other than by any given difference, become ultimately equal.
If you deny it; ſuppose them to be ultimately unequal, and let D be their ultimate difference. Therefore they cannot approach nearer to equality than by that given difference D; which is againſt the ſuppoſition.
Lemma II.
If in any figure AacE (Pl.1.Fig.6.) terminated by the right lines Aa, AE, and the curve acE, there be inſcrib'd any number of parallelograms Ab, Bc, Cd, &c. comprehended under equal baſes AB, BC, CD, &c. and the ſides Bb, Cc, Dd, &c. parallel to one ſide Aa of the figure; and the parallelograms aKbl, bLcm, cMdn, &c. are compleated. Then if the breadth of thoſe parallelograms be ſuppoſ'd to be diminiſhed, and their number to be augmented in infinitum: I ſay that the ultimate ratio's which the inſcrib'd figure AKbLcMdD, the circumſcribed figure AalbmcndoE, and curvilinear figure AabcdE, will have to one another, are ratio's of equality.
For the difference of the inſcrib'd and circumſcrib'd figures is the sum of the parallelograms Kl, Lm, Mn, Do, that is, (from the equality of all their baſes) the rectangle under one of their baſes Kb and the ſum of their altitudes Aa, that is, the rectangle ABla,
