Translation of Gergonne's Géométrie Analitique
This is a translation of Gergonne's paper Recherche du cercle qui en touche trois autres sur un plan ; published in the Annales de Mathématiques pures et appliquées , tome VII (1816-1817), no. X, 1er avril 1817; pp. 289-303. ( Link ) In this paper, Gergonne demonstrates the applications of analytical geometry (i.e. coordinate geometry with algebra, the approach promoted originally by Descartes with his Géométrie ). This approach was criticized for being too cumbersome, being dependent on a particular choice of coordinate system, and so being less general than pure (axiomatic) geometry. To combat this sentiment, Gergonne demonstrates a new solution to Apollonius's problem , derived entirely from algebraic considerations. This was a follow-up to a previous work, Mémoire sur le cercle tangent a trois circles donnés, et sur la sphère tangente a quatre sphères données published in the Mémoires de l'Académie Royale des Sciences de Turin , Vol. 22, 1813-1814 (1816), pp. 20-40...