**Luca Pacioli** was an Italian mathematician who published the influential book *Summa* in 1494 giving a summary of all the mathematics known at that time.

- One reason that this seems likely to be true is the extensive knowledge that Pacioli had of the work of Piero della Francesca and Pacioli's writings were very strongly influenced by those of Piero.
- Pacioli moved away from Sansepolcro while he was still a young lad.
- One has to assume that Pacioli was already well educated in basic mathematics from studies in Sansepolcro and he certainly must have been well educated generally to have been chosen as a tutor to Rompiasi's three sons.
- However, Pacioli took the opportunity to continue his mathematical studies at a higher level while in Venice, studying mathematics under Domenico Bragadino.
- During this time Pacioli gained experience both in teaching, from his role as tutor, and also in business from his role helping with Rompiasi's affairs.
- It was during his time in Venice that Pacioli wrote his first work, a book on arithmetic which he dedicated to his employer's three sons.
- Pacioli certainly seemed to know all the right people for he left Venice and travelled to Rome where he spent several months living in the house of Leone Battista Alberti who was secretary in the Papal Chancery.
- As well as being an excellent scholar and mathematician, Alberti was able to provide Pacioli with good religious connections.
- At this time Pacioli then studied theology and, at some time during the next few years, he became a friar in the Franciscan Order.
- In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic.
- After Zara, Pacioli taught again at the University of Perugia, then at the University of Naples, then at the University of Rome.
- Certainly Pacioli become acquainted with the duke of Urbino at some time during this period.
- The court at Urbino was a notable centre of culture and Pacioli must have had close contact with it over a number of years.
- In 1489, after two years in Rome, Pacioli returned to his home town of Sansepolcro.
- Not all went smoothly for Pacioli in his home town, however.
- Pacioli was banned from teaching there in 1491 but the jealousy seemed to be mixed with a respect for his learning and scholarship for in 1493 he was invited to preach the Lent sermons.
- During this time in Sansepolcro, Pacioli worked on one of his most famous books the Summa de arithmetica, geometria, proportioni et proportionalita Ⓣ(Summary of arithmetic, geometry, proportion and proportionality) which he dedicated to Guidobaldo, the duke of Urbino.
- Pacioli travelled to Venice in 1494 to publish the Summa Ⓣ(Summary of arithmetic, geometry, proportion and proportionality).
- Pacioli broadly used Euclid's Elements, retelling some parts of it.
- In 1494 Ludovico became the duke of Milan and, around 1496, Pacioli was invited by Ludovico to go to Milan to teach mathematics at Ludovico Sforza's court.
- At Milan Pacioli and Leonardo quickly became close friends.
- At this time Pacioli began work on the second of his two famous works, Divina proportione Ⓣ(Divine proportion) and the figures for the text were drawn by Leonardo.
- The golden ratio was also of importance in architectural design and this topic was to form the second part of the treatise which Pacioli wrote later.
- Pacioli and Leonardo fled together in December 1499, three months after the French captured Milan.
- From Venice they returned to Florence, where Pacioli and Leonardo shared a house.
- Pacioli was appointed to teach geometry at the University of Pisa in Florence in 1500.
- Pacioli, like Leonardo, had a spell away from Florence when he taught at the University of Bologna during 1501-02.
- During this time Pacioli worked with Scipione del Ferro and there has been much conjecture as to whether the two discussed the algebraic solution of cubic equations.
- Certainly Pacioli discussed this topic in the Summa Ⓣ(Summary of arithmetic, geometry, proportion and proportionality) and some time after Pacioli's visit to Bologna, del Ferro solved one of the two cases of this classic problem.
- During his time in Florence Pacioli was involved with Church affairs as well as with mathematics.
- After leaving Florence, Pacioli went to Venice where he was given the sole rights to publish his works there for the following fifteen years.
- Pacioli's edition was based on that of Campanus but it contained much in the way of annotation by Pacioli himself.
- In 1510 Pacioli returned to Perugia to lecture there again.
- He also lectured again in Rome in 1514 but by this time Pacioli was 70 years of age and nearing the end of his active life of scholarship and teaching.
- Again it is a work for which Pacioli claimed no originality, describing it as a compendium.
- Despite the lack of originality in Pacioli's work, his contributions to mathematics are important, particularly because of the influence which his book were to have over a long period.
- This biography accused Pacioli of plagiarism and claimed that he stole della Francesca's work on perspective, on arithmetic and on geometry.
- This is an unfair accusation, for although there is truth that Pacioli relied heavily on the work of others, and certainly on that of della Francesca in particular, he never attempted to claim the work as his own but acknowledged the sources which he used.

Born 1445, Sansepolcro (now Italy). Died 1517, Sansepolcro (now Italy).

View full biography at MacTutor

Algebra, Ancient Indian, Geometry, Origin Italy, Number Theory, Special Numbers And Numerals

Parts: 1

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive