chalkdust tax: a 13th century “functional maths” course of great use to commercial tradesmen! One such problem is the following about birds: A certain man buys 30 birds which are partridges, pigeons, and sparrows, for 30 denari. A partridge he buys for 3 denari, a pigeon for 2 denari, and 2 sparrows for 1 denaro, namely 1 sparrow for 1/2 denaro. It is sought how many birds he buys of each kind. The solution to this problem can be found at the end of this article. While it may seem unremarkable to our modern eyes, this bird problem beautifully illustrates Fibonacci’s legacy to mathematics: Liber Abaci introduced the western world to Hindu–Arabic numerals.
Engraving of Leonardo of Pisa.
Leonardo’s book encourages and advocates the use of novem figuras indorum—nine Hindu figures—and tells the reader that with the numerals 9 to 1, along with the sign 0, any number may be wrien. He provides a translation from Roman numerals to his chosen figures.
Leonardo explains place value, intrinsic to maths today, and the radical idea that the position of each numeral shows what power of ten it represents. He goes to great lengths to describe how to calculate with these numerals, with examples of addition, subtraction, multiplication and division set out with increasing diﬀiculty. He explains how to use fractions, ratio and proportion, and shows how to group digits in threes to make large numbers easier to read.
Novem figuras indorum: nine Hindu figures.
It’s interesting to note that, in keeping with the approach of the time, Leonardo describes 0 as a sign, rather than a numeral. He calls the sign “zephyr” meaning “empty”, and groups it along with the operations rather than the digits. 41
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