## Mechanical Geometry Theorem ProvingApproach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. |

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AC intersects line affine geometry algebraically closed algorithm altitude angle arbitrarily chosen ascending chain BC is non-isotropic bisectors Chapter characteristic set circumcenter circumcircle collinear conclusion concurrent configuration constructed in order cyclic quadrilateral detected diagonals equations Euclidean geometry Example F are constructed following nondegenerate conditions geometry statement geometry theorems given triangle intersects line BC inversive wrpt circle irreducible isogonal conjugate isotropic LCIB Line AB intersects line CD line joining line PQ metric geometry midpoint nine-point circle orthic triangle orthocenter orthopole parallel parameters pedal triangle perpendicular to line point of intersection Points H polynomial set prem(g prime ideal proof quadrilateral radical axises Remark Ritt's segments Show sides BC structed in order subsidiary conditions symmedian tan(/CA tan(BC7 tan(CB tangent Theorem Proving uiu2 vertex vertices Wu's method