Treatise on the Arithmetical Triangle

by Blaise Pascal

Genres: Mathematics, Nonfiction

Unknown Binding

About the author

Early work of Blaise Pascal of France included the invention of the adding machine and syringe and the co-development with Pierre de Fermat of the mathematical theory of probability; later, he, a Jansenist, wrote on philosophy and theology, notably as collected in the posthumous Pensées (1670).

This contemporary of René Descartes attained ten years of age in 1633, when people forced Galileo Galilei to recant his belief that Earth circled the Sun. He lived in Paris at the same time, when Thomas Hobbes in 1640 published his famous Leviathan (1651). Together, Pascal created the calculus.

A near-fatal carriage accident in November 1654 persuaded him to turn his intellect finally toward religion. The story goes that on the proverbial dark and stormy night, while Pascal rode in a carriage across a bridge in a suburb of Paris, a fright caused the horses to bolt, sending them over the edge. The carriage, bearing Pascal, survived. Pascal took the incident as a sign and devoted. At this time, he began a series, called the Provincial Letters , against the Jesuits in 1657.

Pascal perhaps most famously wagered not as clearly in his language as this summary: "If Jesus does not exist, the non Christian loses little by believing in him and gains little by not believing. If Jesus does exist, the non Christian gains eternal life by believing and loses an infinite good by not believing.”

Sick throughout life, Pascal died in Paris from a combination of tuberculosis and stomach cancer at 39 years of age. At the last, he confessed Catholicism.

Reviews

[Richard · Rating 2 out of 5]

I read this because it is one of the works on the Second Year list of the 10 Year Reading Plan in the Great Books of the Western World set (Encyclopedia Britannica, 1952). I gave it two stars as just "OK". It is challenging to follow, even for an engineer such as myself, but that would be expected as it is a mathematical treatise. The author starts out by describing how to construct a triangular table of numbers according to certain rules, then in the second section describes the properties of the table, and finally in a third section mentions a couple applications - how the "triangle" could be applied as a tool to topics such as game theory and the binomial theorem. However, it would have been better to have more explanation of the importance and uses of the triangle up front, before going through all the tedious information on construction and the propositions, corollaries, and lemmas on the properties. I also would have appreciated learning how the author knew to set up the rules of the construction of the triangle so that it would yield patterns useful for the applications. If the table were constructed following slightly different rules, then it wouldn't be useful for those later applications, so he must have picked the particular method of construction with those later uses in mind. Overall, I learned much more about the triangle from the Wikipedia article about it. An interesting fact is that this triangle was known in China and other parts of the world much earlier than this treatise of Pascal.

[Claire · Rating 2 out of 5]

Well. I finished it. I understood it through page 6 out of 25. It's part of my Great Works project, and frankly I'm not sure what I'm supposed to get from reading the hardcore math works since no one but a true math professor could begin to grasp them. But whatever.