A History of Mathematics/Modern Europe
We find it convenient to choose the time of the capture of Constantinople by the Turks as the date at which the Middle Ages ended and Modern Times began. In 1453, the Turks battered the walls of this celebrated metropolis with cannon, and finally captured the city; the Byzantine Empire fell, to rise no more. Calamitous as was this event to the East, it acted favourably upon the progress of learning in the West. A great number of learned Greeks fled into Italy, bringing with them precious manuscripts of Greek literature. This contributed vastly to the reviving of classic learning. Up to this time, Greek masters were known only through the often very corrupt Arabic manuscripts, but now they began to be studied from original sources and in their own language. The first English translation of Euclid was made in 1570 from the Greek by Sir Henry Billingsley, assisted by John Dee. About the middle of the fifteenth century, printing was invented; books became cheap and plentiful; the printing-press transformed Europe into an audience-room. Near the close of the fifteenth century, America was discovered, and, soon after, the earth was circumnavigated. The pulse and pace of the world began to quicken. Men's minds became less servile; they became clearer and stronger. The indistinctness of thought, which was the characteristic feature of mediæval learning, began to be remedied chiefly by the steady cultivation of Pure Mathematics and Astronomy. Dogmatism was attacked; there arose a long struggle with the authority of the Church and the established schools of philosophy. The Copernican System was set up in opposition to the time-honoured Ptolemaic System. The long and eager contest between the two culminated in a crisis at the time of Galileo, and resulted in the victory of the new system. Thus, by slow degrees, the minds of men were cut adrift from their old scholastic moorings and sent forth on the wide sea of scientific inquiry, to discover new islands and continents of truth.