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That branch of geometry which treats of the cone and the curves which arise from its sections.

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We may now summarize the contents of the Conics of Apollonius.

In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.

Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.

Astronomy was also enriched by his investigations, and he was led to several remarkable theorems on conics which bear his name.

His treatise on Conics gained him the title of The Great Geometer, and is that by which his fame has been transmitted to modern times.