[HM] Usage of the word abacus

Prof. Lueneburg (luene@mathematik.uni-kl.de)
Tue, 24 Nov 1998 09:12:11 +0100 (MEZ)

>
> Prof. Lueneburg,
>
> I have struggled with some questions regarding translating various
> phrases that Fibonacci uses in his Liber Abbaci. Perhaps you can
> enlighten me.
>
> [1] He writes in the preface of the work (my translation from
> Boncompagni's edition): "I discovered whatever I could about it [the art
> of arithmetic] in Egypt, Syria, Greece, Sicily and Provence, with their
> various methods, and I later travelled to many places of business, and
> learned by means of much study and engagement in disputation. Indeed, I
> have determined that all this--both algorism and the use of the
> Pythagorean arches [arcus pictagore]--
> to be prone to error when compare to the method of the Hindus." What is
> this "arcus pictagore"? Is it a type of abacus with beads on wires?
>
> [2] One of the sections of the book is entitled "On the barter of items
> for sale and the purchase of *bolsonalies*, and on some similar rules".
> What is "bolsonalies"? Might this be a type of insurance contract?
>
> [3] Another section is entitled "On *consolamen* of money and
> corresponding regulations, and on what pertains to *consolamen*. What
> does this word refer to?
>
> Thanks in advance for anything you might be able to share on these
> matters.
>
> Danny Otero
> Xavier University
> Cincinnati, OH
>

Dear Professor Otero,

Concerning the "arcus pictagore" I can repeat only what I know from
the secondary literature. It is the abacus of Gerbert. It had chips,
the so-called apices, whit the numbers 1, 2, ..., 9 on them. (Apex
means cone. In our context, it means what I just said, but also only
the ciphers written on them. This latter Information I got from
Otfried Lieberknecht.) Instead of putting down seven calculi one puts
down a chip with a 7 on it. This sort of abacus seems to have been
very cumbersome to handle. It was used in cloisters and, as it seems,
never used by merchants.

I cannot explain the words bolsonalia and consolamen, but I think I do
know what they are standing for.

Bolsonalia seem to be coins whose value depend on the silver they
contain. Fibonacci gives an interesting hint how to find out the
portion of silver in the coins, if this portion is unknown. I presume
that his hint points to the cineritium-method which is a quantitative
method for determining silver and gold in metals used by alchemists.

Consolari, consolamen means to mix metals, mixture of metals (Legierung
we call it in German. I don't have a dictionary at hand to look up the
English word.)

I admire your boldness to translate librum abbaci of Leonardo Pisano.
Good luck!

If you complete your address (ZIP-code, Department), I shall send you
a copy of my book on the liber abbaci. You will find some of the
vocabulary explained.

All the best, Heinz Lueneburg