2. Proportion, whether it be arithmetical or geometrical, cannot be exposed but in two magnitudes, (of which the former is commonly called the _antecedent_, and the latter the _consequent_ of the proportion) as I have shewn in the 8th article of the preceding chapter. And, therefore, if two proportions be to be compared, there must be four magnitudes exposed, namely, two antecedents and two consequents; for though it happen sometimes that the consequent of the former proportion be the same with the antecedent of the latter, yet in that double comparison it must of necessity be twice numbered; so that there will be always four terms. 3. Of two proportions, whether they be arithmetical or geometrical, when the magnitudes compared in both (which Euclid, in the fifth definition of his sixth book, calls the _quantities of proportions_,) are equal, then one of the proportions cannot be either greater or less than the other; for one equality is neither greater nor less than another equality. But of two proportions of inequality, whether they be proportions of excess or of defect, one of them may be either greater or less than the other, or they may both be equal; for though there be propounded two magnitudes that are unequal to one another, yet there may be other two more, unequal, and other two equally unequal, and other two less unequal than the two which were propounded. And from hence it may be understood, that the proportions of excess and defect are quantity, being capable of more and less; but the proportion of equality is not quantity, because not capable neither of _more_, nor of _less_. And therefore proportions of inequality may be added together, or subtracted from one another, or be multiplied or divided by one another, or by number; but proportions of equality not so. 4. Two equal proportions are commonly called _the same proportion_; and, it is said, that the proportion of the first antecedent to the first consequent is the _same_ with that of the second antecedent to the second consequent. And when four magnitudes are thus to one another in geometrical proportion, they are called _proportionals_; and by some, more briefly, _analogism_. And _greater proportion_ is the proportion of a greater antecedent to the same consequent, or of the same antecedent to a less consequent; and when the proportion of the first antecedent to the first consequent is greater than that of the second antecedent to the second consequent, the four magnitudes, which are so to one another, may be called _hyperlogism_. _Less proportion_ is the proportion of a less antecedent to the same consequent, or of the same antecedent to a greater consequent; and when the proportion of the first antecedent to the first consequent is less than that of the second to the second, the four magnitudes may be called _hypologism_. [Sidenote: The definition and some properties of the same arithmetical proportion.]