Sentence Examples

  • 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.
  • It is convenient to introduce the function =log =log (Q / q) + 01 (4) so that the polygon representing 12 conformally has a boundary given by straight lines parallel to the coordinate axes; and then to determine S2 and w as functions of a variable u (not to be confused with the velocity component of q), such that in the conformal representation the boundary of the and w polygon is made to coincide with the real axis of u.
  • The theory of conformal representation shows that the motion is given by (b-a'.u -a) +?
  • - n)= l b - au - ' (8) a - a u - b (9) dS2 I A I (b-a.b-a') dw m du = 21/(U - b)- ‘ 1 (u-a.0-a')' du - ,r u' Io) the formulas by which the conformal representation is obtained.
  • 7), and so must be excluded from the boundary of u; the conformal re presentation is made now with du= (b-a.b-a') du - (u-b) A l (u-a.0-a) (I) dw m I m' du = 7r u-j - u -j' _ m+m' u-b it u' j.0-j" b = mj i m'j m+m', taking u = co at the source where FIG.7.

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