'Abd al-Rahman al-Sufi's 3-Step Magnitude System

'Abd al-Rahmān al-ūfī's Book of the Fixed Stars dates from around AD 964 and is one of the most important medieval Arabic treatises on astronomy. In this paper we begin with a very brief introduction to the Book of the Fixed Stars. This book contains an extensive star catalogue that lists star coordinates and magnitude estimates for all of the Ptolemaic stars. However, in his book al-hūfī utilized three distinct intermediate magnitude values whereas Ptolemy only mentioned two. We believe that al-hūfī used what we have termed a '3-step intermediate magnitude system,' which is more accurate than Ptolemy's 2-step intermediate system. In this paper we examine in detail the accuracy of this unique 3-step system in comparison with Ptolemy's and modern magnitude values.