The diagram shows what is called the Tusi couple, a theorem first stated and proven by al-Tusi to answer the question of how to generate a linear motion from the combination of two circular motions. Some researchers suggested that Copernicus's work could be an independent proof. However while studying Copernicus's manuscript and the original Arabic manuscript of al-Tusi, scientists willy Hartner who was the president of the international academy of history of science realized that the two proofs used the same alphabetic designators for essential geometric points and came to the conclusion that Copernicus must have copied from altussi's work.
In his 1973 work titled "Copernicus the man the work and its history" Hartner writes that "what proves clearly that we have to do with the case of borrowing is the lettering of the diagrams found in the Tusi's manuscripts and in de Revolutionibus. In both the letters a, d, b, g,and h denote the same characteristic points. A reasonable explanation would be that Copernicus, doubtless in Italy saw the diagram in a manuscript of Tusi's astronomical treaties Tadhkira and asked somebody who knew Arabic to translate the passage for him. As elaborated by George Saliba in his book on Islamic science "where Tusi's proof designated a specific point with Arabic letter "Alif", Copernicus's proof signaled that same point with the equivalent phonetic Latin letter A, where Tusi had "Ba" Copernicus had B etc. except in one case where Tusi had zainand Copernicus had F. The small mis translation is easily explained by the similarity btw two letters zain and fa in medieval Arabic manuscripts which to an inexperienced reader of Arabic manuscripts would likely have been easily misread.
The nearly identical copy of the Tusi couple found in Copernicus's work suggests that Copernicus must have had access to Tusi's work in some form. Copernicus himself likely did not read Arabic. So his access to Tusi's manuscripts would likely have been indirect with the translator interpreting the document for him. The second similarity between Copernicus's mathematics and the works of medieval islamic scholars is found in Copernicus's use of Urdi's lemma. Urdi's lemma was invented by the 13thcentury astronomer and mathematician al-Urdi. Urdi's lemma states that if two lines that are equal in length form equal angles at the baseline then the line joining the two lines is parallel to the baseline. Urdi's lemma was used in the 14th century by Syrian astronomer ibn al-Shatir to unify all planetary models into one geocentric format. Copernicus's use of scientific facts from islamic scholars was not limited to these two mathematical theorems.The first connection between Copernicus and medieval islamic scholars was discovered by modern researchers in the 1950s. In 1957, Otto Neugebauer discovered that the lunar model of ibn al-Shatir was identical to that of Copernicus. Moreover, Copernicus used the same model for the upper planets that al-Shatir used,with of course a transition from a geocentric to a heliocentric model.
Thus, Copernicus also ended up using Urdi's lemma as ibn al-Shatir had done before him. This surprising discovery urged researchers to do further research and led to the creations of many questions that are still open. As evidence of Copernicus's use of medieval islamic mathematical works increases, the question remains how did this information reach Copernicus in Northern Europe? When digging deeper into historical records and archaeological finds it becomes clear that the connections between Renaissance Europe and medieval Islamic texts was quite prominent. Discoveries in the Vatican vaults of both Greek and Arabic copies of al-Tusi's works filled with the annotations of Renaissance scholars suggest that Copernicus and his contemporaries had ready access to research for medieval Islamic scholars. In addition, the existence of hybrid astrolabes which used both Arabic and Latin inscriptions suggest an interest and appreciation by Renaissance scholars for mathematical and scientific discoveries of the medieval Islamic World. Returning to Copernicus, his clear interest in medieval Islamic math characterizes him as a continuation of the shukuk tradition, begun centuries earlier by ibn al-Haytham. The shukuk project came out of the critical treatment of Greek science by islamic scholars and was begun around the year 1000.
The main goal of the project was to reform and correct ancient Greek astronomy. Major contributions to this project were made by the Maragha school and the maragha observatory built under the direction of al-Tusi in the 13th century. Researchers Neugebauer and Swerd low suggested that by copying and using the reformed and new ideas created by the shukuk tradition in his own works, "Copernicus can be looked upon as if not the last surely the most noted follower of the Maraga school." "...and the question therefore is not whether but when, where, and in what form Copernicus learned of Maragha theory." While Copernicus's influence on astronomy was invaluable, he would not have been able to come up with his models without the use of previous works by medieval islamic scholars, most notably al-Tusi, al-Urdi, and al-Shatir. Decades after the connections between Copernicus and medieval Islamic scholars were discovered, many people are still unaware of this connection. Most often the more accurate version of history with more complete info about the background of Copernicus's work is not being taught in schools.In fact, the scientific revolution had already begun centuries earlier by the reforms of ancient Greek texts by medieval islamic scholars.
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