During the Medieval Islamicate period, the astronomical phenomonenon called the “shadow,” the darkness created by a light source encountering a gnomon, underwent a significant transformation when mathematicians began to perceive these shadows as an abstracted idea. We see ideas of ẓila (lit. "shadow," often translated to “Tangent’’) evolve between authors throughout the Medieval Islamicate era, ranging from the empirically-grounded astronomical shadow to an abstracted trigonometric relation. Of these interpretations, we examine three mathematicians, Ḥabash al-Ḥāsib (776CE - after 869), Abū ’l-Wafā’ (940 - 998), and al-Bīrūnī (973 - c. 1050), and how their “Shadows’’ existed within these ideas of the Shadow/Tangent. We specifically look at the diagrams, figures, and models accompanying descriptions of ẓila to gauge each mathematician’s conception of what the Shadow was, be it astronomical, trigonometric, neither, or both.

Predicting eclipses were a central part of Indian astronomy and many texts were written to predict these dramatic celestial events and account for their many features. One of these, the
Parvadvayasādhana (``Computation of the two syzygies'') of Mallāri (fl. late sixteenth century) is a short Sanskrit treatise dedicated exclusively to the computation of lunar and solar eclipses. We take a glimpse into this historical text and related eclipse reckoning sources with a view to the the astronomical diagrams they contain. We examine how these graphical diagrams balance the timelessness of an abstract geometrical rendering with the timebound aspects of an observable astronomical event.

The Greek text of the Almagest contains 197 diagrams. In the translation of al-Ḥajjāj (d. after 813 CE) these diagrams are for the most part faithfully copied. Very few diagrams are missing and rarely diagrams are added. The dots are labelled with the letters which according to the scientific abjad notation represent the same numeric value as the corresponding Greek letters. In one case, an Arabic diagram has preserved the original form which in the Greek manuscript tradition was extended by an additional point, labelled with Iota, a letter otherwise avoided in the Greek diagrams. One diagram in the Arabic text is repeated on the following page for the convenience of the reader. One would expect that the orientation of the diagrams is changed according to the writing direction of Arabic script, but only very few are vertically mirrored. More freedom is found in commentaries on the Almagest. The commentary of Al-Fārābī (d. 950 CE) is preserved in two manuscripts. One contains neither diagrams nor empty spaces for them. In the other manuscript, most diagrams are executed and only a few spaces for diagrams are left empty. Occasionally, diagrams are extended, apparently for didactical purposes. Some preserve the original labelling for the respective points, but other diagrams are relabeled from scratch. These and other observations can provide an insight into the teaching practice of a demanding scientific text such as the Almagest. In the paper to be presented, Isḥāq Ibn Ḥunayn’s translation and more commentaries will be discussed.