But for the clearing of this doctrine (which Mersennus calls intricate) of the composition of proportions, I observed, first, that any two quantities, being exposed to sense, their proportion was also exposed; which is not intricate. Again, I observed that if besides the two exposed quantities, there were exposed a third, so as the first were the least, and the third the greatest, or the first the greatest, and the third the least, that not only the proportions of the first to the second, but also (because the differences and the quantities proceed the same way) the proportion of the first to the last is exposed by composition, or addition of the differences; nor is there any intricacy in this. But when the first is less than the second, and the second greater than the third, or the first greater than the second, and the second less than the third, so that to make the first and second equal, if we use addition, we must, to make the second and third equal, use subtraction; then comes in the intricacy, which cannot be extricated, but by such as know the truth of this doctrine which I now delivered out of Mersennus, namely, that the proportions of excess, equality, and defect, are as _quantity_, _not-quantity_, _nothing want quantity_; or as symbolists mark them 0+1 . 0 . 0-1. And upon this ground I thought depended the universal truth of this proposition, that in any rank of magnitudes of the same kind, the proportion of the first to the last, was compounded of all the proportions (in order) of the intermediate quantities; the want of the proof thereof, Sir Henry Savile calls (_nævus_) a mole in the body of geometry. This proposition is demonstrated at the thirteenth article of this chapter. But before we come thither, I must examine the arguments you bring to confute this proposition, that the _proportion of inequality is quantity, of equality, not quantity_.