'Inbat al-miyah al-khafiyya' (The Excavation of Hidden Waters) was written around 1000 AD by Al-Karaji (953 -1029),  a Persian Muslim mathematician and engineer. This book is regarded as the oldest known book on Hydrology. The book contains technical and scientific details of finding the water level, instruments for surveying, techniques for water searching, construction & maintenance of the conduits and their lining, Qanats etc. The book also describes water flow, the classification of soils, origins of under-ground water, surface indication of underground water, the different types and hydraulic characteristics of aquifers, effects of earth quakes on water resources, procedures for determining water quality, treatment of water etc. The information presented in the book is inline with modern theories, most of which was discovered by the west more than 700 years later!

Al-Karaji had discussed the complete hydrological in al-Khafiyya; the description is scattered throughout the book. At one place in his book, he mentions:

“The transformation of water into air in the hot regions and air into water in the cold regions creates a constant cycle which guarantees the prosperity of the lands”.

He concludes that clouds stem from evaporation on the sea; the sun taking only the freshest water from the surface of sea. For this reason, according to karaji, the water remaining on the surface is the most saline, whereas with increasing depth, the sea water becomes progressively fresher, with fresh water being at the bottom of the sea. Karaji also distinguishes between three types of sub water: original (juveline) water, condensed water and common ground water.

Discussing various techniques for searching for water, Karaji mentions one such technique that involved geology, now called Hydrogeology as follows:

“The higher the ratio of the amount of stone to the amount ofsoil in a particular mountain, the less the chance to find a supply of groundwater. Thereis no groundwater in the small and separated mountains especially those which havehard rocks, because no snow can last long on their tops. In case there would be a chainof mountains covering a vast area, it is more likely to find a good supply ofgroundwater, because such mountains enjoy many valleys that can hold ice and snowuntil summer. If a mountain has a flat top with thick vegetation casting shadow on theground and protecting the soil moisture from sun, there would be a better chance tocome across an aquifer……….all the lands linked to the aforementioned mountains contain a good supply ofgroundwater, especially the land which is the lowest as well as the closest to the Earth’score….”

In al-khafiyya, al-karaji provides information on ditch lining that is inline with modern theories:

“If waterway is loose and permeable, the bed should be covered with large bricks and dark lime… or they have to dig the bed about a meter down, and then refill it with clay and compact it by beetle as the bed ditch stands at the same level. Both sides of the ditch should he inclined and built with the same material. Adding some water to clay makes the ditch more efficient. But the water shouldn’t be cut so that its original moisture remains. Lining the ditch with compacted mixture of clay, sand and loam increase its firmness. Our ancestors said, “let the quadrupeds go through ditches to trample”. Lining the ditches with compacted mixture of slaked lime, sand and clay with original moisture became very stiff after a while. Sometimes the bed of canals became so stiff that well sinkers are not able to dig it. Many times those loose lands are covered with rocks and their porous filled with the mixture of clay, lime and sand.”

In the modern science of hydrology, the amount of the bound of well or Qanat is correlated with the type of ground, the amount of seepage and a steady coefficient. Karaji has shown this knowledge in this regard by writing about the role of depth, seepage and ground in designating a bound.

Karaji has also discussed various aspects of earth sciences in his book. He described the earth as spherical ( not flat):

“The Earth with all the mountains and plains on it has a spherical shape. The earth is doomed to spin all the time. Every element on the earth is being drawn toward the center of the earth….”

He also writes in his book:

“whatever higher than the Earth surface such as a building may fall down, and it is attributable to the same attracting force inherent in the Earth and its sphericity.” 

Karaji, thus, succeeded Newton by several centuries in knowing that the earth has a force he named “the tendency to the center” the same that Newton called gravitation! According to Karaji, water is also affected by the force of gravity like every object on the earth.

Although dams have been constructed since ancient times- the first one in 750 BC - medieval Muslims added many innovation to dam construction, maintenance and usage as is evident from the design of many dams built in Iran, Spain, Afghanistan among other places. The use of trigonometry, astrolobes and complex surveying techniques in the construction of these dams resulted in the survival of a number of these dams till today.

