Although Galileo eloquently championed mathematical methods in science, the main target of his wit and sarcasm in The Assayer was Grassi, a fellow astronomer, whose mathematical methods proved that comets move above the Moon. Galileo countered that comets are an optical illusion, produced by reflected light, so it becomes a meaningless question to ask where they are located.
This copy, with expanded errata, is the usual state of the first edition.
Galileo argued that no proof was available for Grassi’s assumption that comets are physical objects in motion rather than merely an optical effect of sunlight reflecting from vapor. Therefore parallax arguments prove nothing.
Galileo’s provocative sarcasm did nothing to encourage good relations between Galileo and Jesuit astronomers. On the other hand, the book was read with delight at the dinner table by Urban, who wrote a poem praising Galileo for the witty performance.