## Complete Systems of Concomitants of the Three-point and the Four-point in Elementary Geometry ... |

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algebraic sign alternating functions Apollonian circles binary forms centroid Charles Henry Rawlins Complete System.—We Complex Plane Consider consists contain no alternating contain no symmetric coordinates of four cubic quartic curve degenerate conic denote diagonal triangle element occurs Elementary Geometry equation expanding express any given expressed integrally foci following complete system four rows Four-Point in Elementary function of total functions of lower G-point Geometric Equivalents.—We Grace & Young integrally in terms Interchanging irreducible functions Jacobian Johns Hopkins University line at infinity lower degree Metrical Geometry mid-point Monogenic Concomitants obviously irreducible point-set polar system reduces by substituting reduces to wx reference triangle respect roots in ratio Section seminvariants Similarly symmetric functions system of symmetric system will contain Systems of Concomitants Syzygies terms of A2 three linear forms three rows three-point under translation three-term total degree transformation vanishes identically vertex vertices w'ax