8 
Journal of the Mitchell Society. [ May 
same fallacy as the Direction-Theory, proves Euc. I, 32. 
without even mentioning- the dangerous word ‘Direction’. 
“We are told to take any triangle ABC; to produce CA to 
D; to make part of CD, viz., AD, revolve, about A, into the 
position ABE; then to make part of this line, viz., BE, revolve, 
about B, into the position BCF; and lastly to make part of 
this line, viz., CF, revolve, about C, till it lies along CD, of 
which it originally formed a part. We are then assured that 
it must have revolved through four right angles: from which 
it easily follows that the interior angles of the triangle are 
together equal to two right angles. 
“The disproof of this fallacy is almost as brief and elegant 
as the fallacy itself. We first quote the general principle 
that we can not reasonably be told to make a line fulfil two 
conditions, either of which is enough by itself to fix its pos- 
ition: e. g., given three points X, Y, Z, we can not reason- 
ably be told to draw a line from X which shall pass through 
Y and Z; we can make it pass through Y, but it must then 
take its chance of passing through Z; and vice versa. 
