ON MATH HISTORY - BUT DID WE LOOK FAR ENOUGH?

The following comes from Newser, and my comment is below it, and also that of Delta.  

Hugh Murray 

Math Historian Saw Decimals in 1440s Treatise and Freaked Out

Glen Van Brummelen uncovers earliest known use of decimal to indicate base-10 number system

By Arden Dier,  Newser Staff Posted Feb 23, 2024 4:15 PM CST

How old is the decimal? It's a question you've probably never pondered but one that has fascinated certain historians. Fascinated isn't overstating it. When Glen Van Brummelen, a historian of mathematics at Canada's Trinity Western University, spotted a decimal used to indicate tenths of a number in a 15th-century treatise while teaching at a math camp for middle schoolers, "I remember running up and down the hallways of the dorm with my computer trying to find anybody who was awake, shouting 'Look at this, this guy is doing decimal points in the 1440s!'" he tells Nature News. This early appearance of such a decimal, it turns out, is a very big deal to math historians. Science Alert calls "a mind-blowing discovery."

 

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While versions of the decimal have been used as far back as the 900s, German mathematician Christopher Clavius was thought to have been the first to break down whole numbers by tenths, hundredths, and thousandths, in a 1593 treatise on the astrolabe, called Astrolabium. What Van Brummelen had discovered was the same usage in a much older text. In the 1440s, European astronomers made calculations using the sexagesimal numeric system of dividing a 360-degree circle into 60 minutes and dividing minutes into 60 seconds. The system uses 60 as its base in the same way our modern decimal system uses 10 as its base, though this makes multiplication difficult, requiring multiple conversions of values, per Nature News.

Giovanni Bianchini, a Venetian merchant who practiced astrology, found a simpler way—one that marked "a step forward for humanity," José Chabás, a historian of astronomy unconnected with the discovery, tells Live Science. It was while reviewing Bianchini's treastise Tabulae primi mobilis B that Van Brummelen and a colleague noticed he was dividing angles into minutes and seconds but giving the values as numbers with decimals using the base-10 system. Van Brummelen, author of a study published online for Historia Mathematica, believes the method originated with Bianchini, who would've learned calculations using real-world measures through his background in economics. Clavius would've been aware of his work, Chabás says. (More mathematics stories.)

 

My comment:

humura 31 minutes ago

I know little of the history of the abacus, but I recall on the early days of tv, the race between someone using the abacus and a new machine for adding numbers, and if the person using the abacus lost, it was very close.
Might early abacui been set for a base of 10, or 6? If 10, then special operations might have used the tenth system for fractions, and tenths. Where are there archives that might contain such info? Congrats to the man who found the use of the decimal 150 years earlier than known. And that usage might have come from the Muslims or even the ancient would. But the Asian world might provied an earlier application, but using an early calculating machine.

delta253 7 hours ago

That's actually interesting. I was reading last month of Anctient Sumeria using Base 12 arithmetic. Much more convenient than 10, as it has more factors.