Not knowing on my own part any cause of the favour your Lordship has been pleased to express towards me, unless it be the principles, method, and manners you have observed and approved in my writings; and seeing these have all been very much reprehended by men, to whom the name of public professors hath procured reputation in the university of Oxford, I thought it would be a forfeiture of your Lordship’s good opinion, not to justify myself in public also against them, which, whether I have sufficiently performed or not in the six following Lessons addressed to the same professors, I humbly pray your Lordship to consider. The volume itself is too small to be offered to you as a present, but to be brought before you as a controversy it is perhaps the better for being short. Of arts, some are demonstrable, others indemonstrable; and demonstrable are those the construction of the subject whereof is in the power of the artist himself, who, in his demonstration, does no more but deduce the consequences of his own operation. The reason whereof is this, that the science of every subject is derived from a precognition of the causes, generation, and construction of the same; and consequently where the causes are known, there is place for demonstration, but not where the causes are to seek for. Geometry therefore is demonstrable, for the lines and figures from which we reason are drawn and described by ourselves; and civil philosophy is demonstrable, because we make the commonwealth ourselves. But because of natural bodies we know not the construction, but seek it from the effects, there lies no demonstration of what the causes be we seek for, but only of what they may be. And where there is place for demonstration, if the first principles, that is to say, the definitions contain not the generation of the subject, there can be nothing demonstrated as it ought to be. And this in the three first definitions of Euclid sufficiently appeareth. For seeing he maketh not, nor could make any use of them in his demonstrations, they ought not to be numbered among the principles of geometry. And Sextus Empiricus maketh use of them (misunderstood, yet so understood as the said professors understand them) to the overthrow of that so much renowned evidence of geometry. In that part therefore of my book where I treat of geometry, I thought it necessary in my definitions to express those motions by which lines, superficies, solids, and figures, were drawn and described, little expecting that any professor of geometry should find fault therewith, but on the contrary supposing I might thereby not only avoid the cavils of the sceptics, but also demonstrate divers propositions which on other principles are indemonstrable. And truly, if you shall find those my principles of motion made good, you shall find also that I have added something to that which was formerly extant in geometry.