Charles Bossut's Traite elementairede geometrie

This is the title page of the Traité élémentaire de géométrie et de la maniere d'appliquer l'algébre a la géométrie (1775), written by Charles Bossut (1730-1814).  This work was one of many texts written by Bossut in connection with his teaching at several different institutions in France.  It was one of the first books to give a detailed explanation of analytic geometry.

On page 397 and the following pages, Bossut discusses the equation of the circle.  Note that he does not assume that the two coordinate axes are perpendicular.

On pages 398-399, Bossut carefully works out the equation of the circle, displaying it as equation (A) on p. 399.  Note that because his axes are not assumed to be perpendicular, the equation has an xy term.

On page 400, Bossut shows various simplifications of the equation of the circle.  He derives equation (B) in the case where the two axes are perpendicular.  In the next two equations, the position of the origin is simplified.

On pages 424-425, Bossut discusses certain properties of tangents to parabolas and deals with them algebraicially.

On pages 426-427, Bossut proves the familiar property of a paraboloa, that the line from the focus to a point on the parabola makes the same angle with the tangent as the line from that point parallel to the axis.