The four new instruments al-'Urdi. introduces (5, 7, 8, and 9) appear to be a combination of quadrants or rulers (in different ways in order to employ various trigonometric functions) for determining the star's altitude and, by mounting the complex on an elevated circle, for measuring azimuth.
Besides the principal difference in the basic approach to observational instrumentation, another explicit distinction between al-'Urdi's instruments and those described in our treatise is that the former are mostly made of teak from India (53) with only circular parts cast from copper, whereas metals play a more important role in the latter.
Al-'Urdi described only three big circular instruments at Maragha.
The dhira' used in the reconstruction is the royal cubit (dhira' al-malik or al-dhira' al-hashimi) of 665 mm, as used in al-'Urdi's treatise and shown in Table 2.
It is interesting to note that al-'Urdi's "perfect instrument" likewise used a parallactic rule, but inside a circle, so the azimuth was read by putting the chord rule onto the azimuth ring.
(84) None added details concerning use of this instrument for determining the eclipsed diameter or area of the sun or the moon by drawing a circle on the lower pinnula (as our treatise did) or using a circular plate on the lower pinnula (as al-'Urdi did).
In his treatise al-'Urdi presented an improvement on the classical dioptra for determining the eclipsed diameter of the sun or the moon.
On the other hand, the author breaks with the recommendations of his precursor, al-'Urdi, not to use ropes for measuring lengths.
Seemann, "Die Instrumente der Sternwarte zu Maragha nach den Mitteilungen von al-'Urdi," in Sitzungsberichte der physikalisch-medizinischen Sozietat zu Erlangen 60 (1928): 57ff., instrument IV.
But the latter had been introduced long before, by Urdi, and this is not acknowledged in the Ta dil.
Sadr chose to ignore Shirazi's valid solution, applying instead the Urdi configuration referred to above, combined with a spherical Tusi couple.