Editing Magic square (section)

===Latin Europe===
[[File:Sigillum Iovis.jpg|thumb|215px|right|This page from [[Athanasius Kircher]]'s ''Oedipus Aegyptiacus'' (1653) belongs to a treatise on magic squares and shows the ''Sigillum Iovis'' associated with Jupiter]]
Unlike in Persia and Arabia, better documentation exists of how the magic squares were transmitted to Europe. Around 1315, influenced by Arab sources, the Greek Byzantine scholar [[Manuel Moschopoulos]] wrote a mathematical treatise on the subject of magic squares, leaving out the mysticism of his Middle Eastern predecessors, where he gave two methods for odd squares and two methods for evenly even squares. Moschopoulos was essentially unknown to the Latin Europe until the late 17th century, when Philippe de la Hire rediscovered his treatise in the Royal Library of Paris.<ref>{{Cite web|url=https://www.maa.org/press/periodicals/convergence/the-magic-squares-of-manuel-moschopoulos-introduction|title=The Magic Squares of Manuel Moschopoulos - Introduction {{pipe}} Mathematical Association of America|website=www.maa.org}}</ref> However, he was not the first European to have written on magic squares; and the magic squares were disseminated to rest of Europe through Spain and Italy as occult objects. The early occult treaties that displayed the squares did not describe how they were constructed. Thus the entire theory had to be rediscovered.

Magic squares had first appeared in Europe in ''Kitāb tadbīrāt al-kawākib'' (''Book on the Influences of the Planets'') written by Ibn Zarkali of Toledo, Al-Andalus, as planetary squares by 11th century.<ref name="Comes2016"/> The magic square of three was discussed in numerological manner in early 12th century by Jewish scholar Abraham ibn Ezra of Toledo, which influenced later Kabbalists.<ref name="Cammann1969">{{cite journal| last = Cammann | first= Schuyler| title=Islamic and Indian Magic Squares, part II | journal=History of Religions | volume = 8 | issue = 4 | pages= 271–299| date=May 1969 | jstor= 1062018| doi= 10.1086/462589| s2cid= 224806255}}</ref> Ibn Zarkali's work was translated as ''Libro de Astromagia'' in the 1280s,<ref>presently in the Biblioteca Vaticana (cod. Reg. Lat. 1283a)</ref> due to [[Alfonso X]] of Castille.<ref>See ''Alfonso X el Sabio, Astromagia (Ms. Reg. lat. 1283a)'', a cura di A.D'Agostino, Napoli, Liguori, 1992</ref><ref name="Comes2016">{{cite book| last = Comes | first= Rosa | chapter = The Transmission of Azarquiel's Magic Squares in Latin Europe | pages = 159–198 |editor-last1=Wallis |editor-first1=Faith |editor-last2=Wisnovsky |editor-first2=Robert | title = Medieval Textual Cultures: Agents of Transmission, Translation and Transformation | series = Judaism, Christianity, and Islam – Tension, Transmission, Transformation | volume = 6 | publisher = Walter de Gruyter GmbH & Co KG | isbn = 978-3-11-046730-7 | year= 2016 }}</ref> In the Alfonsine text, magic squares of different orders are assigned to the respective planets, as in the Islamic literature; unfortunately, of all the squares discussed, the Mars magic square of order five is the only square exhibited in the manuscript.<ref>Mars magic square appears in figure 1 of "Saturn and Melancholy: Studies in the History of Natural Philosophy, Religion, and Art" by [[Raymond Klibansky]], [[Erwin Panofsky]] and [[Fritz Saxl]], Basic Books (1964)</ref><ref name="Comes2016"/>

Magic squares surface again in Florence, Italy in the 14th century. A 6×6 and a 9×9 square are exhibited in a manuscript of the ''Trattato d'Abbaco'' (Treatise of the Abacus) by [[Paolo Dagomari]].<ref>The squares can be seen on folios 20 and 21 of MS. 2433, at the Biblioteca Universitaria of Bologna. They also appear on folio 69rv of Plimpton 167, a manuscript copy of the ''Trattato dell'Abbaco'' from the 15th century in the Library of Columbia University.</ref><ref>In a 1981 article ("Zur Frühgeschichte der magischen Quadrate in Westeuropa" i.e. "Prehistory of Magic Squares in Western Europe", Sudhoffs Archiv Kiel (1981) vol. 65, pp. 313–338) German scholar Menso Folkerts lists several manuscripts in which the "Trattato d'Abbaco" by Dagomari contains the two magic square. Folkerts quotes a 1923 article by Amedeo Agostini in the Bollettino dell'Unione Matematica Italiana: "A. Agostini in der Handschrift Bologna, Biblioteca Universitaria, Ms. 2433, f. 20v–21r; siehe Bollettino della Unione Matematica Italiana 2 (1923), 77f. Agostini bemerkte nicht, dass die Quadrate zur Abhandlung des Paolo dell'Abbaco gehören und auch in anderen Handschriften dieses Werks vorkommen, z. B. New York, Columbia University, Plimpton 167, f. 69rv; Paris, BN, ital. 946, f. 37v–38r; Florenz, Bibl. Naz., II. IX. 57, f. 86r, und Targioni 9, f. 77r; Florenz, Bibl. Riccard., Ms. 1169, f. 94–95."</ref>
It is interesting to observe that Paolo Dagomari, like Pacioli after him, refers to the squares as a useful basis for inventing mathematical questions and games, and does not mention any magical use. Incidentally, though, he also refers to them as being respectively the Sun's and the Moon's squares, and mentions that they enter astrological calculations that are not better specified. As said, the same point of view seems to motivate the fellow Florentine [[Luca Pacioli]], who describes 3×3 to 9×9 squares in his work ''De Viribus Quantitatis'' by the end of 15th century.<ref>This manuscript text (circa 1496–1508) is also at the Biblioteca Universitaria in Bologna. It can be seen in full at the address http://www.uriland.it/matematica/DeViribus/Presentazione.html {{Webarchive|url=https://web.archive.org/web/20120301085501/http://www.uriland.it/matematica/DeViribus/Presentazione.html |date=2012-03-01 }}</ref><ref>Pacioli states: ''A lastronomia summamente hanno mostrato li supremi di quella commo Ptolomeo, al bumasar ali, al fragano, Geber et gli altri tutti La forza et virtu de numeri eserli necessaria'' (Masters of astronomy, such as [[Ptolemy]], [[Albumasar]], [[Alfraganus]], [[Jabir ibn Aflah|Jabir]] and all the others, have shown that the force and the virtue of numbers are necessary to that science) and then goes on to describe the seven planetary squares, with no mention of magical applications.</ref>