One such magnificent dam was the Band-i Amir dam, built in 960AD over the River Kurr between Shiraz and Istakhr in the province of Fars, Iran by Amir Adud al-Dawla. Band-i Amir dam is 250 feet long and 30 feet high and is considered one of the earliest example of the use of dams for hydropower. The water from this dam powered water-raising wheels and watermills – technology pioneered during medieval Islamic civilization.

Al-Muqaddasi , the notable 10th century geographer, wrote about this dam in his famous book ‘Ahsan at-Taqasim fi Ma`rifat il-Aqalim’ (The Best Divisions for Knowledge of the Regions):

‘Adud al-Dawla closed the river between Shiraz and Istakhr by a great wall, strengthened with lead. And the water behind it rose and formed a lake. Upon it on the two sides were ten water-wheels, like those we mentioned in Khuzistan, and below each wheel was a mill, and it is today one of the wonders of Fars. Then he built a city. The water flowed through channels and irrigated 300 villages.’

Badi-i-Amir was constructed with solid masonry blocks that were connected with iron bars set in lead. Cement mortar was used in the joints that binded the structure and made it watertight. The engineers were thus aware of the importance of the quality of mortar and as Al-Balkhi , wrote ”even an iron tool could not scratch it”.

Owing to this high quality of construction, this dam even after more than 1000 years of construction still survives, although it is now silted up.

Al-Kindi (Latinized as Alkindus) was a 9th century Arab Muslim polymath with contributions in Mathematics & Cryptography, Physics, Philosophy, Astronomy, Chemistry, environment, meterology, Medicine, Music and Psychology; with a number of treatises in these areas. His total number of books, as mentioned in Ibn Nadim's Fihrist is 241 (less than 40 are extant ), out of which  atleast 22 were on philosophy and 9 on logic. 'fi al-falsafat al-awla' (on First Philosophy) is regarded as one of his well-known works.

Excerpts:

On Philosophy:

"Indeed, the human art which is higest in degree and most noble in rank is the art of Philosophy, the definition of which is knowledge of the true nature of things, insofar as is possible for man. The aim of the philospher is, as regards to his knowledge, to attain the truth, and as regards his action, to act truthfully; not that the activity is endless, for we abstain and the activity ceases, once we have reached the truth. We do not find the truth we are seeking without finding the cause; the cause of the existence and continuance of everything is The True One, in that each thing which has being has truth. The True One exists necessarily, and therefore beings exist. The noblest part of philosophy and the highest rank in the First Philosophy, i.e. knowledge of the First Truth who is the cause of all truth."

Arguments against Eternity of the World:

"Now, if there is an infinite body, then whenever a body of finite magnitude is separated from it, that which remains of it will either be a finite magnitude or an infinite magnitude. If that which remains of it is a finite magnitude, then whenever that finite magnitude which is separated from it is added to it, the body which comes to be from them both together is a finite magnitude; though that which comes to be from them both is that which was infinite before something was separated from it. It is thus finite and infinite, and this is an impossible contradiction.”

On Truth:

"We ought not to be embarrassed of appreciating the truth and of obtaining it wherever it comes from, even if it comes from races distant and nations different from us. Nothing should be dearer to the seeker of truth than the truth itself, and there is no deterioration of the truth, nor belittling either of one who speaks it or; conveys it."

Seeking Knowledge:

"Our residence in this phenomenal world is transitory; it is a journey towards the eternal one. The most miserable man, is he who prefers for himself the material above the spiritual, for the material, apart from its ephemeral nature, obstructs our passage to the spiritual world. Man should not `disregard any means to protect himself against all human vices, and he should seek to rise to the highest ends of human virtues..., that is, to the knowledge by means of which we protect ourselves against spiritual and bodily disease, and acquire the human virtues in whose very essence goodness is grounded"

... operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.

ax^m – (- bx^m) = (a + b)x^m

Al-Karaji provided two methods for the solution of quadratic equations. One geometric and the other purely algebraic; the later involving formation of a complete square followed by extraction of square roots.

The historian of mathematics, F. Woepcke, in ‘Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi’ (Paris, 1853), regarded Al-Karaji as "the first who introduced the theory of algebraic calculus”