BOOKS ON ARCHITECTURE
Author(s) 
Euclide
Fréart de Chambray, Roland 
Title 
La perspective d’Euclide... 
Imprint 
Le Mans, J. Ysambart, 1663 
Localisation 
Paris, Binha, 8 Res 1194 
Subject 
Perspective 


Transcribed version of the text

French
In spite of its title La perspective d’Euclide, traduite en français sur le texte grec, original de l’autheur, et demonstrée par Roland Fréart de Chantelou sieur de Chambray, the book must not be considered an essential contribution by its author to the spread of a work by Euclid. It is first of all a scientific addition to the system of judgment founded on reason that Fréart de Chambray was promoting in the field of art. For this theoretician and great admirer of the ancients, Euclid’s clarity and mathematical strictness provided an ideal model for a rational construction of a body of doctrine on artistic excellence. In his Idée de la perfection de la peinturepublished one year earlier in 1662, he was already following an entirely Euclidean approach in setting out six axioms of a science “that scholars have called optics, and that painters and all draftsmen usually call perspective ”.
However his book is not a translation of Euclid’s Optics (that is, Perspective), but a new edition “of the Recension by Theon” as Paul Ver Eecke shows, adding that “nothing in the preface or in the body of the work would indicate that a Greek text was used as a tenet”. Fréart contradicts this last opinion when he mentions “the Greek text is my model...” or “Euclid’s manuscript from which we have taken...”. In fact, the text of the Optics attributed to Euclid (3^{rd} century B.C.) only reached the early modern period bit by bit, according to the desires of copyists and translators, and particularly by the intermediary Theon of Alexandria (second half of the 4^{th} century A.D.). It would not be surprising that Fréart, like most of the translators before him, had confused in good faith a manuscript of the Recension with Euclid’s original text.
Fréart explicitly quotes the Latin translations of this recension. Therefore he refers to Witelo (c. 1225 c. 1300), whose books published during the Renaissance contributed to spreading not only Euclid’s works but also essays on optics by Ibn AlHaytham known as Alhazen (965 ? – 1039). The fortynine quotations by Witelo that Fréart gives are found in the book published by Jean Petri in Nuremberg in 1535 entitled Vitellionis mathematici doctissimi de optica. Another source, quoted fortythree times, is the treatise by François d’Aguilon (15671617) published at the Officina Plantiniana in Antwerp in 1613 (illustrated with drawings by Rubens engraved by Cornelis Galle) entitled Opticorum libri sex philosophis juxta ac mathematicis utiles. This second source is not independent from the first, for Aguilon quotes Alhazen and Witelo.
In addition to these major references, Fréart adds Alhazen (via Witelo and Aguilon) , but also Bartolomeo Zamberti, who put out in Venice in 1505 the first complete Latin version of the Recension (reissued in Paris in 1516, then in Basel in 1546) and Jean Peña (15281568), a professor at the Collège Royal and author of the editio princeps of the Recension in Paris in 1557. He also mentions Giambattista (15351615) six times ; his De refractione optices, published in Naples in 1593 inspired Kepler (15711630). Fréart must have been acquainted with Kepler’s celebrated Ad Vitellionem paralipomena (1604). Likewise he could not have been unaware of the Cours de mathématiques by Pierre Hérigone (15801643), whose fifth volume, published in Paris at the presses of Henry Le Gras, in 1637, contains an Optique d’Euclide augmentée, & demonstrée par nouvelles demonstrations.
Fréart de Chambray’s treatise begins with a preface which is a summary of the prologue by one of Theon’s pupils (he thinks that it is a text by Theon himself), often published with the Recension. He immediately broaches the controversy on the direction of the propagation of light depending on whether “Sight comes about by the Emission of visual Rays”, or on the contrary it comes about only “by receiving species that all visible Objects send to the eye as to a mirror”. He recalls that the theory of emission is “the shared opinion”, but is keen to take up all the specious arguments of the prologue in favor of the theory of the emission of visual rays by the eye and the separation of these rays (a discontinuity which would explain that some of the objects are not seen spontaneously).
