Optics

in Hobbes Studies
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Since Euclid, optics has been considered a geometrical science, which Aristotle defines as a “mixed” mathematical science. Hobbes follows this tradition and clearly places optics among physical sciences. However, modern scholars point to a confusion between geometry and physics and do not seem to agree about the way Hobbes mixes both sciences. In this paper, I return to this alleged confusion and intend to emphasize the peculiarity of Hobbes’s geometrical optics. This paper suggests that Hobbes’s conception of geometrical optics, as a mixed mathematical science, greatly differs from Descartes’s one, mainly because they do not share the same “mechanical conception of nature.” I will argue that Hobbes and Descartes also have in common the quest for a different kind of geometry for their optics, different from that of the Ancients. I will show that this departure is not recent since Hobbes’s approach is already evident in 1636, when he judges the demonstrations of his contemporary friends, Claude Mydorge and Walter Warner. Finally the paper broadly suggests what is noteworthy in Hobbes’s optics, that is, the importance of the idea of force in his mechanics, although he was not able to conceptualize it in other terms than “quickness.”

Hobbes’s Geometrical Optics

in Hobbes Studies




 See John WallisJohannis Wallisii… Elenchus geometriae Hobbianae sive Geometricorum quae in ipsius “Elementis philosophiae” a Thomas Hobbes… proferuntur refutation (Oxoniae: Crook1655) pp. 6–10. Hobbes replied in the Six Lessons to the Professors of Mathematicks (printed with Elements of Philosophy the First Section Concerning Body London: 1656 p. 3) in Thomas Hobbes The English Works of Thomas Hobbes collected and edited by Sir William Molesworth 12 vols. (London: John Bohn 1839) cited as ew vol. vii p. 242: “For men that pretend no less to natural philosophy than to geometry to find fault with bringing motion and time into a definition when there is no effect in nature which is not produced in time by motion is a shame.”


Antoni Malet‘The Power of Images: Mathematics and Metaphysics in Hobbes’s Optics’Studies in History and Philosophy of Sciencevol. 32. 2 (2001) pp. 303–333 here p. 304.


Malet“The Power of Images” p. 317.


 On this point see Malet“The Power of Images” p. 326. In fd dedicatory epistle pp. 76–77 where Hobbes claims his originality by occupying a field Descartes had left blank: “I might bee challenged for building on another man’s ground. Yett philosophical ground I take to be of such a nature that any man may build upon it that will especially if the owner himselfe will nott.”


Thomas HobbesConsiderations upon the reputation loyalty manners & religion of Thomas Hobbes of Malmsbury written by himself by way of letter to a learned person (London: William Crooke1680) p 54; Thomas Hobbes The English Works of Thomas Hobbes collected and edited by Sir William Molesworth 12 vols. (London: John Bohn 1839) hereafter ew vol. iv pp 436–437.


Johannes Kepler‘Ad Vitellionem Paralipomena, Quibus Astronomiæ Pars Optica Traditvr’ in Gesammelte Werkebd. iiAstronomiæ Pars Optica (Munich: Beck 1939).


 See John A. Schuster‘Physico-mathematics and the search for causes in Descartes’ optics – 1619–1637’Synthese185 (2012) pp. 467–499.


Alexandre KoyréEtudes Galiléennes (Paris: Hermann1966) p. 131: “La géométrisation à outrance – ce pêché originel de la pensée cartésienne – […] dissout l’être réel dans le géométrique”; see Alexandre Koyré Galileo Studies transl. by John Mepham (Leiden: Brill 1978) pp. 91–92.


 See Pietro Melis‘Cartesio e Hobbes. Studio sull’ottica’Annali della Facoltà di Magistero dell’Università di Cagliari3 (1983) pp. 243–407.


 See José Médina‘Matière, mémoire et mouvement chez Hobbes’ in Hobbes et le matérialismeA. Milanese J. Berthier (eds.) (Paris: Editions Matériologiques 2016) pp 33–74.


