>>323
AP = sAB
AQ = AB + tBC
AR = AC + uCD
AS = vAD
0<s<1 , 0<t<1 , 0<u<1 , 0<v<1
として
平面α上の点Sは
AS = AP + aAQ + bAR
a,b:実数として
AS = (s+a-ta)*AB + (ta+b-ub)*AC + ub*AD
= vAD

s+a-ta = 0
ta+b-ub = 0
ub = v

v = ub
t = (ub-b)/a
s = ub-b-a

PB/AP･QC/BQ･RD/CR･SA/DS = {(1-s)/s}*{(1-t)/t}*{(1-u)/u}*{v/(1-v)}
={(1-ub+b+a)/(ub-b-a)}*{(a-ub+b)/(ub-b)}*{(1-u)/u}*{ub/(1-ub)}
=(1-ub+b+a)/(1-ub)



どっかおかしいな・・・すまん、わからんｵ