Robert E. Hall wrote the following on al-Khazini:
Al-Khazini later became a mathematical practitioner under the patronage of the Seljuk court, under Sultan Ahmed Sanjar. Little else is known about his life, but it is known that he refused rewards and handed back 1000 dinars sent to him by the wife of an Emir, and that he usually lived on 3 dinars a year.
Al-Biruni and al-Khazini were the first to apply experimental scientific methods to the fields of statics and dynamics, particularly for determining specific weights, such as those based on the theory of balances and weighing. He and his Muslim predecessors unified statics and dynamics into the science of mechanics, and they combined the fields of hydrostatics with dynamics to give birth to hydrodynamics. They applied the mathematical theories of ratios and infinitesimal techniques, and introduced algebraic and fine calculation techniques into the field of statics. They were also the first to generalize the theory of the centre of gravity and the first to apply it to three-dimensional bodies. They also founded the theory of the ponderable lever and created the "science of gravity" which was later further developed in medieval Europe. The contributions of al-Khazini and his Muslim predecessors to mechanics laid the foundations for the later development of classical mechanics in Renaissance Europe.
The first of the book's eight chapters deals with his predecessors' theories on the centre of gravity, including Al-Razi (Latinized as Rhazes), Abū Rayhān al-Bīrūnī, and Omar Khayyám. He also draws attention to the failure of the ancient Greeks to clearly differentiate between force, mass, and weight, and he goes on to show awareness of the weight of the air, and of its decrease in density with altitude. The strict definition for a specific weight is given by Al-Khazini in The Book of the Balance of Wisdom:
After extensive experimentation, Al-Khazini records the specific gravities of fifty substances, including various stones, metals, liquids, salts, amber, and clay. The accuracy of his measures were impressive and comparable to modern values. In another experiment, Al-Khazini discovered that there was greater density of water when nearer to the Earth's centre, which was later proven by Roger Bacon in the 13th century.
Al-Khazini defines heaviness in traditional Aristotelian terms as an inherent property of heavy bodies:
On the basis that there is denser air when nearer to the centre of the Earth (derived from the Archimedes principle), and that the weight of heavy bodies increase as they are farther from the centre of the Earth (derived from al-Quhi and Alhacen's theories that weight varies with the distance from the centre of the Earth), al-Khazini postulated that the gravity of a body varies with its distance from the centre of the Earth:
It appears that what al-Khazini meant by "gravity" ("thiql" in Arabic) is both an idea similar to the modern concept of gravitational potential energy, and the moment of a force relative to a point (both meanings were derived from al-Quhi and Alhacen). In either case, al-Khazini appears to have been the first to propose that the gravity of a body varies with its distance from the centre of the Earth. In his first sense of the word "gravity", the concept was not considered again until Newton's law of universal gravitation in the 18th century, but in his second sense of the word, the concept was considered again by Jordanus de Nemore in the 13th century.
N. Khanikoff, an early translator and commentator of al-Khazini's work, summarized his ideas regarding gravity as follows: