Newton's notes Chronology of Ancient Kingdoms Amended were published posthumously in 1728. It consists of a chronological list of dates and events ranging from 1125 BCE with pharaoh Mephres reigning over Egypt to 331 BCE with Darius the last king of Persia being slain by Alexander the Great. In six subsequent chapters he discusses the civilizations of the Greek, Egyptians, Assyrians, Babylonians and Medes; he describes the temple of Solomon and ends with the empire of the Persians. Before this 'official' publication of 1728, an abstract made by Newton had been translated into French and was published prematurely in 1725 together with critical comments by Etienne Souciet (which were added anonymously). Because of Newton's iconoclastic views on chronology, these publications unchained a vivid controversy among scientists of the 18th century. Some of them believed in Newton and his scientific methods, others contested his computations with arguments that did or did not rely on science or just on the infallibility of the Bible.
The authors of this book present a thorough analysis of the notes of Newton, to explain how he came to these conclusions about ancient history. Their analysis is both broad and deep, which allows the reader to almost look into the head of Newton as he was constantly revising and improving his ideas along with his analysis of the texts and how he adapted his measurements and computations. Buchwald and Feingold largely rely on unpublished notes by Newton and many other primary sources.
They start with a discussion of Newton's views on the reliability of our senses when doing experiments and how it was possible to obtain accurate results out of multiple experiments. This, and subsequent analysis of Newton's way of thinking is placed in a broad historical perspective. They start from the ancient Greek views and show how this evolved during subsequent centuries to result in the different viewpoints on the matter among Newton and his contemporary colleagues. The authors continue to sketch the ideas about chronology and how it was perceived in the 17th century in which Newton formed his own ideas. In their next chapter, they move to Newton's views on prophecies and idolatry. For Newton, the prophecies were symbols that should be interpreted and used as a starting point for computations that should ultimately result into numbers. The mythology is some kind of sublimated history because the gods refer to kings and rulers of ancient time. Another chapter is devoted to population dynamics. An active dispute was going on about how many people lived on earth before and after the deluge, and how to compute these numbers. Newton then comes to his idea that kingdoms appear only late in history. He gets precise dates by studying ancient written sources about Persia, Egypt and Greek history. From astronomical events that he can find there, he can place a star at a particular position in the zodiac. Taking into account the precession of the earth which shifts the position of the corresponding equinox over the centuries, he was able to pin a date for the event mentioned in the text. Each of these elements that led to Newton's conclusions are elaborated in a separate chapter. How Newton evaluated words and verified them against truth is illustrated with the investigation that he did as the warden of the Royal Mint. The different stories about the leaking of Newton's summary of his notes and the premature publication of the French translation Abrégé de la chronologie de M. le Chevalier Isaac Newton, fait par lui-même (1725) in Paris is told with all details. The authors describe in detail the initial reactions and the lively discussions that broke loose in England and in France, certainly after the publication of the full notes in 1728, shortly after Newton's death the year before.
The more technical details are collected in different appendices: a very useful list of definitions and conventions and the mathematics and computations used by Newton to find the dates. The practical computations by Newton are not mentioned in the published text, but that is amply illustrated by the authors with unpublished notes by Newton. Because of the tsunami of names of persons and sites of all ages that play a role in this book, it is very practical to consult the extensive index, and of course, given the many citations and quotes, there is also an extensive list of references.
Although it is not necessary, it certainly helps to be familiar with the books of the Old Testament, and with ancient kingdoms and the Greek mythology. If not, you will probably need a great deal of wikipedia look-ups. The Chronology and many other of Newton's publications are freely available for example via the project Gutenberg as well as via the project Newton.
With this book Buchwald and Feingold have provided the specialists with an overwhelming source of information. But anyone interested in history, i.e., ancient history but also the history up to the 17th century and before, will love the insightful discussion of ideas and the overwhelming stream of detailed facts and citations. The reader is taken by the hand and is guided through Newton's life and how his ideas have matured. A glimpse in the mind of a genius. The style and vocabulary used is not the simplest, but nevertheless it reads fluently. A highly recommended reading indeed.