A nomogram for calculating extended terms
The simplest form of nomogram is a graphical device for representing a functional relationship between three variables in a manner which is often more convenient for practical reference than that of plotting a series of contours for chosen values of one of the three variables on a Cartesian graph. We develop the basis of such a nomogram by means of analytical geometry in this section.The condition that three points (ξ1, η1), (ξ2, η2) and (ξ3, η3) shall be collinear is commonly expressed by means of the determinantIf the relationship between three variablesa, bandcwhich we wish to represent nomographically isF (a,b,c) = o, (2)and we can express (2) in the determinantal form [similar to (1)]wheref1f2(a),f2(b),f3(c),g1(a),g2(b) andg3(c) represent (generally) different functions ofa, bandc, it is apparent that we can associateany three particular values ofa, bandcsatisfying (2) with the pointson a Cartesian graph; and they will be collinear because (3) is of the same form as (1).