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White. The of a piece always are the form of verticals, take straight lines, and always horizontals, diagonals, or obliques. NOTE. logistic radii GEOMETRIC PLANES. Whenever the geometric symbols appertaining to one or more kindred pieces and to one or more adverse pieces are combined in the same evolution then that ; part of the surface of the chessboard upon which such evolution is executed is termed in this theory a G-eo' metric Plane. Geometric Planes are divided into three classes I. : STRATEGIC.

At of PLANE TOPOGRAPHY. The Piece Exposed is 37 that adverse integer of chess a given evolution may be whose capture mathematically demonstrated. in force THE PIECE EXPOSED. (P. ) FIGURE 31. Black. While. NOTE. upon The Piece Exposed always is situated either one of the sides or at one of the vertices of the zone of evolution. MAJOR TACTICS. 38 A Disturbing Integer is an adverse piece which prevents the Prime Tactical Factor from occupying the Point of Command, or the Supporting Factor from occupying the Point of Co-operation.

MAJOR TACTICS. 22 LOGISTIC SYMBOL OF THE QUEEN. FIGURE 18. Black. White. NOTE. The from the centre logistic radii of a piece of its geometric symbol always extend to the perimeter. LOGISTIC SYMBOLS. 23 LOGISTIC SYMBOL OF THE KING. FIGURE 19. Black. White. The of a piece always are the form of verticals, take straight lines, and always horizontals, diagonals, or obliques. NOTE. logistic radii GEOMETRIC PLANES. Whenever the geometric symbols appertaining to one or more kindred pieces and to one or more adverse pieces are combined in the same evolution then that ; part of the surface of the chessboard upon which such evolution is executed is termed in this theory a G-eo' metric Plane.

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