A painter among geometers
“The slightest pretext was sufficient for him to extend his knowledge.”
— Fontenelle, Éloge de M. de La Hire
Laurent de La Hyre, « Allégorie de la Géométrie », oil on canvas, 104 × 218 cm, Fine Arts Museums of San Francisco.
Philippe de La Hire was born in Paris in 1640. As the eldest son, he received drawing and painting lessons from his father Laurent de la Hyre (1606-1656), who saw him as his successor. Indeed, Laurent de la Hyre was a well-known artist, a member of the Royal Academy of Painting and Sculpture; painters, engravers and mathematicians attended the family house. His son's education included geometry, perspective, architecture, as well as the art of drawing sundials, i.e. gnomonics.
But, when his father died in 1656, the health of La Hire deteriorated. A travel to Italy, which was a very popular experience among the artists, seemed to be a means to strengthen his physical condition: he went to Rome, then Venice in 1660. He discovered models of Antiquity, practiced drawing and improved his knowledge in mathematics. His passion for geometry led him to study the work of Apollonius, a Greek mathematician and astronomer of the third century renowned for his research on tapered sections.
When, four years later, his mother asked him to come back, he settled in Paris as a painter, although he was more and more a geometer. He attended the erudite society and was close to Abraham Bosse (1602-1676), a master engraver, member of the Academy of Painting and dear friend of his father. They both shared a great interest in art and science. Thereafter, Bosse initiated him to the Manière Universelle de M. Desargues pour pratiquer la perspective by Gerard Desargues (1591-1661) which was also read and used by La Hire’s father. The work of Desargues, the founder of projective geometry, will influence him widely.
Attributed to Philippe de La Hire, House adjacent to the apse of a church, 13,1 x 20,2 cm, Paris, Ecole Nationale Supérieure des Beaux-Arts
Abraham Bosse confronted him with a stonecutting problem: how to establish reliable rules to build a rampant arch, i.e. an arch whose support is higher on one side than on the other. By ingeniously combining Apollonius’s theorem and Desargues’s method, he provided a solution in his first booklet, in 1672. Many geometry publications followed, which were praised in the Journal des Savantssometimes. In autumn 1675, rumor had it that Philippe de la Hire would be competing with Leibniz to be admitted the the Royal Academy of Sciences.
 “The spelling differs”, as notes Hélène Rousteau-Chambon in an article written for the national commemorations (Hélène-Rousteau Chambon, Philippe de La Hire, in Le Livre des Commémorations nationales 2018, sous la direction d’Hervé Lemoine, Éditions du patrimoine, Centre des monuments nationaux, Paris, 2018, pp. 89-90).
 Renté Taton, « Philippe de La Hire », in Dictionary of scientific biography, 1973, vol. 7, p. 576.
 Madeleine Pinault Sørensen, Biographie, op. cit., p.17.
 Fontenelle, op. cit., p. 76.
 Thierry Verdier, Les années romaines, 1660-1664. La naissance d’une culture scientifique, in Philippe de La Hire, 1640-1718 : entre architecture et sciences, op. cit., p. 27.
 Girard Desargues et Abraham Bosse, Manière universelle de M. Desargues, pour pratiquer la perspective par petit-pied, comme le géométral, ensemble les places et proportions des fortes et foibles touches, teintes ou couleurs, par A. Bosse, 1648.
 René Taton, op. cit., p. 93.
 Guy Picolet, « La Hire entre sciences et architecture : une chronologie », op. cit., p. 262.