By the thirteenth century, all the ingredients necessary for medieval Latin scholars to exercise an evaluative response to texts of mathematical astronomy, increasingly available and varied, were present: adequate numeracy, and use of astronomical tables, as well as preceding authorities’ manuscript texts and illustrations. Thus, it is asked how the exemplary thinker Albertus Magnus (1200–1280) addressed ideas and sources on astronomy. Visual imagery or modeling is key to understanding the approach of his predecessors and his own, as demonstrated in 1243–1244 in Albertus’s earliest writings on lunar phase phenomena. As can be seen through parametric modeling of his sources’ ideas and his own, Albertus, in understanding his authorities, modified their analytical accounts to his own ends.