Diophantus lived about 250 A.D., _that is, in the third century of that Arabian Culture_ whose organic history, till now smothered under the surface-forms of the Roman Empire and the “Middle Ages,”[59] comprises everything that happened after the beginning of our era in the region that was later to be Islam’s. It was precisely in the time of Diophantus that the last shadow of the Attic statuary art paled before the new space-sense of cupola, mosaic and sarcophagus-relief that we have in the Early-Christian-Syrian style. In that time there was once more _archaic_ art and strictly geometrical ornament; and at that time too Diocletian completed the transformation of the now merely sham Empire into a Caliphate. The four centuries that separate Euclid and Diophantus, separate also Plato and Plotinus—the last and conclusive thinker, the Kant, of a fulfilled Culture and the first schoolman, the Duns Scotus, of a Culture just awakened. It is here that we are made aware for the first time of the existence of those higher individualities whose coming, growth and decay constitute the _real substance of history_ underlying the myriad colours and changes of the surface. The Classical spirituality, which reached its final phase in the cold intelligence of the Romans and of which the whole Classical Culture with all its works, thoughts, deeds and ruins forms the “body,” had been born about 1100 B.C. in the country about the Ægean Sea. The Arabian Culture, which, under cover of the Classical Civilization, had been germinating in the East since Augustus, came wholly out of the region between Armenia and Southern Arabia, Alexandria and Ctesiphon, and we have to consider as expressions of this new soul almost the whole “late-Classical” art of the Empire, all the young ardent religions of the East—Mandæanism, Manichæism, Christianity, Neo- Platonism, and in Rome itself, as well as the Imperial Fora, that Pantheon which is the _first of all mosques_. That Alexandria and Antioch still wrote in Greek and imagined that they were thinking in Greek is a fact of no more importance than the facts that Latin was the scientific language of the West right up to the time of Kant and that Charlemagne “renewed” the Roman Empire. In Diophantus, number has ceased to be the measure and essence of _plastic things_. In the Ravennate mosaics man has ceased to be a _body_. Unnoticed, Greek designations have lost their original connotations. We have left the realm of Attic καλοκάγαθία the Stoic ἀταραξία and γαλήνη. Diophantus does not yet know zero and negative numbers, it is true, but he has _ceased_ to know Pythagorean numbers. And this Arabian indeterminateness of number is, in its turn, something quite different from the controlled variability of the later Western mathematics, the variability of the _function_.