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  • Watson G. N. (Cambridge University Press. Cambridge, UK, 1956-01-01)
    The problem which I enunciate and solve in this paper seems to have originated in the study of properties of polyhedral functions. It is a problem of elementary analytical geometry of three dimensions, and the solution ...
  • Scott T. (Cambridge University Press. Cambridge, UK, 1940-01-01)
    1. The invariants and covariants of a system of two conics have been much studied2 but little has been said about those of three conies. Three conics have a symmetrical invariant Ω123, or in symbolical notation (a b c)2. ...
  • Russell A. D. (Cambridge University Press. Cambridge, UK, 1945-01-01)
    In the figure, ABC is a triangle with B > C; AF is made equal to AC, AE bisects the angle A, and BDEG is a rectangle. It is easily seen that the angles marked α are equal, that B − α = C + α, and hence that α = ½ (B − C). Then:
  • Неизвестный автор (Cambridge University Press. Cambridge, UK, 1956-01-01)
  • Walker A. G. (Cambridge University Press. Cambridge, UK, 1945-01-01)
    In this article is described the construction of a thread model of a hyperboloid of one sheet (H) and its asymptotic cone (C). It ia simple to make, requiring only cardboard and thread, and can be made collapsible and of ...
  • Goodstein R. L. (Cambridge University Press. Cambridge, UK, 1949-01-01)
    The familiar Lemma introduced by Goursat in his proof of Cauchy's theorem suggests the following necessary and sufficient condition for differentiability of a complex function f(z).
  • Walls Nancy (Cambridge University Press. Cambridge, UK, 1944-01-01)
    Morley's theorem states that if ABC be any triangle, and if those trisectors of the angles B and C adjacent to BC meet in L, and M, N be similarly constructed, then the triangle LMN is equilateral.
  • Waterson A. (Cambridge University Press. Cambridge, UK, 1944-01-01)
    In this note an expansion is found for the expression xn + yn in terms of x + y and of xy. Two illustrative applications are appended.
  • Russell A. D. (Cambridge University Press. Cambridge, UK, 1949-01-01)
    Theorem. If a circle cut all the sides (produced if necessary) of an equilateral polygon, the algebraic sum of the intercepts between the vertices and the circle is zero; i.e., if any side AB of the polygon be cut by the ...
  • Watson G. N. (Cambridge University Press. Cambridge, UK, 1959-11-01)
    Various improvements in the formula which was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).
  • Wilson N. Y. (Cambridge University Press. Cambridge, UK, 1959-11-01)
    A and B study an array of counters, placed in straight lines on a table, in separated groups (e.g. 28, 53, 1, 16). The counters are to be removed under the following conditions :– Each “player” may take away (1) one counter ...
  • Turnbull H. W. (Cambridge University Press. Cambridge, UK, 1956-01-01)
  • Newns W. F. (Cambridge University Press. Cambridge, UK, 1954-01-01)
    A classical theorem of Cantor states that the class of all sub-classes of a given class has a cardinal greater than that of the given class. This theorem is here established in a sharpened form, which was suggested to me ...
  • Schlapp Robert (Cambridge University Press. Cambridge, UK, 1949-01-01)
    ColinMaclaurin, of West Highland ancestry, a son of the manse, was born at Kilmodan, between the Kyles of Bute and upper Loch Fyne, in February 1698. His father, who was minister there, died soon after, and his mother died ...
  • Turnbull H. W. (Cambridge University Press. Cambridge, UK, 1940-01-01)
    Cardboard or wire models of ellipsoids and hyperboloids exist which consist of two sets of circular sections. They cover the quadric surface with curvilinear quadrilaterals, whose sides remain constant in length when the ...
  • Waddell Agnes H. (Cambridge University Press. Cambridge, UK, 1945-01-01)
    In many cases, when a colony of micro-organisms such as moulds, yeasts or bacteria grows on the plane surface of a solid medium (e.g. agar), starting from a single cell, the colony tends to grow as an ever expanding circle. ...
  • Walker A. G. (Cambridge University Press. Cambridge, UK, 1947-01-01)
    1. The following description of the projective geometry of a finite number of points in 2-space is almost certainly known to those acquainted with projective geometry or with modern algebra. The object of this brief account ...
  • Etherington I. M. H. (Cambridge University Press. Cambridge, UK, 1947-01-01)
  • Houstoun R. A. (Cambridge University Press. Cambridge, UK, 1956-01-01)
  • Bückner Hans (Cambridge University Press. Cambridge, UK, 1952-01-01)
    Consider the nth order differential equation where the coefficients cv are real constants and f is a real function continuous in the interval a≦ x ≦ b. The following theorem will be proved in §4: If the characteristic ...