The rules of demonstration are but of two kinds: one, that the principles be true and evident definitions; the other, that the inferences be necessary. And of true and evident definitions, the best are those which declare the cause or generation of that subject, whereof the proper passions are to be demonstrated. For science is that knowledge which is derived from the comprehension of the cause. But when the cause appeareth not, then may, or rather must we define some known property of the subject, and from thence derive some possible way, or ways, of the generation. And the more ways of generation are explicated, the more easy will be the derivation of the properties; whereof some are more immediate to one, some to another generation. He therefore that proceedeth from untrue, or not understood definitions, is ignorant of that he goes about; which is an ill-favoured fault, be the matter he undertaketh easy or difficult, because he was not forced to undergo a greater charge than he could carry through. But he that from right definitions maketh a false conclusion, erreth through human frailty, as being less awake, more troubled with other thoughts, or more in haste when he was in writing. Such faults, unless they be very frequent, are not attended with shame, as being common to all men, or are at least less ugly than the former, except then, when he that committeth them reprehendeth the same in other men. For that is in every man intolerable, which he cannot tolerate in another. But to the end that the faults of both kinds may by every man be well understood, it will not be amiss to examine them by some such demonstrations as are publicly extant. And for this purpose I will take such as are in mine and in your books, and begin with your _Elenchus_ of the geometry contained in my book _De Corpore_; to which I will also join your book lately set forth concerning the _Angle of Contact, Conic Sections_ , and your _Arithmetica Infinitorum_; and then examine the rest of my philosophy, and yours that oppugn it. For I will take leave to consider you both everywhere as one author, because you publicly declare your approbation of one another’s doctrine.