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

.

Ptolemy's Table of Chords​

Ptolemy's Table of Chords