“the first published work on probability theory”

FIRST EDITION. This volume contains the first printing of Huygens’s famous treatise on games of chance, De Ratiociniis in Ludo Aleae (pp. 521-534), “the first published work on probability theory. It won immediate recognition and became the standard text on probability theory for the next 50 years” (Hald, A History of Probability).

“Huygens’s presentation dominated the literature for half a century due to its accessibility and near monopoly. And his solutions to the problems of Pascal and Fermat previously solved were fine examples of the work of a good mathematical mind. But there was one part of the tract that was strikingly original, and even today appears surprisingly modern” (Stephen M. Stigler, “Chance is 350 Years Old,” Chance, v. 20, 2007). Stigler goes on to explain that when Huygens began his treatise by listing the first principles of probability [e.g., when you have equal chances to win a or b, then your expectation (the fair price to play the game) is (a+b)/2, etc.], he did not present them as definitions or axioms as is customary but as “propositions: assertions that required – and were given – proofs. And the proofs were extraordinary for the time, with strong hints of late 20^th-century financial mathematics. Three hundred fifty years ago, Huygens was the first published scientific probabilist, as well as the first financial engineer, constructing hedges and derivative contracts in order to extend probability theory from common notions of fairness in symmetric situations to very different asymmetric markets” (Stigler).

“Schooten made an original contribution to mathematics with his Exercitationes Mathematicae (1657). Book I contains elementary arithmetic and geometry problems similar to those found in van Ceulen’s collection. Book II is devoted to constructions using straight lines only and Book III to the reconstruction of Apllonius’ Plane Loci on the basis of hints given by Pappus. Book IV is a revised version of Schooten’s treatment of the kinematic generation of conic sections, and book V offers a collection of interesting individual problems. Worth noting, in particular, is the restatement of Hudde’s method for the step-by-step building-up of equations for angular section and the determination of the girth of the folium of Descartes: x³ + y³ = 3 axy. Also noteworthy is the determination of Heronian triangles of equal perimeter and equal area (Roberval’s problem) according to Descartes’s method (1633). As an appendix Schooten printed Huygens’s De ratiociniis in aleae ludo, which was extremely important in the development of the theory of probability” (DSB). Schooten had offered to publish Huygens’s work as an appendix to his forthcoming book after Huygens sent him the manuscript. Schooten translated the treatise into Latin from Huygens’s Dutch. The work was reprinted as an introduction to Bernoulli’s Ars Conjectandi (1713).

$18,000