Item #3801 Examen des œuvres du Sr Desargues. CURABELLE, Jacques.
Examen des œuvres du Sr Desargues
Examen des œuvres du Sr Desargues
Examen des œuvres du Sr Desargues
Examen des œuvres du Sr Desargues

Examen des œuvres du Sr Desargues

Paris, L’Anglois dit Chartres, 1644. 4°, 81 pages ; copy rebound in an old vellum. Some damp-staining. Item #3801

Rare first edition of this polemic text against Girard Desargues, the founder of projective geometry.
It is illustrated with 16 geometrical engravings in the text, including 6 full-page.
“The word Stereotomy or Cutting Solids firstly appeared in 1644 in the Jacques Curabelle’s libel case against Desargues : Examen des oeuvres du Sieur Desargues.” (Giuseppe Fallacara, Digital Stereotomy and Topological Transformations : Reasoning about Shape Building, 2006.)
On 29 December 1643, the foreman mason Jacques Curabelle, who would later become an architect and engineer to the King, had obtained permission to publish a Course of Architecture in 4 volumes, the first on Stereonomy. This work was never achieved apart from the Examen des œuvres de Desargues, in which Curabelle criticises Desargues’ New Geometry based on his own “Stereotomy”.
“It contains literal quotations of [Desargues]’s lost ‘Brouillon’ [Brouillon project d'une atteinte aux événements des rencontres d'un cône avec un plan], the beginning of the New geometry. Moreover here we find the first printed mentioning of ‘La Pascale’, the mystic hexagram, published in 1640 by the sixteen years old Pascal in a broadside, known only by one copy which survived.” (Weill)
In this book, Curabelle discloses the mathematical errors made by his contemporary. Desargues' new system, based on projective geometry, raised a heated dispute among Jesuit scholars. Long underestimated, Desargues was only rehabilitated in the 19th century by Monge and other great scientists.
This copy was annotated by two different hands developing geometrical demonstrations : the first is a 17th-century hand, probably contemporary (pages 20-21), the second slightly later, end of the 17th or beginning of the 18th century.
[Pages 20-21] “Demonstration / Les triangles BND, KND sont rectangles en N, et ont les costez BN, K-N egaux, donc BD, KD sont egaux, et partant D centre est d’un cercle qui passe par B et D [in fact, K]. Les triangles BOD, KOD sont egaux et semblables, car ils ont tous les costez egaux chacun au sien, donc l’angle OKD est égal à l’angle OBD c’est-à-dire OFH qui est son egal a cause des paralleles AE, FH. Donc les triangles OYK, OZF sont égaux et semblables et rectangles, donc l’angle HYF est droit. Et OZ est egal a OY. Et partant les restantes ZK, YF sont egales, donc les triangles rectangles HZK, HYF sont egaux et semblables, et HK, HF sont egales, et H est centre d’un cercle qui passe par K et F. De plus le centre D estant en BD, l’arc KLB touchera la droite perpendiculaire sur BD en B. De mesme l’arc KMF touchera FE perpend[iculairement] sur HF en F. Et les deux cercles ayant leurs centres D H dans la mesme droite DHK, leurs circonferences se toucheront en K, ce qu’il falloit demonstrer.” The same hand also amended very precisely pages 23, 24 and 55.
The second hand added corrections to the text and drew a small diagram next to an engraved figure.

Price: €5,400.00