The main motivation for this redefinition of spread is to be able to establish an analogous Cotes Euler Identity using Spreads and sectors. It will serve to draw attention o Eulers method of proceeding to derive the Euler identities, and why they represent a re definition of the sine and cosine ratios? To move from rational forms to infinite fractional forms as Taylor expansions naturally requires a redefining of purpose and intention of use.
Towards the end , catch how Norman explains Euler's thinking about Arcs, radians etc. This type of thinking was first explored by Roger Cotes, and after Euler , Grassmann uses it to explain how the hyperboloc projective geometry actually works , and how it is related to the Euler formulae.
Now i want to modify Normans spread idea to bring it in line with Euclid and these other 2 thinkers, simply by replacing angles and arc by sectors .
These curved gnomon are related to the right gnomon by pythagoras theorem and the analogia of Eudoxus.
The spread of a sector is now a function that inputs a sector and outputs a square..
A function is a method or algorithm hat uses any allowed unput to output a single result. Like any imperial functionary they have just one specific role to play and that is defined as immutable.