Reagere, reactio does not belong to classical Latin. Reagere appears, as late as the fourth century A.D., in Avienus, but not reactio. Nonetheless, antiquity was not unaware of the concept of reciprocal action, where the “patient” reacts in return on the agent. The Aristotelian doctrine of antiperistasis occupied physicists up until the time of Galileo: “All movers, as long as they move, are at the same time moved.” The Latin authors dispense with reagere and reactio. It is the verb pati, designating the passive state to which the prefix re is added in the aphorism attributed to the Scholastics in the 18th century dictionaries: omnis agens agendo repatitur.

What strikes me at the outset, and prompts the title, is that nothing exhibits more clearly than mathematics the complicity between man, God and Satan. That man should have knowledge so luminous, so absolute, would seem impossible did he not share, under whatever doubt or qualification, in the divine. On the other hand, the arrogation of that knowledge, its over-reaching distortion and delimitation of mind and world, hints how far it reenacts the revolt of Lucifer.

The first term in the title of this study might give some surprise. As I hope to prove, however, hieroglyphic writing happens to be the only key enabling us to gain entry to the Egyptian universe. Not only art and mythology, but also the laws, institutions and even daily life itself were “thought hieroglyphically” on the banks of the Nile.

The status a society assigns to woman largely depends upon the basic structure of that society itself. While considering the emergence of the traditional social structure in India, it is interesting to see how diverse struggling racial groups became parts of an integrated hierarchical society in which the invading immigrants formed the elite stratum. We also see how the values of the elite stratum were forcefully imposed on the integrated culture that emerged as a result of this interaction, how the immigrants suffering from a deep-seated feeling of insecurity performed various rites and rituals to ward off the fear of extermination; how the womenfolk belonging to a stock which was not only racially and culturally different but inimical too, were given a low position; and how due to extraneous origin of womenfolk a feeling of suspicion against them was deeply ingrained in the society.

In European cities there is a clear-cut separation between center and suburbs. During the Middle Ages mainly the dictates of military strategy brought about the crowding of the population inside a belt of ramparts. Periodically this corset of walls proved too narrow, and consequently suburbs grew up along the roads leading from the city. These suburbs were in turn incorporated into the city, to be protected by a new enclosure, causing the (older walls to become circular avenues. Paris is a classic example; with its three successive lines of avenues surrounding concentric areas.

Do not believe that the philosophy that has reached us through the writings of Aristotle, Abû Nasr (al-Fârâbî), and the book of Healing (of Ibn Sinâ), will satisfy your longing; neither that any of the Andalusians has written anything adequate on this matter. For the men of superior understanding who lived in Andalusia before the spread of logic and philosophy in that country, devoted their lives to the mathematical sciences…; but could do nothing more…” Ibn Tufayl, Hayy ibn Yaqzân, p. 12.

Much remains to be done by way of determining exactly the ways in which Arab thought penetrated Western Islam-I refer both to its sociological extension and the depth of its psycho-cultural effect. The question thus posed is of considerable historical importance, above all if one wishes to cover the whole period from the beginning of the Eighth Century (i.e. the end of the First/beginning of the Second Century of the Hegira), up to the present day. In fact, the spread of Arab thought to the Maghreb, and its penetration in depth, was accelerated again after the reconquest of the politically autonomous areas. This situation lends our research a certain topicality, whence spring both advantages and disadvantages: there is the advantage of historical knowledge not being limited to an erudite accumulation of facts about a past that has no links with any extant community; yet there is the problem that it is hard not to evoke the past in order to justify present ideological ventures.