1. Rafael Bombelli

2. Life and Times
Bombelli was mentored by Pier Francesco Clementi- an Engineer-Architect
Lived in Bologna, Italy as an hydraulic engineer draining wetlands for the Apostolic Camera
(Catholic Church)
Followed works done by
del Ferro, Cardan, Ferrari and Tartaglia
The papal states
Pope Paul III ( )
The Spanish Inquisition was founded in The Church was still VERY powerful in Bombelli’s time. His work was done after Copernicus but before Galileo.

3. Square Roots Bombelli’s method using continued fractions to calculate square roots:
If the + sign is used, a2 = the square below n,
If the – sign is used, a2 = the square above n.

4. An Example:

5. First wrote down how to calculate with negative numbers
First wrote down rules of how to multiply, add and subtract imaginary numbers
3 Books (“Geometrical Parts”4&5 never completed)
Book III included 143 problems from Diophantus’ Arithmetica
143 out of 272 problems in the book. He worked on a translation of Diophantus’ Arithemetica with Antonio Maria Pazzi

6. Rules of Negative Numbers
Plus times plus makes plus
Minus times minus makes plus
Plus times minus makes minus
Minus times plus makes minus
Plus 8 times plus 8 makes plus 64
Minus 5 times minus 6 makes plus 30
Minus 4 times plus 5 makes minus 20
Plus 5 times minus 4 makes minus 20

7. Rules of Complex Numbers
Plus of minus times plus of minus makes minus (+√-n )(+√-n) = -n
Plus of minus times minus of minus makes plus (+√-n )(-√-n) = +n
Minus of minus times plus of minus makes plus (-√-n)(+√-n) = +n
Minus of minus times minus of minus makes minus (-√-n)(-√-n) = -n

8. Bombelli’s Notation Roots-Quadrato(2), cubo(3),quadroquadrato(4),
numero detto primo relato(5)

9. Thank You!!
References
J J O'Connor and E F Robertson, “Rafael Bombelli” July 16, 2006
A very detailed biography
Curtin, Sandifer, Stoudt, “Rafael Bombelli’s L’Algebra” July 16,
An interesting site discussing L’Algebra
Wikipedia, “Rafael Bombelli” July 16,2006
A short biography with description of his method to calculate square roots
Kevin Wood © August 2006