 Chapters 3–10 are concerned in one way or another with axiomatic presentations of geometry. This is understandable given the reputation of Euclid’s Elements as a model of rigorous reasoning and certain results. It is interesting therefore that the Logic also, while acknowledging the virtues of the work of Euclid and other geometers, offers some pointed criticisms. Applying logical method to geometry was among Arnauld’s many special interests. He wrote a book entitled, New Elements of Geometry (1667) in which he attempted to remedy the faults discussed here in Part IV of the Logic. The authors treatment begins with some rules for synthetic demonstrations, especially in geometry. There are no surprises here. Terms must be scrupulously defined; propositions that are taken to be axiomatic must be completely certain, and so on. As stated, the rules might appear obvious, but they are elaborated in a decidedly Cartesian way. The point of rules for definitions, for example, is to ensure that linguistic terms become precisely associated with distinct ideas. It follows that definitions will be useless for those who do not have prior access to the ideas in question. Regarding rules for axioms, the main point that emerges is that they must be distinctly perceived in the Cartesian sense put forward in Part I on ideas and Part II on propositions. This means that axioms derive from innate resources and not from sensory experience and that attributes must be clearly and distinctly perceived as included in subjects. It also means that no sincere skeptical questions can arise from properly chosen axioms. A good deal of Part IV recapitulates Descartes’ unfinished manuscript, Rules for the Direction of the Native Intellect (c. 1628). This was unpublished in Latin until after the fifth edition of the Logic, but Arnauld had access to at least part of some version of the manuscript. Chapter 7 offers as examples of “some important axioms” others provided by Descartes in his replies to the second set of objections to the Meditations (CSM II, 116–117).