A First Course in Nomography

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'pa, v) Take the line through P given by a, h. The equation of this line is Y=h + {b-a)X, where {X, Y) are the coordinates of any point on it. Since P is on this line this equation also holds for (^, >]) the coordinates of P itself. This is true for all lines through P. Hence the a, b intercepts for all lines through P satisfy the single equation f]^b + (b-a)^, I. E.
-a—- 6 + 1=0.
PARALLEL COORDINATES 91 Let then the equation, given to be solved, be written A{x)a-\-B{x)h + 1=^0, so that A{x) an
...d B{x) are known functions of x. If there is to be a definite graduation a; at P it follows that the two equations and A{x)a-\-B{x)b + 1=^0, are both true for any number of straight lines through P. This means that the equations are really the same, so that we must have Aix)j, B{x)=-^^, ^ A{x) 1 '^ A{x)-hB{xy ' A{x)-\-B{x) If we eliminate x we obtain an equation between f, V, telling us w^hat the relation between the co- ordinates of P must be if P is to be a graduation in the nomogram, i. E. A point on the x curve/ This relation defines the x curve, which can be plotted.

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