| CURVES I CURVES IN SPACE SECTION 1. PARAMETRIC EQUATIONS OF A CURVE 2. OTHER FORMS OF THE EQUATIONS OF A CURVE 3. LINEAR ELEMENT 4. TANGENT TO A CURVE 5. ORDER OF CONTACT. NORMAL PLANE 6. CURVATURE. RADIUS OF FIRST CURVATURE 7. OSCULATING PLANE 8. PRINCIPAL NORMAL AND BINORMAL 9. OSCULATING CIRCLE. CENTER OF FIRST CURVATURE 10. TORSION. FRENET-SERRET FORMULAS 11. FORM OF CURVE IN THE NEIGHBORHOOD OF A POINT. THE SIGN OF TORSION 12. CYLINDRICAL HELICES 13. INTRINSIC EQUATIONS. FUNDAMENTAL THEOREM 14. RICCATI EQUATIONS I 15. THE DETERMINATION OF THE COORDINATES OF A CURVE DEFINED BY ITS INTRINSIC EQUATIONS 16. MOVING TRIHEDRAL 17. ILLUSTRATIVE EXAMPLES 18. OSCULATING SPHERE 19. BERTRAND CURVES 20. TANGENT SURFACE OF A CURVE 21. INVOLUTES AND EVOLUTE8 OF A CURVE 22. MINIMAL CURVES CHAPTER II CURVILINEAR COORDINATES ON A SURFACE. ENVELOPES 23. PARAMETRIC EQUATIONS OF A SURFACE 24. PARAMETRIC CURVES 25. TANGENT PLANE 26. ONE-PARAMETER FAMILIES OF SURFACES. ENVELOPES SECTION 27. DEVELOPABLE SURFACES. RECTIFYING DEVELOPABLE 28. APPLICATIONS OF THE MOVING TRIHEDRAL 29. ENVELOPE OF SPHERES, CANAL SURFACES CHAPTER III LINEAR ELEMENT OF A SURFACE. DIFFERENTIAL PARAME-TERS CONFORMAL REPRESENTATION 30. LINEAR ELEMENT 31. ISOTROFIC DEVELOPABLE 32. TRANSFORMATION OF COORDINATE8 33. ANGLES BETWEEN CURVES. THE ELEMENT OF AREA 34. FAMILIES OF CURVES 35. MINIMAL CURVES ON A SURFACE 30. VARIATION OF A FUNCTION 37. DIFFERENTIAL PARAMETERS OF THE FIRST ORDER 38. DIFFERENTIAL PARAMETERS OF THE SECOND ORDER 39. SYMMETRIC COORDINATES 40. ISOTHERMIC AND ISOMETRIC PARAMETERS 41. ISOTHERMIC ORTHOGONAL SYSTEMS 42. CONFORMAL REPRESENTATION 43. ISOMETRIC REPRESENTATION. APPLICABLE SURFACES 44. CONFORMAL REPRESENTATION OF A SURFACE UPON ITSELF. 45. CONFORMAL REPRESENTATION OF THE PLANE 46. SURFACES OF REVOLUTION 47. CONFORMAL REPRESENTATIONS OF THE SPHERE CHAPTER IV GEOMETRY OF A SURFACE IN THE NEIGHBORHOOD OF A POINT 48. FUNDAMENTAL COEFFICIENTS OF THE SECOND ORDER. 49. RADIUS OF NORMAL CURVATURE 50. PRINCIPAL RADII OF NORMAL CURVATURE. 51. LINES OF CURVATURE. EQUATIONS OF RODRIGUE8 52. TOTAL AND MEAN CURVATURE 53. EQUATION OF EULER. DUPIN ~NDICATRIX 54. CONJUGATE DIRECTIONS AT A POINT. CONJUGATE SYSTEMS 55. ASYMPTOTIC LINES. CHARACTERISTIC LINES 50. CORRESPONDING SYSTEMS ON Two SURFACES 57. GEODESIC CURVATURE. GEODESICS 58. FUNDAMENTAL FORMULAS …… CHAPTER V FUNDAMENTAL EQUATIONS THE MOVING TRIHEDRAL CHAPTER VI SYSTEMS OF CURVES GEODESICS CHAPTER VII QUADRICS RULED SURFACES MINIMAL SURFACES CHAPTER VIII SURFACES OF CONSTANT TOTAL CURVATURE W-SURFACES SURFACES WITH PLANE OR SPHERICAL LINES OF CURVATURE CHAPTER IX DEFORMAT OF SURFACES CHAPTER X dEFORMATION OF SURFACES THE METHOD OF WEINGARTEN CHAPTER XI INFINITESIMAL DEFORMATOION OF SURACES CHAPTER XII RECTILINEAR CONGRUECNS CHAPTER XIII CYCLIC SYSTEMS CHAPTER XIV TRIPLY ORTHOGONAL SYSTEMS OF SURFACES INDEX |
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