TRANSMUTATION
, or Transformation, in Geometry, denotes the reduction or change of one figure or body into another of the same area or solidity; as a triangle into a square, a pyramid into a cube, &c.
Transmutation, in the Higher Geometry, has been used for the converting of a figure into another of the same kind and order, whose respective parts rise to the same dimensions in an equation, and admit the same tangents, &c.
If a rectilineal figure be to be Transmuted into another, it is sufficient that the intersections of the lines which compose it be transferred, and lines drawn through the same in the new figure. But if the figure to be Transmuted be curvilinear, the points, tangents, and other right lines, by means of which the curve line is to be defined, must be transferred.
