caption death_date death_place religion birth_place image_size fields workplaces birth_date known_for doctoral_students image article_title name alma_mater
guillaume-jules hoüel 14 june 1886 périers protestant thaon , france 100px mathematics bourges , bordeaux pau , pyrenees-atlantiques alencon , caen 7 april 1823 lobachevski & bolyai translations quaternion textbook charles-ange laisant juleshouel.jpg jules hoüel
 jules hoüel École normale supérieure
jules hoüel

guillaume-jules hoüel -lrb- born 7 april 1823 in thaon ; died 14 june 1886 in périers -rrb- was a french mathematician .
he entered the École normale supérieure in 1843 and received his doctoral degree in 1855 from the sorbonne .
he was sought by urbain le verrier at the paris observatory , but chose instead to return to thaon to study there .
in 1859 he began to teach at bordeaux .
in 1863 hoüel expressed his doubts about the verifiability of the parallel postulate of euclid .
in 1867 hoüel produced french translations of two key publications of non-euclidean geometry : lobachevski 's `` geometrical studies on the theory of parallels '' and bolyai 's `` science of absolute space '' .
hoüel published a four volume work titled `` théorie Élémentaire des quantités complexes '' .
volume four , published in 1874 , began with an discussion of properties of algebraic operations -lrb- commutativity , associativity , distribution , and inverses -rrb- and used the algebra of quaternions and versors to describe spherical trigonometry .
however , in 1890 p. g. tait revealed his dissatisfaction with hoüel 's changes in notation with text that tait had given for hoüel 's use .
tait wrote : the earliest offender in this class was the late m. hoüel who , while availing himself of my permission to reproduce , in his `` théorie Élémentaire des quantités complexes '' , large parts of this volume , made his pages absolutely repulsive by introducing fancied improvements in the notation .
in 1876 hoüel reviewed a russian language quaternion textbook written by romer -lrb- 1868 -rrb-
