CONSTRUCTION OF THE CANON. 17
their logarithms or artificial numbers increasing arithmetically.
23.To increase arithmetiually is, in equal times, to be augmented by a quantity always the same.
Thus from the fixed point b let a line be produced indefinitely in the direction of d. Along this let the point a travel from b towards d, mov- ing according to this law, that in equal moments of time it is borne over the equal spaces b 1, 1 2, 2 3,3 4,4 5 c. Then we call this increase by b 1, b 2, b 3, b 4, b 5, &c, arithmetical. Again, let b 1 be represented in numbers by 10, b 2 by 20, b 3 by 30, b 4 by 40, b 5 by 50; then 10, 20, 30, 40, 50, &c., increase arithmetically, because we see they are always increased by an equal number in equal times.
24.To decrease geometrically ts this, that in equal times, First the whole quantity then each of its successive remainders ts diminished, always by a like proportional part.
Thus let the line T S be radius. Along this let the point G travel in the direction of S, so that in equal times it is borne from T to 1, which for example may be the tenth part of T S; and from 1 to 2, the tenth part of 1 S; and from 2 to 3, the tenth part of 2 S; and from 3 to 4, the tenth part of 3 S, and so on. Then the sines T S, 1 S, 2 S,
3S
