Why it matters

This is the book that turned "the mathematics of gambling" into "probability theory" as a formal discipline. De Moivre had presented an early version of the work to the Royal Society in 1711; by 1718 he'd expanded it into the first true textbook on the subject in English, dedicated to his close friend Isaac Newton. Within its pages are the first clear statements of ideas so foundational that most people who use them today have no idea they originated here — conditional probability, the multiplication rule for independent events, expectation itself as a formal concept. In a later edition, De Moivre would go on to derive an early form of what we now call the central limit theorem, one of the single most important results in all of statistics. Everything from actuarial science to modern risk modeling has a direct lineage back to this book — De Moivre and Edmund Halley are jointly credited as founders of the field of actuarial science itself. It's not an exaggeration to say this is the moment "gut feeling about luck" became "mathematics."

Why we're looking

The draw is the claimed association: an unrestored-text copy in contemporary calf said to carry the bookplate of Philip Stanhope, 2nd Earl Stanhope (1714–1786), an FRS with a lifelong mathematical interest who is independently documented as a friend of Thomas Bayes. On relative value, there is another copy in significantly worse condition for sale on AbeBooks at $9000. This isn't the single finest surviving copy, but among genuine, currently-verifiable period firsts, it's the best combination of price, originality and provenance.

Watch out for

The seller's own description states the binding is rebacked with the original spine laid on — restoration that materially separates this from the unrestored copies specialist dealers advertise as such. The description is also truncated mid-sentence in the reference list and no seller is identified, so ask for the full condition report, the completeness statement, and photographs of the Stanhope bookplate and title page before going further. The Stanhope provenance is the seller's claim and the basis for calling it "documented" is not spelled out; the ESTC number cited does match the 1718 first edition, and the stated collation is consistent with the institutional record of 2 preliminary leaves, xiv, 175 pp.