In the first instance the definition is less extensive than the term defined, since it applies only to equilateral triangles. This fault may be amended by decreasing the intension, which we do by eliminating the reference to the equality of the sides. In the second instance the definition is more extensive than the term defined. We must accordingly increase the intension by adding a new attribute 'and all its angles right angles.' Rule 2. Violation. A triangle is a figure with three sides and three angles. One of the chief merits of a definition is to be terse, and this definition is redundant, since what has three sides cannot but have three angles. Rule 3. Violations. A citizen is a person both of whose parents were citizens. Man is a human being. Rule 4. Violations. A net is a reticulated fabric, decussated at regular intervals. Life is the definite combination of heterogeneous changes, both simultaneous and successive, in correspondence with external co-existences and sequences. Rule 5. Violations. A mineral is that which is neither animal nor vegetable. Virtue is the absence of vice. § 381. The object of definition being to explain what a thing is, this object is evidently defeated, if we confine ourselves to saying what it is not. But sometimes this is impossible to be avoided. For there are many terms which, though positive in form, are privative in force. These terms serve as a kind of residual heads under which to throw everything within a given sphere, which does not exhibit certain positive attributes. Of this unavoidably negative nature was the definition which we give of 'accident,' which amounted merely to saying that it was any attribute which was neither a difference nor a property. § 382. The violation of Rule 3, which guards against defining a thing by itself, is technically known as 'circulus in definiendo,' or defining in a circle. This rule is often apparently violated, without being really so. Thus Euclid defines an acute-angled triangle as one which has three acute angles. This seems a glaring violation of the rule, but is perfectly correct in its context; for it has already been explained what is meant by the terms 'triangle' and 'acute angle,' and all that is now required is to distinguish the acute-angled triangle from its cognate species. He might have said that an acute-angled triangle is one which has neither a right angle nor an obtuse angle: but rightly preferred to throw the same statement into a positive form.