Talk:Ptolemy's table of chords

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edit·history·watch·refresh Stock post message.svg To-do list for Ptolemy's table of chords:
  • Further inline citations, including:
  • It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy
  • (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of 7½°).
  • Several centuries passed before more extensive trigonometric tables were created.
  • Page numbers in Glowatzki and Göttsche?
  • The parts about the three distinct methods of computing chords.
  • More on the geometric theorems: Their precise statements, how they are proved, how they are used in deriving trigonometric identities, how those identities are used in computing chords.
  • History of editions of the book including those in Arabic.
  • When did more extensive tables supersede this one? Which century?
  • How did the table influence later work?
  • And probably other things.........

Untitled[edit]

I found a cite for "an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of 7½°)" Paul August 02:15, 12 March 2011 (UTC)
Most, or maybe all, of the assertions are in the listed references, but I'd have to sort out which is which. I'll probably get to that in the coming weeks if no one beats me to it. Michael Hardy (talk) 02:36, 12 March 2011 (UTC)

Sixtieths[edit]

The details of the description of the meaning of the "sixtieths" column doesn't seem to make a lot of sense. How is it scaled? --Dfeuer (talk) 21:14, 7 July 2013 (UTC)

Arc vs. Chord[edit]

The article currently states "For tiny arcs, the chord is to the arc as π is to 3, or more precisely, the ratio can be made as close as desired to π/3 ≈ 1.04719755 by making θ small enough. Thus, for the arc of (1/2)°, the chord is slightly more than the arc."

This statement has the arc and chord reversed. The arc is always longer than chord since in Euclidean Geometry the shortest path between two points is a straight line. It should state: For tiny arcs, the arc is to the chord as π is to 3, or more precisely, the ratio can be made as close as desired to π/3 ≈ 1.04719755 by making θ small enough. Thus, for the arc of (1/2)°, the chord is slightly less than the arc. — Preceding unsigned comment added by 212.21.46.23 (talk) 11:00, 20 May 2014 (UTC)