Coalternate angles between parallels dc and fK
Euclid's theory of parallels: are alternate interior angles equal?
The page works through Euclid's theory of parallels. Leonardo draws two parallel lines, dc and fK, crossed by a diagonal and marks the coalternate interior angles as equal, concluding that the lines are equidistant while noting that an 'adversary' denies it. A second figure below bends one of the parallels to meet the other straight line, showing that in that arrangement the coalternate angles become unequal.
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Coalternate interior angles imply equidistant parallels
Two parallel lines dc and fK are crossed by a diagonal, with the alternate interior angles marked equal by dots. Because the coalternate interior angles are equal, the lines dc and fK are equidistant. Leonardo records that an adversary maintains this is not so.
Counter-case: bending a parallel makes the angles unequal
In the lower figure one parallel is extended and bent to meet the other straight line, and a further line is drawn to the meeting point. The angle produced at the diagonal is greater than its matching angle. Leonardo notes that here the coalternate angles are unequal.