The continuous reprints that I had to make of my 'Elementary and Sublime Geometry Course', from 1810 onwards; the other works so far published by me from that period; and more than anything else the many tasks of my profession, and the tasks set for me by the Government, have, up till now, delayed me from publishing my 'Course of Elementary and Sublime Analysis' which was earlier promised by me. And this Course should also be distributed in four volumes, in the same way as the Geometric Course; and the first of these which is now published contains the entire Analysis of the Finite; the second will include the application of this same topic to Geometry; the third gives a careful introduction to the Analysis of the Infinite; and the final fourth one presents the Analysis of the Infinite itself. Since it is not my purpose to be known as a writer of books; but rather to free once and for all my country from the servitude of resorting to foreign courses, often patching them together, so that it was not possible to avail oneself of those of a single author, so I have never sought, nor will I ever seek, to replace the course of Mathematics our distinguished Fergola has already made, who therefore finds himself having composed the aforementioned two last volumes, and subsequently perfected them in making them available; so that now they can see the light in public with the advantage of mathematical youth; I will make all my efforts with such a worthy subject, since I am so pleased that he allowed them to be printed by me, which he has often promised me. I would not have decided to undertake this task had it not been that after publishing the first two volumes, the poor health of Mr Fergola made it right for him to abandon the thought of publishing them when he did. Without describing here in detail the content of each volume, and the method by which it will be treated, which will be best done at the beginning of each of them; I will limit myself for now only to account for the first which is now in the public domain. It is divided into three parts: the first of which includes the Algebraic Algorithm, or the calculation of algebraic quantities; the second, the determinate analysis; and the third is the indeterminate one.

Although sometimes, Illustrious Fergola, I have the opportunity to meditate on the originals of the Greek geometers, it is my strength that I remain more convinced, that their inventions in Geometry greatly outweigh the discoveries of this kind made in our times. And it seems to me, that as long as we do not possess with our methods as many different doctrines about geometrical loci, as many as the ancients have invented in abundance; that the most wise books of the porisms of sage Euclid will not be returned as the culmination of the modern analysis (very difficult work); and that in addition we will not discover alternative methods to solve problems beyond the fourth degree, it is a fact that we recognize far less than the ancients. Abandoning therefore their guide, as is mostly done nowadays, and keep a little of their precepts, and their works do not make perfect sense, for those who want to embark on the arduous career of geometric invention, giving themselves entirely to modern analysis, it is the same, as a learned Italian used to say, to enter without a thread into a dark labyrinth. Descartes, Fermat, Ugenio, Newton, Leibniz, the Bernoullis, Euler, and many others who lived in times not far from us cultivated with great ardent love the works of the ancients, and they studied them deeply; and new important discoveries, and new methods were still seen to derive from their considerations: nor did the last century after them, if truth be told, add much to their inventions. We must treat therefore that branch of Geometry which belongs to the ancients, as something to be praised, to do otherwise is a fault.