Is this anything like what you are looking for?
In[1]:= data =
Table[{RandomReal[{1,2}], RandomReal[{1.35,1.65}], RandomReal[{1.35,1.65}], RandomReal[{1,2}]}, {20}]
Out[1]= {
{1.61555, 1.54121, 1.41361, 1.65261},
{1.8799, 1.56107, 1.42576, 1.78373},
{1.2543, 1.63576, 1.35505, 1.17759},
{1.38954, 1.62712, 1.49634, 1.99046},
{1.45715, 1.45802, 1.47354, 1.9938},
{1.96083, 1.4335, 1.51761, 1.26775},
{1.64853, 1.42011, 1.36215, 1.67745},
{1.56973, 1.35722, 1.49714, 1.86257},
{1.50301, 1.63805, 1.58112, 1.85021},
{1.11028, 1.41526, 1.63507, 1.17726},
{1.61768, 1.56544, 1.4358, 1.58676},
{1.18028, 1.56652, 1.44555, 1.29729},
{1.8237, 1.60931, 1.51301, 1.30859},
{1.01127, 1.53756, 1.53543, 1.92896},
{1.58628, 1.63435, 1.57445, 1.64518},
{1.50125, 1.63471, 1.54999, 1.60091},
{1.17622, 1.40375, 1.38231, 1.90849},
{1.96473, 1.59353, 1.55827, 1.37177},
{1.2098, 1.63267, 1.49444, 1.56277},
{1.37147, 1.55571, 1.36636, 1.62468}}
In[2]:= filterdata = data//.{h___,{ax_,bx_,cx_,dx_},{ay_,by_,cy_,dy_},t___} /;
Not[.9 <= bx/cy <= 1.1] || Not[.9 <= by/cx <= 1.1] -> {h, t}
Out[2]= {
{1.45715, 1.45802, 1.47354, 1.9938},
{1.96083, 1.4335, 1.51761, 1.26775},
{1.61768, 1.56544, 1.4358, 1.58676},
{1.01127, 1.53756, 1.53543, 1.92896},
{1.58628, 1.63435, 1.57445, 1.64518},
{1.96473, 1.59353, 1.55827, 1.37177}}
What that does is repeatedly look for any adjacent pair of {ai,bi,ci,di}, {ai+1,bi+1,ci+1,di+1} and if either of the two ratios is too large then both those adjacent pairs are removed from the list.
Hopefully if you manually do this for the example random data set I created you should come up with the same result.
If this doesn't do what you are wanting then perhaps you can find another way to explain what Mathematica should do, perhaps showing an example that includes enough cases to make it clear.
