Excerpt from Bianchini’s “Compositio instrumenti”. Reproduced with permission from the Biblioteca Estense di Modena (Cod. Lat. 145, f. 7r). Credit: Mathematical history (2024). DOI: 10.1016/j.hm.2024.01.001
A historian of mathematics at Trinity Wester University in Canada discovered the use of a decimal point by a Venetian merchant 150 years before its first known use by German mathematician Christopher Clavius. In his article published in the journal Mathematical historyGlen Van Brummelen describes how he found evidence for the use of decimals in a volume titled “Tabulae” and its importance to the history of mathematics.
The invention of the decimal point led to the development of the decimal system, which made it easier for people working in several fields to calculate non-integer numbers (fractions) as easily as whole numbers. Before this new discovery, the first known use of the decimal point was by Christopher Clavius as he created astronomical tables. The resulting work was published in 1593.
The new discovery was made in part of a manuscript written by Giovanni Bianchini in the 1440s: Van Brummelen was discussing a section of trigonometric tables with a colleague when he noticed that some numbers had a point in the middle. An example was 10.4, which Bianchini then multiplied by 8 in the same way as is done with modern mathematics. The discovery shows that a decimal point for representing non-integer numbers appeared about 150 years earlier than historians of mathematics thought.
Giovanni Bianchini worked as a merchant in Venice for many years before being appointed to an administrative position on an important estate owned by the powerful d’Este family. In this role, he also managed assets and investments, giving him a strong background in mathematics. He also published texts on astronomy, demonstrating his ability to trace planetary motion and predict when an eclipse would occur.
This discovery suggests that Bianchini played a more important role than previously thought in the development of the fundamental principles of mathematics. Van Brummelen notes that as a merchant, Bianchini would have traveled widely, particularly to places in the Islamic world, where mathematical concepts were being developed, which could have influenced his use of non-integer numbers and the manner of representing them easier.
More information:
Glen Van Brummelen, Decimal fractional numeration and the decimal point in 15th century Italy, Mathematical history (2024). DOI: 10.1016/j.hm.2024.01.001
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