Book of Various Mathematical and Physical Speculations

...because I have always experienced in your Highness a paternal kindness in fostering and exalting me, and also because, prompted by the inquiries of your Highness, I have composed not a few things which are contained in this volume. There is the additional fact, which I have always thought should be considered in these dedications, that your Highness has made such progress in Mathematics that you can even be a fit judge of my labors. Wherefore, your Highness has both equaled the glory of the ancient Persian Kings and led us, as it were, into a certain hope for the happiness of this age, if Plato’s prophecy is true: that the Republic will be blessed in which Princes philosophize. May your Highness, therefore, not disdain to receive with your accustomed humanity this little book, which is due to you on so many accounts. May God always lead all your thoughts and endeavors to most happy conclusions, and preserve you in safety for a very long time.

Decorative historiated woodcut initial 'C' depicting a scholar or religious figure seated at a desk or lectern with an open book, inside a study or cell.

SINCE at various times I have contemplated many things in diverse disciplines—partly prompted by eminent men, my patrons and friends, who sought my opinion upon them, and partly from an innate desire in me for perceiving their reason and cause—I thought I ought not to neglect imparting my writings, of whatever sort they may be, in those sciences to students; not doubting that they will bring them some convenience and utility, especially since in investigating and weighing questions of this kind, no one (to my knowledge) has hitherto labored. For nothing has been handed down by me in these books which I remember either to have read or to have heard from others; for if I have touched upon the things of others, I have written them either with some difference in demonstration or more clearly; but if by chance another has handed down the same things, either his labors have not reached me, or the memory of their perfection has slipped away. For as Aristotle himself felt, it can easily happen that the same opinions come into the minds of several people. Indeed, it can happen to one writing much that, when he has written something a long time ago, now having forgotten it, he repeats the same thing, which has even happened to me sometimes.

In these books, however, I have not undertaken the task of handing down any complete science, lest I should uselessly repeat those things which have already been handed down by others, and seem to myself to have wished to acquire praise from the labors of others. For the volumes of individual sciences have already been collected and arranged in order by others—and if there are very few books whose every opinion and every discovery belong to a single author, I except the volumes of Archimedes. And since there are many who do not hesitate to bring forth into public even a single thing discovered by themselves, I thought the same was even more permissible for me, who have thought out many things, even if they are heterogeneous among themselves and expressed in whatever manner.

In meditating upon these things, among the Arithmetical authors whom I have consulted, the principal one was Niccolò Tartaglia, since it is well known that he collected almost everything written by others; nor did I think that others of the principal ones I could read should be omitted, among whom are Girolamo Cardano, Michael Stifel, Gemma Frisius, Joannes Noviomagus, Cuthbert Tunstall, and others of this kind. Nevertheless, the opportunity of inspecting the volumes of certain of those who are cited by Tartaglia—such as Leonardo Pisano, Prosdocimo, Giovanni Infortunato, Fra Luca, Piero Borghi, and some others...