[...]... Europe Many of these items originated in India and Ceylon; their long journey took them northwest to the head of the Persian Gulf, then by boat up the Tigris to Baghdad or Mosul, and by camel on to Syria or to the Red Sea ports of Egypt and to the Nile Dominating the Mediterranean trade were the ships from Pisa, Genoa, and Venice While most of Italy was at that time under the rule of either the Holy Roman... first they would simply stand and watch the master at work, then they would graduate to standing alongside the expert, handing him the counters from bowls placed next to the counting board, and finally they would reach the stage when, under the watchful eye of the master, they could perform some of the computations themselves Yet even in the hands of an expert, the counting board, like any form of abacus,... symbol just like the other nine This meant developing the rules for doing arithmetic using this additional symbol along with all the others This second step—changing the underlying conception so that the rules of arithmetic operated not on the numbers themselves (which excluded 0) but on symbols for numbers (which included 0)—was the key Over time it led to a change in the conception of numbers to a more... with the exchange of books and information The oldest dated Latin manuscript containing the Hindu-Arabic numerals—though it did not show how to use them in calculations—is the Codex Vigilanus, a compilation of historical documents written in 976 in Spain and found in the monastery of Albelda in the Rioja (Asturias) The manuscript is a copy made by the monk Vigila of an earlier work, the Etymologies of. .. Latin manuscripts provide most of the early examples of place-value numerals usage outside India Thus some of Leonardo’s written sources for Hindu-Arabic arithmetic may have been in Latin, the oldest surviving being a copy of al-Khwārizmī’s Arithmetic Another available Latin treatise on the system was Liber ysagogorum alchorismi, which may have been written by Adelard of Bath Unlike the majority of the. .. Mūsā al-Khwārizmī, which can be translated as “Father of ‘Abdallāh, Mohammed, son of Moses, native of the town of al-Khwārizmī”.22 The form parallel to Leonardo Pisano (Leonardo of Pisa) would therefore be Mu ammad al-Khwārizmī (Muhammad of Khwārizmī), and the one parallel to Leonardo filius Bonacci Pisano (Leonardo, son of Bonacci, of Pisa) would be Mu ammad ibn Mūsā al-Khwārizmī (Muhammad, son of Moses,... creative mathematical talent, or did he merely assemble and transcribe the works of others? Contemporary authorities disagree, saying variously: [He was] the greatest mathematician of the time, and if one takes all the circumstances into account, one of the greatest of all time [Al-Khwārizmī] may not have been very original It is impossible to overstress the originality of the conception and style of al-Khwarīzmī’s... numbers and arithmetic is the world’s only truly universal language Writing numbers as we do makes arithmetic adding, subtracting, multiplying, and dividing pairs of numbers routine Provided you start out by placing the two numbers correctly—in the case of addition, subtraction, or multiplication, one number beneath the other, with their digits lined up vertically starting from the right the rest of. .. Emperor, the king of Sicily, or the pope, these three great seafaring cities functioned in many respects like nation-states, as did the inland cities of Florence and Milan With strong armies and navies, not only were the Italian city-states able to fend off attacks from land and sea; they also gained strongholds elsewhere, including some key ports on the shores of North Africa By the middle of the twelfth... Pisano (“Port of Pisa”, nowadays part of the busy Mediterranean port-city of Livorno), several miles to the south of the Arno’s mouth, along the seacoast Their cargoes were then unloaded and carried into Pisa on narrow, oared galleys or on river flatboats propelled by hand using a pole Other changes were also affecting the lives of the Pisans in Leonardo’s time During the tenth century, as the five hundred . as “al-Khwārizmī’s Arithmetic. ” Al-Khwārizmī’s second book, completed around 830, was al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala, which translates literally as The abridged book on. since cal- culations required constant swapping of symbols. In adopting the Hindu-Arabic numer- als as mere markers, Gerbert missed the real power of Hindu-Arabic arithmetic. The ap- pearance of Gerbert’s. break the tedium of the hundreds of practical problems that dominate the book. Part of the reason Leonardo has been overlooked, whereas comparable figures like Co- pernicus, Galileo, and Kepler