Fifteenth and sixteenth century arithmetic texts: what can we learn from them? (Q1310987)

The article gives a survey of the format and contents of arithmetic books written in the 15th and 16th centuries. Some problems which were popular in these texts are discussed together with their mathematical and social implications. The author emphasizes that some of the problems can still be found in American textbooks in 19th century. -- Some errors should be noted: ``mensa Pythagoria'' instead of ``Pythagorica''; ``Aurilla'' instead of ``Aurillac''; ``Regunculi'' instead of ``Reguncule''; ``mediato'' instead of ``mediatio''; ``Sacrobasco'' instead of ``Sacrobosco''; ``Deophantus'' instead of ``Diophantus''. -- It is not known that Robert of Chester was the translator of al-Khwārizmī's arithmetical work, and there is no reason to suppose that its title was ``Algorithmi de numero indorum''. -- ``Practica'' is not only the name for some abacus arithmetics and algorithms, but also for some geometrical texts. -- I do not see why the author supposes (and states) that (exactly) 30 practical arithmetics were published up to 1500 and that there were 16 editions of Pietro Borghi's ``Libro dabacho'': \textit{W. Van Egmond} could not find more than 13 editions, which are listed in his modern and thorough catalogue ``Practical Mathematics in the Italian Renaissance'', Florence 1980 (which the author does not mention). -- The title of Gemma Frisius' work is not ``Arithmetica Practicae'', but ``Arithmeticae practicae methodus facilis'', and his name is not ``Frisius'' alone, as the author gives it in note 21. -- Nicomachus did not write ``that unity was not a polygonal number''; it is more likely that he thought that unity was not a number at all. -- It is not true that symbols for the specific operations were not written until about the middle of the sixteenth century: the Southern German ``cossists'' did use such symbols from the second half of the 15th century on. -- We cannot be sure that ``the Arabs followed Egyptian traditions'' in using the concepts of doubling and halving; it is also possibly that they used them as special operations, because they are needed in extracting the square root.