Unpublished paper, 'Two connected memoirs: I. On a tangential property of the regular hypocycloids and epicycloids. II. On theorems relating to the regular polyhedras which are analogous to those of Dr Matthew Stewart on the regular polygons' by Henry M [Martyn] Jeffery

Description

In the first memoir, Jeffery aims to establish the following theorems: Firstly, that the product of the perpendiculars drawn from all the cusps in each of these roulettes on any tangent is a function of the perpendicular only, which is drawn on the same tangent from the centre of the fixed circle, on which the roulette is generated; secondly, that the sums of the cotangents of the angles which any tangent to the roulette makes with the vectors drawn from the cusps to the point of contact is a function of the cotangent of the angle made by the vector drawn from the centre with the same tangent line, and of the perpendicular drawn from the centre. In the second memoir, Jeffery proposes 'to consider a group of five surfaces, whose orthogonal projections are the tricuspid and quadricuspid hypocycloids, and which have the property, that the product of the perpendiculars drawn on any tangent plane from all the summits of one of three regular polyhedra (which are cuspidal points on those surfaces), is a function of that perpendicular only which is drawn on the same tangent plane from the centre of the sphere circumscribed about the polyhedron.'

Annotations in ink throughout. Marked on front as 'Archives Dec 21/82'. Includes nine geometrical figures in the text.

Subject: Geometry

Received 3 June 1882 / 8 June 1882.

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 34 of the Proceedings of the Royal Society as '(I.) On a tangential property of regular hypoeycloids and epicycloids. (II.) On theorems relating to the regular polyhedra which are analogous to those of Dr. Matthew Stewart on the regular polygons'.

Reference number

AP/61/10

Earliest possible date

1882

Physical description

Ink and graphite pencil on paper

Page extent

25 pages

Format

Manuscript