Augustus de Morgan was an English mathematician who lived from 1806-1871. He uses the term "paradox" to mean a person who has views or theories contrary to the established system, in a variety of fields, including mathematics, the sciences in general, religion, politics, etc.
This book is a single paperback book containing both Volumes 1 and 2. This was originally published as two volumes in 1915. However, the material all dates from the 1860's and earlier, and Volume 1 was apparently published in that time.
This book is about people as revealed in their books and letters. In most or all cases, these were books or pamphlets or letters which were in de Morgan's collection. They are taken in chronological order, meaning the subject will jump from geometry to atomic theory to religion and back again. Some are described in a few sentences or paragraphs, some in a page or two, and some run on for multiple pages.
One of the more common themes is the squaring of the circle or the related question of the calculation of pi. It might be assumed that de Morgan would go into detail about the methods used, the errors introduced, refutation of the false ideas, etc. But this is a book mainly about people, and so you'll find a discussion of this or that person, and generally what their ideas were, but in most cases, not a detailed analysis of their work or their errors.
A general understanding of mathematical and scientific principles is helpful when reading the work, although, as noted, it is not a book of math theorems. Fortunately, most of the French and Latin quotations have been translated by the editors.
The value of the work seems to me to be threefold. First, it reviews a great number of works and people, many of which were obscure in their own day, and many of which would be impossible to find today. Secondly, it serves as a window into the 19th century (and earlier) world of math and science, the ways of thinking, and the relationships between different groups. Thirdly, de Morgan does have occasional real gems of humor or wording in his work, and what might be otherwise very dry writing is made considerably more interesting by his sense of humor.