Unpublished paper, 'On clinant geometry, as a means of expressing the general relations of points on a plane, realising imaginaries, and extending the theories of anharmonic ratios' by Alexander J [John] Ellis

Description

The serious difficulties presented by 'imaginaries' in plane geometry arise from treating the 'principle of signs' as a matter of convention, and not as a particular case of a general operation here termed a clinant, which consists in altering the length of a line in a given ratio, and rotating it through a given angle. As the calculus of clinants furnishes a geometrical representation for every algebraical result, imaginaries disappear, and there is no longer any apparent disagreement between analysis and geometry. Many theories, as, for example, those of anharmonic ratios, hitherto only established for points on a straight line, are also easily extended by means of clinants to embrace any points upon a plane. The object of the present paper is to establish and illustrate these facts.

Annotations in pencil. Marked on front as 'Archives Oct 30 [18]63'.

Subject: Mathematics / Geometry

Received 28 January 1863. Read 26 February 1863. Communicated by Arthur Cayley.

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 12 of the Proceedings of the Royal Society as 'On clinant geometry, as a means of expressing the general relations of points in a plane, realizing imaginaries reconciling ordinary algebra with plane geometry, and extending the theories of anharmonic ratios'.

Reference number

AP/45/2

Earliest possible date

1863

Physical description

Ink and graphite pencil on paper

Page extent

24 pages

Format

Manuscript