- PROJECTIVE AND DESCRIPTIVE GEOMETRY 363
FIGURE 8. Desargues' theorem for two triangles in the same plane.{A", C, Â}, {B", A, C}, and {C", A, B}, with Ê as the third vertex of the triangle
whose base ends in the second and third points in all three cases. (There is no other
conceivable way to proceed, so that in a sense the proof is a mere computation.)
When the ratios AK : A A'', Â Ê : ÂÂ', and CK : CC are eliminated from the
three resulting equations, the result can be written as the equation
C"B' _ A"B' B"C
C"A' ~ A"C B"A! '