Brian Tung wrote:

Ernie Wright wrote:

Doing this calculation gives one a renewed appreciation for what
Hipparchus was able to accomplish before trigonometry was invented.

Modern trigonometry, yes, but they had similar and basically sufficient
mathematical tools.

Indeed. There's no mathematically important difference between using
sines and using chords.

Your point stands, though: Very impressive. Then again, of course, he
was Hipparchus, not some doof.

That's pretty much what I was trying to say. He didn't need *any* of
the tools I perhaps doofily relied on. And unlike us, he couldn't peek
at the answers in the back of the book.

As Brian already knows, almost none of Hipparchus's original writing has
survived. We have to rely mainly on the bits and pieces conveyed to us
by Ptolemy in the Almagest. Ptolemy's description of lunar parallax
calculations is in book V part 17. The diagram (Fig. 5.13 in Toomer's
translation) shows the situation pretty clearly.

- Ernie http://home.comcast.net/~erniew