Unlike the Dialogue Concerning the Two Chief World Systems, it was not published with a license from the Inquisition; after the heresy trial based on the earlier book, the Roman Inquisition had banned publication of any work by Galileo, including any he might write in the future. After the failure of attempts to publish the work in France, Germany, or Poland, it was picked up by Louis Elzevir in the Netherlands, where the writ of the Inquisition was of little account.
The same three men as in the Dialogue carry on the discussion, but they have changed. Simplicio, in particular, is no longer the stubborn and rather dense Aristotelian; to some extent he represents the thinking of Galileo's early years, as Sagredo represents his middle period.
The sciences named in the title are the strength of materials and the motion of objects. Galileo worked on an additional section on the force of percussion, but was not able to complete it to his own satisfaction.
The discussion begins with a demonstration of the reasons that a large structure proportioned in exactly the same way as a smaller one must necessarily be weaker. Later in the discussion this principle is applied to the thickness required of the bones of a large animal, possibly the first quantitative result in biology.
This is not finished. The Science