Question 1209518
.


After reading the @greenestamps comment to Edwin's comment,
I can not leave this subject without my comment.


The point by @greenestamps turns upside down all Euclidian geometry
and all the known Math logic.



Consider one example, this statement, which is one of the many theorems of Euclidian geometry: 


            in isosceles triangles, the angles at the base are congruent.



This statement relates to all isosceles triangle.


Then, following to the @greenestamps logic, it is enough to check or to prove it 
for equilateral triangles, ONLY.



But it is clear to everyone, that this logic does not work.



In all textbooks on Geometry, you will find the proof of the statement valid 
for ALL isosceles triangles.  No one Geometry textbook says that for proving 
general statement, it is enough to check or to prove it for some special/specific case.


Are all these textbooks (including Euclid himself) incorrect and teach us in wrong way ?