The book was a polemic against the treatise on the comets of 1618 by Orazio Grassi, a Jesuit mathematician at the Collegio Romano. In this matter Grassi, for all his Aristotelianism, was right and Galileo was wrong. Galileo incorrectly treated the comets as a play of light rather than as real objects.
In 1616 Galileo may have been silenced on Copernicanism. In 1623 his supporter and friend, Cardinal Maffeo Barberini, a former patron of the Lynx and uncle of Cardinal Francesco Barberini, became Pope Urban VIII. The election of Barberini seemed to assure Galileo of support at the highest level in the Church. A visit to Rome confirmed this.
The title page of The Assayer shows the crest of the Barberini family, featuring three busy bees. In The Assayer, Galileo weighs the astronomical views of a Jesuit, Orazio Grassi, and finds them wanting. The book was dedicated to the new pope. The title page also shows that Urban VIII employed a member of the Lynx, Cesarini, at a high level in the papal service. This book was edited and published by members of the Lynx.
Again Galileo insisted that physics should be mathematical. According to the title page, he was the philosopher or physicist of the Grand Duke of Tuscany, not merely the mathematician. Physics or natural philosophy spans the gamut from processes of generation and growth (represented by a plant) to the physical structure of the universe, represented by the cosmic cross-section. Mathematics, on the other hand, is symbolized by telescopes, and an astrolabe. This is the book containing Galileo’s famous statement that mathematics is the language of science. Only through mathematics can one achieve lasting truth in physics. Those who neglect mathematics wander endlessly in a dark labyrinth. From the book:
|“||Philosophy [i.e. physics] is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.||”|
Although The Assayer contains a magnificent polemic for mathematical physics, ironically its main point was to ridicule a mathematical astronomer. This time, the target of Galileo’s wit and sarcasm was the cometary theory of a Jesuit, Orazio Grassi, who argued from parallax that comets move above the Moon. Galileo mistakenly countered that comets are an optical illusion.
Galileo’s polemical tone was common at the time. However, the book was read with delight at the dinner table by Urban VIII, who had written a poem lauding Galileo for his rhetorical performances.
- Galileo Galilei, The Assayer, as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237-8.
Other sources 
- Galileo Galilei, Il Saggiatore (in Italian) (Rome, 1623); The Assayer, English trans. Stillman Drake and C. D. O'Malley, in The Controversy on the Comets of 1618 (University of Pennsylvania Press, 1960).
- Pietro Redondi, Galileo eretico, 1983; Galileo: Heretic (transl: Raymond Rosenthal) Princeton University Press 1987 (reprint 1989 ISBN 0-691-02426-X); Penguin 1988 (reprint 1990 ISBN 0-14-012541-8)