WOLFRAM|DEMONSTRATIONS PROJECT

Ptolemy's Table of Chords
​

​
table
picture
semicircle
page number
1
2
3
4
αº
40
​​​​​
partes
m
2
41
2
33
This Demonstration shows a reconstruction of Ptolemy's table of chords. He used 120 partes as the diameter of a circle. The chord is the red line in the semicircle. In modern terms, the table shows the values of
chord(αº)=120sin(αº/2)
as
αº
goes from 1/2º to 180º. The fractional parts of the chord lengths were expressed in sexagesimal (base 60) notation. After the columns for the arc and the chord (partes for integer part,
m
for 1/60, 2 for 1/3600), a third column is labeled "sixtieths" (
m
for integer part, 2 for 1/60, 3 for 1/3600), calculated by
2chord
2αº+1
2
-chord(αº)
. In the semicircle diagram,
α
runs from 0 to 120 partes.
Example:
chord(10º)=120sin(5º)≈10.4587≈10+27/60+31/3600
.