Thus Fréart stays with the text of the prologue and in no way does he rely on the work relating to the physiology of vision by Alhazen, d’Aguilon, Kepler, even Descartes, to modify his remarks slightly. Nevertheless, he concludes that “the radical founding principles of the Theorems of Perspective always remain equally in one opinion or the other” for effectively the essential part of Euclid’s optics is based on the rectilinear propagation of light apart from the direction of that propagation.
The Recension follows a classic Euclidean plan : seven definitions followed by fiftyseven propositions which are their logical consequences. These propositions do not all belong to what presentday science calls optics ; most are propositions on perspective, but accounts can also be found which “concern rather the trade of the surveyor that that of the Painters”. Proposition 19 is influenced by catoptrics, propositions 52 to 58 bring in motion ; finally some propositions are purely geometrical, in particular those using the idea of inscribed angles.
Fréart’s translation follows this plan with a few modifications of detail for more clarity. Thus there are twelve axioms and fiftysix theorems whose wording is strictly based on Theon’s text. On the other hand he moves totally away from the Euclidian style in the demonstrations of the theorems. He abandons the rigor of a mathematical argument in favor of commentary and a rapid justification of each proposition. Either he considers that the demonstration of the theorem is obvious and then “it is a waste of time to search in geometric demonstrations for truths that are so clear and so well understood”, or he alludes to familiar knowledge, “one must not look for any demonstration more natural than ordinary experience”, or he gives special attention to the obvious character of the figure, “the only lineal figure is here a demonstration too perceptible to the eye for there still to be need to confirm it more through discourse”. Nonetheless he is not averse to indicating the necessary broad lines of the geometric demonstrations and for the most demanding readers he refers to Witelo and Aguilon (less frequently to other translators) by giving precise references.
As a result, free from the clumsy expressions of an abstract treatise on geometry, Fréart de Chambray writes a text that is more pleasant to read, full of judicious remarks which sometimes break away from the domain of geometry. Therefore, regarding the shortening of lengths depending on distancing, he gives the example of “the column of Trajan that one sees in Rome” in which the height of the bands of the sculpted frieze increases in going towards the top. Likewise, in dealing with the proposition formulating that the eye, placed in rhe plane of a circle sees only one segment, he indicates that “Painters who know Perspective often put this lesson into practice” and does not hesitate to pursue the explanation, giving as a reason particularly “the horizontal line of the Painting, on which one must always put the distance point and the point of view”. His commentary is also sometimes about the translations he uses. He often criticizes Della Porta who reasons “rather as a Sophist than as a Geometer...”, and who claims “to want to appear more subtle and more enlightened about perspective than Euclid himself”. But he praises Aguilon, “Aguilonius, who appears to me much more judicious and far more learned in this matter, was satisfied with adjusting two or three words of Euclid’s text, in order to clarify the understanding of it”.
Therefore we are not dealing with a rediscovery of Theon of Alexandria’s text, but a solid and pleasant commented restitution of a Greek text which, while not Euclid’s, is not very far from it. Intended for erudite persons or, as Fréart de Chambray says, “to the studious”, studying it will permit them to get a precise idea of the contents of ancient optics and give pride of place back to Euclid’s principles, “the certainty of which is clear and direct, and the rigor unwavering”. Moreover this early modern work on a prestigious ancient author could only confirm Fréart’s reputation as a humanist scholar and favor his career as expert in the fields of science and the arts.
JeanPierre Manceau (Tours) – 2012
Critical bibliography
R. Fréart de Chambray, Parallèle de l’architecture avec la moderne (Paris, 1650). Critical edition established by F. Lemerle, followed by l’Idée de la Perfection de la peinture, edition established by M. Stanic, Paris, École nationale supérieure des BeauxArts, 2005.
Paul Ver Eecke, Euclide. L’Optique et la Catoptrique, Œuvres traduites pour la première fois du grec en français avec une introduction et des notes, Paris, Blanchard, 1959.
Marie Lacoarret, “Les traductions françaises des œuvres d’Euclide ”, Revue d’histoire des sciences et de leurs applications, 101, 1957, pp. 3858.
N. G. Poudra, Histoire de la Perspective ancienne et moderne, Paris, Corréard, 1864.
I. Pantin, Les Fréart de Chantelou. Une famille d’amateurs au XVIIe siècle entre Le Mans, Paris et Rome, Le Mans, Création & Recherche, 1999.
