It is in sciences as in plants; growth and branching is but the generation of the root continued; nor is the invention of theorems anything else but the knowledge of the construction of the subject prosecuted. The unsoundness of the branches are no prejudice to the roots, nor the faults of theorems to the principles. And active principles will correct false theorems if the reasoning be good; but no logic in the world is good enough to draw evidence out of false or unactive principles. But I detain your Lordship too long. For all this will be much more manifest in the following discourses, wherein I have not only explained and rectified many of the most important principles of geometry, but also by the examples of those errors which have been committed by my reprehenders, made manifest the evil consequence of the principles they now proceed on. So that it is not only my own defence that I here bring before you, but also a positive doctrine concerning the true grounds, or rather atoms of geometry, which I dare only say are very singular, but whether they be very good or not, I submit to your Lordship’s judgment. And seeing you have been pleased to bestow so much time, with great success, in the reading of what has been written by other men in all kinds of learning, I humbly pray your Lordship to bestow also a little time upon the reading of these few and short lessons; and if your Lordship find them agreeable to your reason and judgment, let me, notwithstanding the clamour of my adversaries, be continued in your good opinion, and still retain the honour of being, My most noble Lord, Your Lordship’s most humble and obliged servant, THOMAS HOBBES. LONDON, _June 10, 1656_. LESSONS OF THE PRINCIPLES OF GEOMETRY, &c. TO THE EGREGIOUS PROFESSORS OF THE MATHEMATICS, ONE OF GEOMETRY, THE OTHER OF ASTRONOMY, IN THE CHAIRS SET UP BY THE NOBLE AND LEARNED SIR HENRY SAVILE, IN THE UNIVERSITY OF OXFORD. LESSON I. I suppose, most egregious professors, you know already that by geometry, though the word import no more but the measuring of land, is understood no less the measuring of all other quantity than that of bodies. And though the definition of geometry serve not for proof, nor enter into any geometrical demonstration, yet for understanding of the principles of the science, and for a rule to judge by, who is a geometrician, and who is not, I hold it necessary to begin therewith.