# Tag Info

### What does this cover of a 1508 German book on arithmetic depict?

The image appears to depict a counting board. Since the context is mercantilism, it is most likely depicted being used by tax collectors or accountants. The symbols are most likely stylizations.
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### Has the idea that the result of division of positive number by negative number should be negative ever been controversial?

Much has been written about various roadblocks to the acceptance of negative numbers, and I have a folder containing photocopies of a few such papers, but I don't have time now to look for that folder....
• 3,552
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### Did Archimedes view fractions as "numbers"?

No, Archimedes, and ancient Greeks generally, did not see fractions as numbers, and they did not use fractions as we use them today, they did not use them at all. What they used was ratios of ...
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### Why did the romans use IV and why doesn't it overcomplicate things?

I'd like to add my comment as an answer to have memory of a side comment. As I was saying the subtractive notation was a way of sparing characters in carving and this is the reason behind it becoming ...
• 1,768
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### Who Invented The Number Line?

Not mentioned in the linked thread is Bombelli, who although not widely published until after cited “candidates” Stevin and Wallis, came before them per Bourbaki’s historical notes (my emphasis): (......
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### Regula Pigri: How far does it date back?

The regula pigri from the question is a particular instance of what is called complementary multiplication in the literature, as it involves the decimal complement of the factors. Johannes Tropfke, ...
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### Did Rafael Bombelli write any commentary about his rules for arithmetic involving negative numbers?

Leo Corry's recent text, A Brief History of Numbers, offers an authoritative account of these matters. According to Corry, Bombelli's attitude to negative numbers was the same as Cardano's. Bombelli ...
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### Are there any arithmetic problems studied by Euler still open?

Here are some open problems that go back to Euler or, in the last case, his contemporary Goldbach. The classification of all idoneal (convenient) numbers. They were introduced by Euler and he ...
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### What does this cover of a 1508 German book on arithmetic depict?

The image may depict the new form of doing arithmetic by writing numbers, as opposed to the old style of using the counting board. Two image attestations around the same time. A 1503 print of Gregor ...
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### Who Invented The Number Line?

Somebody did or several people did. We just don't know whom and its exceedingly unlikely we will ever know. What we can find out is the oldest example of a number line. I suggest for this the Ishango ...
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### Is multiplication postulated axiomatically in Peano arithmetic?

There needs to be a distinction made between the terms Peano axioms and Peano arithmetic. The OP is conflating the two terms, hence the confusion. In this wikipedia article (as of 11/21/21), it says, ...

### Is there a complete translation of "Arithmetices principia" by Peano?

We see one complete English translation of Peano's Latin text Arithmetices principia: nova methodo – which is only 49 pages in its entirety, with just twenty pages numbered in: VII The principles of ...
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### Is there any meaningful history behind harmonic mean?

A mathematical relation linking the "harmonic series" with the "harmonic mean" is the following: Let $\{s_n\}$ be the harmonic series s_1=1,\; s_2 = \frac 12, \; s_3 = \frac 13,.....

### How was addition and multiplication of natural numbers defined before 1870 (Cantor and modern set theory)?

The addition and multiplication of numbers were seen as so intuitively obvious that no-one bothered to formalise them before the modern period with Peano's axioms and also the development of set ...
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### How was addition and multiplication of natural numbers defined before 1870 (Cantor and modern set theory)?

In the first appendix (Note I) to his 1821 book Analyse Algebrique, Cauchy discusses multiplication of signs in detail, and then gives the following definition of addition: Ajouter au nombre A le ...
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1 vote

### A text or YouTube channel with a comparison between pre-Cartesian with post-Cartesian mathematics

Descartes is credited with introducing coordinates to geometry and it is often called analytic geometry compared with the 'synthetic' geometry of Euclid. However, Weyl denounced this as an "act ...
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1 vote

### What does this cover of a 1508 German book on arithmetic depict?

It seems to depicture the page setting of a math book in the new technique developed by Johannes Gutenberg. If you look closely you can see the math letters. The year 1508 was within a gold rush ...
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