To the sixteenth article you bring no argument, but fall into a loud _oncethmus_ (the special figure wherewith you grace your oratory), offended with my unexpected crossing of the doctrine you teach, that proportion consisteth in a quotient. For that being denied you, your _a/b - c/d + e/f - g/h + i/k_ comes to nothing, that is, to just as much as it is worth. But are not you very simple men, to say that all mathematicians speak so, when it is not speaking? When did you see any man but yourselves publish his demonstrations by signs not generally received, except it were not with intention to demonstrate, but to teach the use of signs? Had Pappus no analytics? or wanted he the wit to shorten his reckoning by signs? Or has he not proceeded analytically in a hundred problems (especially in his seventh book), and never used symbols? Symbols are poor unhandsome, though necessary, scaffolds of demonstration; and ought no more to appear in public, than the most deformed necessary business which you do in your chambers. “_But why_,” say you, “_is this limitation to the proportion of the greater to the less?_” I will tell you; because iterating of the proportion of the less to the greater, is a making of the proportion less, and the defect greater. And it is absurd to say that the taking of the same quantity twice should make it less. And thence it is, that in quantities which begin with the less, as one, two, four, the proportion of one to two is greater than that of one to four, as is demonstrated by Euclid, Elem. 5, prop. 8; and by consequent the proportion of one to four, is a proportion of greater littleness than that of one to two. And who is there, that when he knoweth that the respective greatness of four to one, is double to that of the respective greatness of four to two, or of two to one, will not presently acknowledge that the respective greatness of one to two, or two to four, is double to the respective greatness of one to four? But this was too deep for such men as take their opinions, not from weighing, but from reading.