# Ptolemy's Table of Chords

Ptolemy's Table of Chords

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 as 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, for 1/60, 2 for 1/3600), a third column is labeled "sixtieths" ( for integer part, 2 for 1/60, 3 for 1/3600), calculated by . In the semicircle diagram, runs from 0 to 120 partes.

chord(αº)=120sin(αº/2)

αº

m

m

2chord-chord(αº)

2αº+1

2

α

Example: .

chord(10º)=120sin(5º)≈10.4587≈10+27/60+31/3600