If two lines are divided in such a way that any point on one corresponds to one and only one point on the other, the lines are said to be divided homographically, and any relation between the segments which gives the variable point on one corresponding uniquely to a variable point on the other is a homographic equation.

These equations are of two types:

(α), which contains the term xx', may be said to be of the second order, and (β), in which the term xx' is wanting, may be said to be of the first order.

If n quantities, which are known to the nearest whole number, are added together, find the probability that their sum so obtained is correct to the nearest whole number.

Let the probability that the error is between x and x + dx be p dx.

If n = 2, and x>0,

p dx=Probability that first error is between x – 1/2 and 1/2,

and that second error is within a given dx of its possible range

from – 1/2 to 1/2,

= (1– x)dx ; ∴ p = 1–x.

If x<0, p = 1+x.