In 1494 Luca Pacioli (a Franciscan monk and geometer) traveled to Venice to publish Summa de arithmetica, geometria, proportioni et proportionalita, which had the goal of being a comprehensive summary of mathematical knowledge at the time. Almost none of the mathematics featured was Pacioli’s original work, but he did give credit to those who produced the results he mentioned, which included thinkers like Euclid, Boethius, Sacrobosco, and Fibonacci . It had a completely summary of Euclid’s Elements and it studied games of chance (Pacioli presented an attempt at a solution to a problem in this subject which was later deemed incorrect). A revolutionary aspect of this text is that it was published in Italian (the vernacular), not Latin.  The publishing of this work also established Pacioli’s name in the academic and intellectual communities at the time, most definitely catching the attention of da Vinci (who bought a copy as soon as it was published). It is reasonable to speculate that da Vinci recruited Pacioli to the Milan court because he was so impressed by this work.

Sources

Isaacson, Walter. Leonardo Da Vinci. Simon & Schuster Paperbacks, 2018.

“Luca Pacioli.” Luca Pacioli (1445-1517), School of Mathematics and Statistics, University of St. Andrews, Scotland, www-history.mcs.st-and.ac.uk/Biographies/Pacioli.html.

The image source is Wikimedia Commons, and it is in the public domain in the United States because it was published (or registered with the U.S. Copyright Office) before January 1, 1924.

In this year Luca Pacioli and Leonardo da Vinci’s joint work De Divina Proportione was published in Venice; this text focused on the role of proportions and ratios in architecture, art, anatomy, and math. Pacioli provided the mathematical content (again, most of his work was unoriginal) and da Vinci provided sixty illustrations of geometric figures. Each geometric figure was depicted in two ways: solid faces and then solid edges. The solid face representation was more typical of the time but was disadvantageous in the fact that it was difficult to get a sense of the whole shape. The other approach is the solid edge approach, in which each of the edges are emphasized and the sides are left “see through.” This was a novel approach to geometric representation at the time, although it is debated whether da Vinci invented this representation. It is also a possibility that he was sketching wooden figures of these shapes as constructed by Pacioli. In either case, da Vinci’s perfection of perspective certainly aided in the two-dimensional representation of these shapes. It is important to note that these geometric figures were the only sketches of da Vinci that were published during his lifetime.  

Sources

Isaacson, Walter. Leonardo Da Vinci. Simon & Schuster Paperbacks, 2018.

“Luca Pacioli.” Luca Pacioli (1445-1517), School of Mathematics and Statistics, University of St. Andrews, Scotland, www-history.mcs.st-and.ac.uk/Biographies/Pacioli.html.

The image source is Wikimedia Commons, and it is in the public domain in the United States because it was published (or registered with the U.S. Copyright Office) before January 1, 1924.