The assistance of Ty Harness in my attempt to make sense of the methodology of the ancient geometers is gratefully acknowledged. Any mistakes or erroneous conclusions found on this page, however, are totally my own doing.
Cubes Pyramids Frustums - pdf file
Eratosthenes' Panel Model - GeoGebra file
Eratosthenes' Panels - interactive html file
Archytas' Constructing Two Means - pdf file
Archytas' 3D Simulation - interactive html file
Eudoxus and Descartes - pdf file
Menaechmus' Compass - Physical Model - pdf file
Archimedes' On Conoids - pdf file
Archimedes' On Conoids P7 Three Solutions - GeoGebra file
Apollonian Cone Cevians - interactive html file
Composite Archimedes-Apollonius Model - GeoGebra file
About Conics - Part 1. Angle Chords - html file
Timoshenko Particles - pdf file
Catapults & Cube Roots - pdf file
Frustum Formula, Means and Eratosthenes' Mesolabe - pdf file
This quotation
from the 1830's "Penny Cyclopaedia of the Society for the Diffusion of
Useful Knowledge" contends that
"Modern writers
employ fractions instead of ratios, and with great advantage. But the
student who leaves untouched that consideration of ratio which includes
incommensurables as well as commensurables will never be more than a
mathematician to a certain number of decimal places."
Then in a 2012
conference paper I found this comment about a theorem the author was
preparing to discuss.
"...(I first found
[it] in a newspaper, sent in by a GEOM (Geometrically Excited Old Man).
For some reason, some elderly men continue to be intrigued by geometry,
usually in a negative manner, trying to prove every angle can be
trisected, etc.)..."
As an
octogenarian I feel obligated to disclose that I may be only a two bit
mathematician but I am at least half a GEOMeter.