148 



INDEX. 



Parting, 17. 



Perception, 95. 



Physics, 8, 33, 38. 



TT, 117 et seq., 127, 138 et seq. 



Plato, 39, 98. 



Polygons, magical, 59 et seq. 



Porta, John, 133. 



Postulates, 121. 



Powers, 20. 



Prime numbers, problem of the fre- 

 quency of, 31. 



Principle of no exception, 14. 



Prizes offered circle-squarers, 116. 



Probabilities, IAI. 



Problems, fundamental, 120 ; solvable 

 with straight edge and compasses, 142. 



Ptolemy, 32, 128, 129. 



Pure arithmetic, 8 et seq. 



Pythagoras, 27, 123, 136. 



Quadratrix, 124. 



Quadrature of the circle, in Egypt, 114; 



D stands and falls with the problem of 



rectification, 119; numerical, 117 et 



seq. 

 Quantities, four variable, 77; negative, 



12 et seq. 

 Quaternions, 25. 



Radicand, 20. 



Rays, 69. 



Real numbers, 23. 



Rectification of the circle, numerical, 



117 et seq. 

 Regiomontanus, 132. 



Rhind Papyrus, 29, 122. 

 Riemann, 37, 79, 100. 

 Riese, Adam, 45. 



Romans, 3, 73; squaring of the circle 

 among, 128 et seq. 



Romanus, Adrianus, 133, 134. 



Rudio, 127, 141. 



Sauveur, 45, 61. 

 Scaliger, Joseph, 133. 

 SchefHer, 45, 46, 59, 61. 

 Schlegel, 65. 78. 

 Schroder, E., 9, n. 

 Science, in. 



Seconds, 128. 



Series, infinite, 133 et seq. ; Leibnitz's, 

 138. 



Shakespeare, 41. 



Shanks, 139. 



Sharp, Abraham, 139. 



Shortest line, 82. _ 



Slade, 101. 



Smith, D E., 143. 



Snell, 134. 



Socrates, 98. 



Solvability of problems. 121. 



Sophists, 124. 



Space, curvature of, 85 ; four-dimen- 

 sional, 64 ; intuition of, 94 ; of expe- 

 rience, 83 ; of multiple dimensions, 

 great service to science, 85. 



Spheres in space, 70 et seq. 



Spirits, existence of four-dimensional, 98 

 et seq.; of the dead, 65. 



Spirit-rappings, 101. 



Spirit-writing, 101. 



Spiritualistic, mediums, 90 et seq.; 

 seance, in. 



Spiritualists, 64. 



Squaring of the circle, 30, 112-143 



Squares in space, 71. 



Stifel, Michael, 45. 



Straight edge and compasses, to con- 

 struct with, 119 et seq. 



Subtertraction, n. 



Subtraction, 10 et seq., 73 et seq. 



Subtrahent, n. 



Summands, 9. 



Supernatural influences, no et seq. 



Sylvester II., 131. 



Symbols, 2. 



Symmetry, 91. 



Talmud, 123. 



Ten, 4. 



TCTpa-yuvi&iv, 115. 



Thales, 123. 



Thing-in-itself, 98. 



Third degree, operations of the, 19. 



Three Bodies, problem of, 31. 



Time, 36. 



Triangle, sum of the angles of a, 83. 



Trisection of the angle, 30. 



Tweniy, as base, 5. 



