At the seventeenth article, you show again the same confusion. Return to the eighth figure: “_if in a time given a body run over two lengths, one with uniform, the other with accelerated motion_”; as for example, if in the same time A C, a body, run over the line A B with uniform motion, and the line A H with motion accelerated; “_and again in a part of that time it run over a part of the length A H, with uniform motion, and another part of the same with motion accelerated_;” as for example, in the time A M it run over with uniform motion the line A I, and with motion accelerated the line A B. _I say the excess of the whole A H above the part A B, is to the excess of the whole A B above the part A I, as the whole A H to the whole A B._ But first you will say, that these words _as the whole A H to the whole A B_, are left out in the proposition. But you acknowledge that it was my meaning; and you see it is expressed before I come to the demonstration. And therefore it was absurdly done to reprehend it. Let us therefore pass to the demonstration. Draw I K parallel to A C, and make up the parallelogram A I K M. And supposing first the acceleration to be uniform, divide I K in the midst at N; and between I N, and I K, take a mean proportional I L. _And the straight line A L, drawn and produced, shall cut the line B D in F, and the line C G in G_ (which lines C G, and B D, as also H G and B F, are determined, though you could not carry it so long in memory, by the demonstration of the thirteenth article). _For seeing A B is described by motion uniformly accelerated, and A I by motion uniform in the same time A M; and I L is a mean proportional between I N (the half of I K) and I K; therefore by the demonstration of the thirteenth article, A I is a mean proportional between A B and the half of A B, namely A O. Again, because A B is described by uniform motion, and A H by motion uniformly accelerated, both of them in the same time A C, B F is a mean proportional between B D and half B D, namely B E; therefore by the demonstration of the same thirteenth article, the straight line A L F produced will fall on G; and the line A H will be to the line A B, as the line A B to the line A I. And consequently as A H to A B, so H B to B I; which was to be demonstrated._ And by the like demonstration the same may be proved, where the acceleration is in any other proportion that can be assigned in numbers, saving that whereas this demonstration dependeth on the construction of the thirteenth article, if the motion had been accelerated in double proportion to the times, it would have depended on the fourteenth, where the lines are determined. Which determinations being not repeated, but declared before, in the thirteenth article, to which this diagram belongeth, you take no notice of, but go back to a figure belonging to another article, where there was no use of these determinations. But because I see that the words of