Coroll. II. In motion uniformly accelerated, the lengths transmitted in equal times, taken in continual succession from the beginning of motion, are as the differences of square numbers beginning from unity, namely, as 3, 5, 7, &c. For if in the first time the length transmitted be as 1, in the first and second times the length transmitted will be as 4, which is the square of 2, and in the three first times it will be as 9, which is the square of 3, and in the four first times as 16, and so on. Now the differences of these squares are 3, 5, 7, &c. Coroll. III. In motion uniformly accelerated from rest, the length transmitted is to another length transmitted uniformly in the same time, but with such impetus as was acquired by the accelerated motion in the last point of that time, as a triangle to a parallelogram, which have their altitude and base common. For seeing the length D E (in fig. 1) is passed through with velocity as the triangle A B I, it is necessary that for the passing through of a length which is double to D E, the velocity be as the parallelogram A I; for the parallelogram A I is double to the triangle A B I. 4. In motion, which beginning from rest is so aclerated, that the impetus thereof increases continually in proportion duplicate to the proportion of the times in which it is made, a length transmitted in one time will be to a length transmitted in another time, as the product made by the mean impetus multiplied into the time of one of those motions, to the product of the mean impetus multiplied into the time of the other motion.