Understanding Calculus

Adelphi’s Robert Bradley, Ph.D., and Salvatore Petrilli, Ph.D., translated the revered calculus textbook, A’ Lanalyse des inifiniment petits.

The first book to explain and teach calculus was written in French and published in 1696. Now, 317 years later, three professor have revisited history and are on the cusp of completing the first faithful translation of Analyse des infiniment petits, or An Analysis of the Infinitely Small.

The history behind this piece of scholarly literature is immense. To embark on such a literary trek to understand the book’s creation, one would need to understand French, German and Latin, not to mention complex mathematics.

Enter Adelphi’s Robert Bradley, Ph.D., Salvatore Petrilli, Ed.D., both of the Department of Mathematics and Computer Science, and C. Edward Sandifer, Ph.D., professor emeritus at Western Connecticut University. Alongside the approximate 180-page first edition of An Analysis of the Infinitely Small, Drs. Bradley, Petrilli and Sandifer will include the 30-page translated Latin text that is the basis for the first four chapters of the published book and about 50 pages of translated German excerpts that are the basis for some of the chapters of the book.

“We hope and believe this will be of great use, not only to academic professors like us,” Dr. Bradley said. “Master’s to [post] graduate students studying the history of mathematics, who understand calculus from a modern point of view and want to see how calculus was done at its inception, will find use here too. It was very different.” He noted that knitting together the Latin and German texts to the original book had never been done before. This edition will enable easy cross-referencing and be of great use to serious scholars.

The translation’s significance lies heavily in its historical value. “It’s important not for mainstream scientific reasons but for a mathematics history of ideas,” Dr. Bradley said, adding that the discovery and refinement of calculus has been one of the great stories of western civilization. He explained that it was only through the publication and understanding of calculus that this mathematical study would soon be applied toward solving problems in physics.

“This is when calculus becomes this practical and important tool…if you can figure out physics, then you can understand the real world. That’s why this is a subtext for the whole scientific revolution,” he said. Dr. Bradley also noted that one reason physicists Galileo and Sir Isaac Newton became great was their healthy understanding of calculus.

Tackling such an involved project, that has its beginnings in July 2009 and got its feet late in 2010, has been no easy task. One issue within the translation process that Dr. Petrilli and Dr. Bradley marked as slightly tedious was translating phrases from the 1600s, that aren’t in use today.

Many discussions were had among the team on whether or not some paragraphs needed to be broken apart. Some of the sentences go on for half a page, sometimes three-quarters of a page and you get lost in the translation. You have to know when to stop,” Dr. Petrilli said. “Usually we’ll let a long sentence stand because there’s no good alternative,” Dr. Bradley said, laughing.

The book is still in progress, but is targeted for completion within the next few months.