The name is absent

Rectilinear Drawing         57

can be approximated to by drawing suitable parallel families
(or parts thereof) and then making suitable erasures of
parallel families. More specifically, one need only draw the
families of parallel lines appearing in the sum wherever the
corresponding f is positive; and then make the necessary
erasures wherever / is negative; in fact the two components
have then the desired algebraic sum which is positive or zero.

Consequently we conclude that any drawing in the finite
part of the plane corresponding to a continuous positive (or
zero) density function can be approximated to by means of
a finite set of continuous one-parameter families of parallel
straight lines and by subsequent one-parameter families of
parallel erasures.

3. TWO-PARAMETER FAMILIES OF STRAIGHT LINES

An arbitrary straight line I has been specified by two
coordinates ʃ and φ, of which the first is a radial coordinate,
the second an angular coordinate of period 2τr (see fig. 2);
furthermore (ʃ, φ) and (— ʃ, <p+τr) then correspond to the
same straight line. There is thus a two-parameter family of
such straight lines.

When we attach a continuous two-parameter “distribu-
tion function” /(ʃ, <p) to such straight lines we mean that
the mass due to the straight lines with an angle between φ
and φ-∖-dφ and traversing a small area à A is nearly given by

/(ʃ, <p)dAdφ,

where ʃ denotes the distance of some such line through dA
from the origin 0.

More precisely, consider a series of n angles increasing
from 0 to 2π through small equal increments ∆φ so that
n∆⅛? =2τr; and suppose that, for each such <ρ, for ʃ increasing
from 0 to S by small equal increments Δj so that n∆r = S,

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