Rafael Bombelli
Rafael Bombelli (baptised on 20 January 1526; died 1572)[a][1][2] was an Italian mathematician.
Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers.
In his 1572 book, L'Algebra, Bombelli solved equations using the method of del Ferro/Tartaglia.
He introduced the rhetoric that preceded the representative symbols +i and -i and described how they both worked.
Rafael Bombelli was baptised on 20 January 1526[3] in Bologna, Papal States.
He was born to Antonio Mazzoli, a wool merchant, and Diamante Scudieri, a tailor's daughter.
When Pope Julius II came to power, in 1506, he exiled the ruling family, the Bentivoglios.
Rafael's grandfather participated in the coup attempt, and was captured and executed.
Later, Antonio was able to return to Bologna, having changed his surname to Bombelli to escape the reputation of the Mazzoli family.
Rafael received no college education, but was instead taught by an engineer-architect by the name of Pier Francesco Clementi.
Bombelli felt that none of the works on algebra by the leading mathematicians of his day provided a careful and thorough exposition of the subject.
Instead of another convoluted treatise that only mathematicians could comprehend, Rafael decided to write a book on algebra that could be understood by anyone.
His text would be self-contained and easily read by those without higher education.
Bombelli introduced, for the first time in a printed text (in Book II of his Algebra), a form of index notation in which the equation
[4] in which he wrote the U3 as a raised bowl-shape (like the curved part of the capital letter U) with the number 3 above it.
Full symbolic notation was developed shortly thereafter by the French mathematician François Viète.
Perhaps more importantly than his work with algebra, however, the book also includes Bombelli's monumental contributions to complex number theory.
Before he writes about complex numbers, he points out that they occur in solutions of equations of the form
This was a big accomplishment, as even numerous subsequent mathematicians were extremely confused on the topic.
Bombelli avoided confusion by giving a special name to square roots of negative numbers, instead of just trying to deal with them as regular radicals like other mathematicians did.
At the time, people cared about complex numbers only as tools to solve practical equations.
As such, Bombelli was able to get solutions using Scipione del Ferro's rule, even in casus irreducibilis, where other mathematicians such as Cardano had given up.
After dealing with the multiplication of real and imaginary numbers, Bombelli goes on to talk about the rules of addition and subtraction.
Crossley writes in his book, "Thus we have an engineer, Bombelli, making practical use of complex numbers perhaps because they gave him useful results, while Cardan found the square roots of negative numbers useless.
"[5] In honor of his accomplishments, a Moon crater was named Bombelli.
Bombelli used a method related to simple continued fractions to calculate square roots.
He did not yet have the concept of a continued fraction, and below is the algorithm of a later version given by Pietro Cataldi (1613).
into itself yields a continued fraction for the root but Bombelli is more concerned with better approximations for
Bombelli's method should be compared with formulas and results used by Heros and Archimedes.
