Antonio Magliabechi wrote Letter L-290 to Leeuwenhoek about the book dedicated to him
The book was Arcana Naturae Detecta, which appeared in 1695 and which Leeuwenhoek dedicated to Magliabechi in a letter of August 1695.
Jacobus Gronovius (1645-1716) was a professor of history and Greek at Leiden after 1679. He carried on a correspondence with Magliabechi and gave to Leeuwenhoek letters from Magliabechi. See Letter L-182 of 30 October 1686.
The duke was Cosimo III De' Medici (1642-1723), after 1670 grand duke of Tuscany. The prince-cardinal was Cosimo's brother Francesco Maria De' Medici (1660-1710).
On 7 September 1696, Leeuwenhoek wrote to Magliabechi,
After that time I received Your most kind letter of the 5th of June, which the very famous Gronovius, when travelling through our city, sent to me through the intermediary of someone else, since he himself had no time to visit my house. And it is just because this letter came so late into my hands that I have not been able to reply to it sooner.
In both these letters, Illustrious Sir, you lavish such honourable designations on me and you extol so greatly both the dedication of my book to Your Illustrious Name and the matters contained therein that I remember them not without shyness, because I do not even merit a thousandth part of the things which You do not disdain to say about me and my work.
Indeed, I consider that I have acquired enough and more than enough fame if my modest work is somewhat appreciated by the learned, and even much more so if my work seems to be worthy of being given a place in the well-furnished library of the Most Serene Duke and of the Most Eminent Prince and Cardinal, which I learn from your letter has taken place.
Meanwhile I humbly beg you, if in future you should send me a letter, to refrain from extolling me with so many names and titles and only to write to me as to a citizen of modest birth, whom these titles do not fit at all, and thus you will oblige me very much.