## Abstract

In mature symbolic algebra, from Viète onward, the handling of several algebraic

unknowns was routine. Before Luca Pacioli, on the other hand, the

simultaneous manipulation of three algebraic unknowns was absent from

European algebra and the use of two unknowns so infrequent that it has rarely

been observed and never analyzed.

The present paper analyzes the five occurrences of two algebraic unknowns in

Fibonacci’s writings; the gradual unfolding of the idea in Antonio de’

Mazzinghi’s Fioretti; the distorted use in an anonymous Florentine algebra

from ca 1400; the regular appearance in the treatises of Benedetto da Firenze;

and finally what little we find in Pacioli’s Perugia manuscript and in his

Summa. It asks which of these appearances of the technique can be counted as

independent rediscoveries of an idea present since long in Sanskrit and Arabic

mathematics – metaphorically, to which extent they represent reinvention of

the hot water already available on the cooker in the neighbour’s kitchen; and it

raises the question why the technique once it had been discovered was not

cultivated – pointing to the line diagrams used by Fibonacci as a technique

that was as efficient as rhetorical algebra handling two unknowns and much

less cumbersome, at least until symbolic algebra developed, and as long as the

most demanding problems with which algebra was confronted remained the

traditional recreational challenges.

unknowns was routine. Before Luca Pacioli, on the other hand, the

simultaneous manipulation of three algebraic unknowns was absent from

European algebra and the use of two unknowns so infrequent that it has rarely

been observed and never analyzed.

The present paper analyzes the five occurrences of two algebraic unknowns in

Fibonacci’s writings; the gradual unfolding of the idea in Antonio de’

Mazzinghi’s Fioretti; the distorted use in an anonymous Florentine algebra

from ca 1400; the regular appearance in the treatises of Benedetto da Firenze;

and finally what little we find in Pacioli’s Perugia manuscript and in his

Summa. It asks which of these appearances of the technique can be counted as

independent rediscoveries of an idea present since long in Sanskrit and Arabic

mathematics – metaphorically, to which extent they represent reinvention of

the hot water already available on the cooker in the neighbour’s kitchen; and it

raises the question why the technique once it had been discovered was not

cultivated – pointing to the line diagrams used by Fibonacci as a technique

that was as efficient as rhetorical algebra handling two unknowns and much

less cumbersome, at least until symbolic algebra developed, and as long as the

most demanding problems with which algebra was confronted remained the

traditional recreational challenges.

Original language | English |
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Journal | Ganita Bharati |

Volume | 41 |

Pages (from-to) | 23-67 |

ISSN | 0970-0307 |

Publication status | Published - 2019 |