Those things are said to be _essentially_ predicated; first, when the predicate is not only total, but constitutes the essence of the subject; instances of this kind are, animal of man; tree of the plantain; a line of a triangle; for a triangle is that which is contained under three right-lines. But here we must observe, that not every total predicate is an essential one; thus, whiteness is predicated of every swan, because it is inherent in every swan, and at every instant of time; but because whiteness does not constitute the essence of a swan, it is not essentially predicated; and this, first, is one of the modes of essential predication of the greatest importance in demonstration. The second mode is of accidents, in the definition of which their common subject is applied: thus, a line is essentially inherent in rectitude, because in its geometrical definition, a line is adopted; for rectitude is no other than a measure, equally extended between the points of a line. In the same manner, imparity is contained in number; for what is that which is odd, but a number divided into unequal parts? Thus, virtues are resident in the soul, because, in their definition, either some part of the soul, or some one of its powers, is always applied. The third mode of essential predicates pertains to accidents which are inseparably contained in some particular subject, so as to exclude a prior existence in any other subject; such as colour in superficies. The fourth mode is of things neither contained in another, nor predicated of others; and such are all individuals, as Callias, Socrates, Plato. Causes are likewise said to exist substantially, which operate neither from accident nor fortune. Thus, digging up the ground for the purposes of agriculture, may be the cause of discovering a treasure, but it is only an accidental one. But the death of Socrates, in despite of vigilance, is not the result of a fortuitous cause, but of an essential one, viz. the operation of poison. 9. These posterior significations of essential predicates are added more for the sake of ornament than use; but the two former have a necessary existence, since they cannot but exist in the definition of names which predicate the essence of a thing, and in subjects which are so entirely the support of accidents, that they are always applied in their definition. But it is a doubt with some, whether those accidents are necessary, which cannot be defined independent of their common subject? To this we answer, that no such accident can, from its nature, be contained in every individual of any species; for curvature is not contained in every line; nor imparity in every number; from whence we infer, that neither is curvature necessarily existent in a line, nor parity in number. The truth of this is evident from considering these accidents abstracted from their subjects; for then we shall perceive that a line may exist without curvature, and number without imparity.