Alan E. Shapiro‘Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century’Archive for History of Exact Sciences11 (1975) pp. 134–266 p. 144: “Hobbes began the kinematic tradition in the continuum theory of light Rejecting Descartes’s static continuum theory and explanation of reflection and refraction based on an analogy to a moving body Hobbes attempted to give a kinematic description of the rectilinear reflected and refracted motion of a pulse.”


Jean Bernhardt‘Hobbes et le mouvement de la lumière’Revue d’histoire des sciences30/1 (1977) pp. 3–24 p. 16 fn. 34.


Shapiro‘Kinematic Optics’ p.151.


Warner to Payne 17 Oct. 1634blms Add. 4279 fol. 307 in James Orchard Halliwell (ed.) A Collection of Letters Illustrative of the Progress of Science in England from the Reign of Queen Elizabeth to that of Charles the Second (London: Historical Society of Science 1841) p. 65.


 See Thomas HobbesSeven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury; with an apology for himself and his writings (London: William Crook1662) iv (ew vol. vii p 31) where Hobbes still gives the same answer to the question “How comes the light of the sun to burn almost any combustible matter by refraction through a convex glass and by reflection from a concave? […] the whole action of the sun-beams are enclosed within a very small compass: in which place therefore there must be a very vehement motion; and consequently if there be in that place combustible matter such as is not very hard to kindle the parts of it will be dissipated and receive that motion which worketh on the eye as other fire does. The same reason is to be given for burning by reflection. For there also the beams are collected into almost a point” (Thomas Hobbes Problemata physica (London: Andrea Crook1662) iv: ol vol. iv p. 332).


Payne to Warner June 21 1635ms Add. 4279 fol. 182 in Halliwell A Collection of Letters pp. 65–66.


Jan PrinsWalter Warner (ca. 1557–1643) and his Notes on Animal Organisms (Utrecht: Ph.D Dissertation thesis1992) p. 242 n. 27.


MalcolmAspects of Hobbes pp. 80–81.


Mydorge 1639 [Claude MydorgeProdromi catoptricorum et dioptricorum: sive conicorum operis ad abdita radii refexi et refracti mysteria prævii et facem præferentis. Libri quatuor priores (Paris: I. Dedin1639)] was commissioned by Sir Charles Cavendish who appears as the beneficiary of the dedicatory epistle: the first two books were published in 1631 (Paris). It contains four former books reprinted in 1641 (Paris Dedin) and in 1660 (Paris Guillemot). Mersenne included them in his Geometriæ Universæ Synopsis (1644) under the title De sectionibus conicis. The section devoted to optics consists in four latter books expected to be published in a second volume. Mydorge sent his manuscript to Charles Cavendish via his brother William (see letter 18 Hobbes to Newcastle 13/23 June 1636 hc vol. I pp. 32–34). This ms seems to be lost. The reason why the second volume has not been published is revealed by John Collins in his letter to James Gregory dated March 14 1671/72 [Isaac Newton Correspondence 7 vols. ed. by H.W. Turnbull (Cambridge: Cambridge University Press 1959) I letter 47 p. 118]: “they complaine in France (as we doe here) that their Booksellers will not undertake to print mathematicall Bookes here thence it came to passe that the four latter books of Mydorge were never printed as the former had not been unless Sir Charles Cavendish had given 50 crownes as a Dowry with it.” Collins makes doubtless reference to the second edition of Prodromi which contains the same dedication to Cavendish and mentions the other four books forthcoming.


Jean LeurechonRecreation mathematicque; composee de plusieurs problemes plaisants et facetieux; en faict d’arithmeticque geometrie mechanicque opticque et autres parties de ces belles sciences (Pont-à-Mousson: Jean Appier Hanzelet1624) reprinted several times. The official edition is dated 1630 ‘chez Anthoine Robinot’.


Claude Mydorge / Jean LeurechonExamen du livre des récréations mathématiques et de ses problèmes en géométrie méchanique optique & catoptrique où sont aussi discutées et restablies plusieurs expériences physiques y proposées par Claude Mydorge (Paris: Antoine Robinot1630) pp. 186–187.

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