## The Foundations of Mathematics: A Contribution to the Philosophy of Geometry |

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absolute abstract anyness apriority arithmetic Augustus De Morgan Bolyai boundary called causation Common Notion conception concrete congruent cube curvature definite determined direction domain element etry Euclid Euclidean geometry Euclidean systems existence experience figures Foundations of Geometry four-dimensional fourth dimension G. B. Halsted Gauss geom Grassmann halves idea ideal construction infinite Kant latter laws laws of form Lobatchevsky logic Magic Squares manifold mathe mathematical space mathematicians matics measurement metageometry method mind motility nature non-Euclidean non-Euclidean geometry norm Open Court parallel axiom parallel lines philosophical philosophy of mathematics plane geometry position possible posteriori postulate priori priori constructions problem produce Professor proposition pseudosphere pure form pure reason pure space purely formal real space relations Riemann right angles scope of motion sense-impressions space-conception sphere straight line straightest line surface theorem of parallel thinking subject three co-ordinates three planes tion tive transcendental triangle tridimensional truth two-dimensional universal