Page:The Construction of the Wonderful Canon of Logarithms.djvu/41

CONSTRUCTION OF THE CANON. 17 their logarithms or artificial numbers increasing arithmetically.



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.



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