I’m still working with the blackboard theme (see previous post). And Euclid is still working to prove this set of propositions (numbers 6, 7, and 8) by showing that there are absurd consequences if his original statement isn’t true. Proposition 7 states:
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in another pint and equal to the former two respectively, namely each to that which has the same extremity with it.
The statement, I think, is nearly incomprehensible unless one draws a picture of the words…and this English translation has been made much clearer than the original Greek according to Sir Thomas Heath. As in Proposition 6, it is impossible to draw an angle or line equal to another, and at the same time, show that object is greater.