Tracing the history of medieval astronomy
We shall next show how the remaining individual chords can be derived from the above, first of all setting out a theorem which is extremely useful for the matter at hand.
Having derived a handful of special angle-chord relationships, Ptolemy next set out to derive a more general theorem to get the rest. So Ptolemy constructs a new diagram from which to start his calculations.
Now that we’ve introduced a bit about Ptolemy’s math we can take a look at his derivation of the chord tables. Exactly what those are we’ll get into later, once we have played around with some geometry that will hopefully clarify that issue.
To start, Ptolemy considers the following figure.
Continue reading “The Almagest – Book I: Special Angle Chords”
