Born: about 800 in Baghdad, Iraq
Died: after 873 in Iraq

The three Banu Musa brothers are almost indistinguishable and most of the information is at this link. However, there is some information specific to the eldest: Jafar Muhammad ibn Musa ibn Shakir.

It certainly appears that of the three brothers, he was the best mathematician. In addition to making perhaps the major contribution to the geometry text described above, Jafar Muhammad also wrote Premises of the book of conics which was a critical revision of Apollonius's Conics.

1. Al-Dabbagh, Biography in Dictionary of Scientific Biography (New York 1970-1990). 
   http://www.encyclopedia.com/doc/1G2-2830900258.html

Articles:

1. D El-Dabbah, The geometrical treatise of the ninth-century Baghdad mathematicians Banu Musa (Russian), in History Methodology Natur. Sci., No. V, Math. Izdat. (Moscow, 1966), 131-139.
2. Banu Musa, The Encyclopaedia of Islam VII (Leiden, 1993), 640-641.
3. Banu Musa, Encyclopaedia Iranica III (London, 1989), 716-717.
4. R Rashed, Archimedean learning in the Middle Ages : the Banu Musa, Historia Sci. (2) 6 (1) (1996), 1-16.
5. T Sato, Quadrature of the surface area of a sphere in the early Middle Ages - Johannes de Tinemue and Banu Musa, Historia Sci. No. 28 (1985), 61-90.