Salih Zeki ve Asâr-ı Bâkiye
Salih Zeki and Asâr-ı Bâkiye
Yazar: İnönü, Erdal
Dergi: Osmanlı Bilimi Araştırmaları, Vol. 7 No. 1, 2005
Anahtar kelimeler: Matematik, İslam, trigonometri, ondalık kesirler, Salih Zeki, Asâr-ı Bâkiye ; Mathematics,Islam,trigonometry,decimal fractions,Salih Zeki,Asâr-ı Bâkiye,Athar-i Baqiya

In commemoration of the hundred fortieth anniversary of the birth of Salih Zeki (1864-1921), the last renown Ottoman mathematician, a summary and evaluation of his book on the development of mathematics in Islam, Asâr-ı Bâkiye [Athar-i Baqiya]is presented. Originally, the book was planned to have four volumes, dealing separately with trigonometry, arithmetic and algebra, astronomy and geometry. Unfortunately, only the first two volumes have been printed (1913). Recently, the science historians at Ankara University transcribed these two volumes into modern Turkish and, my presentation is based on this edition completed in 2004. In his preface, Salih Zeki explains his aim in writing this book as “indicating the additions brought by Eastern mathematicians to the old edifice of Greek mathematics, and establishing clearly the levels of development at which this legacy was transmitted to Western scientists.” The first volume on trigonometry starts with explaining how the old astronomers, including Ptolemaios (c.100-c.170) dealt with angles, using only the chords, and a relevant theorem of Menelaus (c.100). He continues with the introduction of the concepts and tables of trigonometric terms, such as sines by Thabit ibn Qurra (836-901), followed by Jabir al-Battani (c.858-929) and tangents by Abu'l-Wafa al-Buzjani (940-998). Through a detailed analysis of various astronomical or trigonometric tables, he makes it clear that the science of trigonometry is essentially the creation of Eastern mathematicians (mostly Islamic, following a beginning in India). I may add that this conclusion is shared by the statements of Western historians, such as Paul Tannery (in 1893) and Colin Ronan (in 1983). The second volume relates in detail how the present number characters (both Arabic and Latin) evolved from Indian numerals through the book Kitab fi el Hisab el-Hindi by al-Khwarizmi (c. 780-c. 850) which was written to teach the people how to use numbers in their daily lives. There were two kinds of numerals in al-Khwarizmi’s book, both taken from Indian mathematics. One of them, through the translations Liber Abaci, 1202 by L.Fibonacci (1170-post 1240) and Summa di Arithmetica, Geometria (1494) by L.Pacioli (c. 1445- c.1514) led to the development of Latin numerals, and the other, through the works of Islamic mathematicians gave rise to Arabic numerals. Salih Zeki presents several arguments to refute the claim made by some Western historians that the Indian-Arabic numerals were first invented in ancient Greece by the followers of Pythagoras (c.570-c.490). Finally, he gives two examples to show that decimal fractions were first used by Islamic mathematicians; one is the decimal expression of π by Jamshid Ghiyath al-Din al-Kashi (d. 1429) obtained in Samarkand around 1420, which was valid to the sixteenth decimal point, and the other is the decimal expression used for the trigonometric tables prepared by the astronomer Taqi al-Din (d.1585) in Istanbul, around 1570.As a conclusion, I wish to express the view that, Salih Zeki’s Asâr-ı Bâkiye, both by documenting attempts to clarify the priorities in the development of mathematics, and in providing a detailed explanation of many interesting computations by ancient mathematicians, remains an important reference work for historians of mathematics all over the world.

In commemoration of the hundred fortieth anniversary of the birth ofSalih Zeki (1864-1921), the last renown Ottoman mathematician, a summaryand evaluation of his book on the development of mathematics in Islam, Asâr-ıBâkiye [Athar-i Baqiya]is presented. Originally, the book was planned to have four volumes, dealingseparately with trigonometry, arithmetic and algebra, astronomy and geometry.Unfortunately, only the first two volumes have been printed (1913). Recently,the science historians at Ankara University transcribed these two volumes intomodern Turkish and, my presentation is based on this edition completed in2004. In his preface, Salih Zeki explains his aim in writing this book as“indicating the additions brought by Eastern mathematicians to the old edificeof Greek mathematics, and establishing clearly the levels of development atwhich this legacy was transmitted to Western scientists.” The first volume on trigonometry starts with explaining how the oldastronomers, including Ptolemaios (c.100-c.170) dealt with angles, using onlythe chords, and a relevant theorem of Menelaus (c.100). He continues with theintroduction of the concepts and tables of trigonometric terms, such as sines byThabit ibn Qurra (836-901), followed by Jabir al-Battani (c.858-929) andtangents by Abu'l-Wafa al-Buzjani (940-998). Through a detailed analysis ofvarious astronomical or trigonometric tables, he makes it clear that the scienceof trigonometry is essentially the creation of Eastern mathematicians (mostlyIslamic, following a beginning in India). I may add that this conclusion isshared by the statements of Western historians, such as Paul Tannery (in 1893)and Colin Ronan (in 1983). The second volume relates in detail how the present number characters(both Arabic and Latin) evolved from Indian numerals through the book Kitab fiel Hisab el-Hindi by al-Khwarizmi (c. 780-c. 850) which was written to teachthe people how to use numbers in their daily lives. There were two kinds ofnumerals in al-Khwarizmi’s book, both taken from Indian mathematics. One ofthem, through the translations Liber Abaci, 1202 by L.Fibonacci (1170-post1240) and Summa di Arithmetica, Geometria (1494) by L.Pacioli (c. 1445-c.1514) led to the development of Latin numerals, and the other, through theworks of Islamic mathematicians gave rise to Arabic numerals. Salih Zeki presents several arguments to refute the claim made by someWestern historians that the Indian-Arabic numerals were first invented inancient Greece by the followers of Pythagoras (c.570-c.490). Finally, he givestwo examples to show that decimal fractions were first used by Islamicmathematicians; one is the decimal expression of π by Jamshid Ghiyath al-Dinal-Kashi (d. 1429) obtained in Samarkand around 1420, which was valid to thesixteenth decimal point, and the other is the decimal expression used for thetrigonometric tables prepared by the astronomer Taqi al-Din (d.1585) inIstanbul, around 1570.As a conclusion, I wish to express the view that, Salih Zeki’s Asâr-ıBâkiye, both by documenting attempts to clarify the priorities in thedevelopment of mathematics, and in providing a detailed explanation of manyinteresting computations by ancient mathematicians, remains an importantreference work for historians of mathematics all over the world.