Al-Kindi supports Euclid and Ptolemy’s theory of visual extramission: that
the eye emits rays that fall on objects to sense the rays in succession.
Following Galen’s anatomical model, al-Kindi suggests that these rays are
not material, but that their visual power transforms the ambient air. He
discounts the theory of intromission because it contradicts Euclidian
mathematics. In asserting mathematics as the model for sensation within
the intrinsic and immutable pattern of nature, al-Kindi affirmed
Mu’tazilite rationalism. In contrast, ibn Sina argued vehemently against
the model of extramission through his observation of how sight functions
in mirrors.^39
Unlike al-Kindi, the Brethren of Purity underscored the metaphysical
utility of geometric knowledge inherited from the Pythagorean tradition
through the Latin quadrivium of Boithius (d. 524 CE).^40 For them, geo-
metry (handasa) was a mathematical science that entailed knowing mag-
nitudes and distances (or dimensions). Like al-Farabi, they divided it into
two practices: the sensible, of use to artisans; and the intelligible (or
conceptual), used to understand the motion of heavenly bodies and the
impact of musical harmonies on the corporeal embodied soul as well as the
non-corporal intellect.^41 They held that geometry’s dependence on vision
made it more readily understood than the mathematical science we know
as algebra (al-jabr, meaning‘the reunion of broken parts’), recently devel-
oped by Muhammad ibn Musa al-Khwarizmi (780–850), from whose
name derives the word‘algorithm.’^42 Similarly, Abu al-Hasan al-Amiri
(d. 922), who worked to reconcile philosophy, Sufism, and Islam at the
Buyid court in Khorasan, considered geometry’s“sensual prototypes”as
easier to understand than arithmetic and pragmatically useful for
artisans.^43
They considered the imagination as regulating aflow of knowledge from
the senses toward abstraction. Things in the world (knowable entities) are
apprehended by the sense faculties (sight, sound, taste, etc.). The imagina-
tive faculty accounts for these and relays the information to the imaginary
and cognitive faculties that preserve the sensory impressions in memory.
The soul relies on these memories and therefore does not need sense data.
The imagination thus bridges the practical arts of the sensible world and
the theoretical arts of the intelligible world. This cultivates a capacity for
abstraction. For them, the apprentice of mathematics is progressively
trained to minimize reliance on the senses. The intellect learns to
(^39) Sinai, 2015 : 285. (^40) El-Bizri, 2012 :2. (^41) El-Bizri, 2012 :44–46, 79–91.
(^42) El-Bizri, 2012 :4. (^43) Necipoğlu,2017a: 20.
Isometric Geometry in Islamic Perceptual Culture 283