XXVI. An investigation of a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs with some other new and useful theorems deduced therefrom

@article{LandenXXVIAI,
  title={XXVI. An investigation of a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs with some other new and useful theorems deduced therefrom},
  author={John Landen},
  journal={Philosophical Transactions of the Royal Society of London},
  pages={283 - 289}
}
  • John Landen
  • Philosophical Transactions of the Royal Society of London
In a paper, which the Society did me the honour to publish in the Philosophical Transactions for the year 1771, I announced, that I had discovered a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs; and I promised to communicate the investigation of such theorem. I now purpose to perform my promise; and, being pleased with the discovery (by which we are enabled to bring out very elegant conclusions in many interesting enquiries, as well… Expand

Figures from this paper

Landen survey
Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearance in the literature. To Henry, who provides inspiration, tasteExpand
Numbers and Functions: From a Classical-Experimental Mathematician's Point of View
TLDR
This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics, on exploring the connections between these functions and topics in number theory and combinatorics. Expand
On the solution of a Riesz equilibrium problem and integral identities for special functions
The aim of this note is to provide a quadratic external field extension of a classical result of Marcel Riesz for the equilibrium measure on a ball with respect to Riesz s-kernels, including theExpand
LANDEN TRANSFORMS AS FAMILIES OF (COMMUTING) RATIONAL SELF-MAPS OF PROJECTIVE SPACE
The classical (m,k)-Landen transform Fm,k is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m’th roots of unity.Expand
The derivation of algorithms to compute elliptic integrals of the first and second kind by Landen-transformation
This paper deals with elliptic integrals of first and second kind and their solution by Landen-transformation. It is explained how the Landen-transformation works and how the different algorithms canExpand
Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, p, and the Ladies Diary
Paper 8: Gert Almkvist and Bruce Berndt, “Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, pi, and the Ladies Diary,” American Mathematical Monthly, vol. 95 (1988), pg. 585–608.Expand
Jacobi-Sohncke Type Mixed Modular Equations And Their Applications
In this paper, we establish Jacobi-Sohncke type several new mixed modular equations for composite degrees 1, 3, and . As an application, we establish the modular relations between theExpand
Difference Equations Everywhere: Some Motivating Examples
This work collects several situations where discrete dynamical systems or difference equations appear. Most of them are different from the examples used in textbooks and from the usual mathematicalExpand
A Geometric View of Rational Landen Transformations
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
Ramanujan's Most Singular Modulus
We present an elementary self-contained detailed computation of Ramanujan’s most famous singular modulus, k210, based on the Kronecker Limit Formula.
...
1
2
...