Eratosthenes angle measurement

[Taylor_1989]

I am writing an article on Eratosthenes and am having a little trouble on how he actual found the angle of the stick. Because as far as I can gather there was no series solutions for any of the trig defin no calculators. All he knew was the length of the shadow and the height of the stick. I have personally tried scribing triangle inside a circle and seeing if I could see a relation but I cant.

I think the problem is I don’t actually know where sine and cosine come from, in how they where developed from a geometry stand point.

Could someone please give some advcie on the matter please

 

[fresh_42]

I've heard he used a simultaneous measurement ~40 mi. south of Alexandria in a well.
Have you already read this one: http://www.eaae-astronomy.org/eratosthenes/eratosthenes-99456

 

[brainpushups]

I am writing an article on Eratosthenes and am having a little trouble on how he actual found the angle of the stick. Because as far as I can gather there was no series solutions for any of the trig defin no calculators. All he knew was the length of the shadow and the height of the stick. I have personally tried scribing triangle inside a circle and seeing if I could see a relation but I cant.

I've never seen a source that accounts for exactly how he made his measurement, but I'd wager it was a direct measurement and not something he calculated. Heath's book on Aristarchus mentions Eratosthenes measurement and claims that he measured the angle cast by the gnomon on his scaphe. The wikipedia article I linked speculates that he may have used a compass to measure the angle.