Cambridge University Press по журналам "Edinburgh Mathematical Notes"
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(Cambridge University Press. Cambridge, UK, 19560101)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 ...

(Cambridge University Press. Cambridge, UK, 19560101)There are two alternative methods of defining the concept of “convergence” of a sequence, one involving explicit mention of the limit, the other (Cauchy's condition) giving a necessary and sufficient condition in terms of ...

(Cambridge University Press. Cambridge, UK, 19400101)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. ...

(Cambridge University Press. Cambridge, UK, 19390101)Since the publication of my article on “The advantage of differentials in the technique of differentiation” both Dr H. A. Hayden and Prof. A. Oppenheim have kindly pointed out to me that there is a much shorter solution ...

(Cambridge University Press. Cambridge, UK, 19520101)The purpose of this note is to generalise the DirichletLiouville formula which expresses a certain type of multiple integral in terms of a single integral. In our formula the multiple integral will involve several arbitrary ...

(Cambridge University Press. Cambridge, UK, 19560101)The wellknown multiple integral where Rn is the region defined by x1 ≥ 0, x2 ≥ 0, …., xn ≥ 0, x1 + x2 + …. + xn ≤ 1, and where a0, a1, …, an are positive constants, can be evaluated either in the classical way using the ...

(Cambridge University Press. Cambridge, UK, 19450101)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:

(Cambridge University Press. Cambridge, UK, 19560101)

(Cambridge University Press. Cambridge, UK, 19450101)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 ...

(Cambridge University Press. Cambridge, UK, 19601201)The theorem concerned is the following: iff is continuous in [a, b], and f exists and is finite except at an enumerable set of points and Lebesgue integrable in [a, b], then

(Cambridge University Press. Cambridge, UK, 19490101)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).

(Cambridge University Press. Cambridge, UK, 19440101)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.

(Cambridge University Press. Cambridge, UK, 19611201)It seems a pity that Hamiltonian dynamics—contact transformations and so on—is regarded as a fearsome subject, too timeconsuming to teach to most students; for it is the one branch of dynamics to point a way to new ...

(Cambridge University Press. Cambridge, UK, 19440101)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.

(Cambridge University Press. Cambridge, UK, 19490101)That the determinant where hr is the rth complete homogeneous symmetric function in a set of n arguments, is equal to the quotient of a particular pair of alternants was shown essentially by Jacobi in 1841 and by Trudi ...

(Cambridge University Press. Cambridge, UK, 19490101)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 ...

(Cambridge University Press. Cambridge, UK, 19591101)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).

(Cambridge University Press. Cambridge, UK, 19560101)Let f be a continuous complexvalued function of a real parameter whose real and imaginary parts are of bounded variation in the range (a, b) of the parameter, so that the range of f is a rectifiable plane curve. The main ...

(Cambridge University Press. Cambridge, UK, 19390101)Given an infinity of polygons which form the boundary of a finite number of polyhedra, we shall consider the complex K consisting of the polyhedra, and of the faces, edges and vertices of the polygons. We consider only ...

(Cambridge University Press. Cambridge, UK, 19520101)The object of this note is to give simpler proof* of two formulae involving the function ψ (z) which I have proved elsewhere by more complicated methods.
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