Equivalence of Alberti's and the Distance Point Construction

The following is a direct, geometrical proof of the equivalence of Albertiís and the distance point construction.  Specifically, this means that the viewing distances CD and NR are the same.

Fig. 21 Ė Albertiís construction and the distance point construction superimposed.

The left portion of Fig. 21 shows Albertiís construction, with the NR being the viewing distance.  The right portion has the viewing distance as CD, a result of the distance point construction. 

Since the lines RD and GH are parallel, triangles CDF and GFH are similar.  Hence,


In addition, triangles RNE and EHG are also similar.  

However, NE = x and EG = y.  It follows that


Hence, CD is the same length as NR.